The Economics of Football, 2nd Edition

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The Economics of Football

The second edition of this popular book presents a detailed economic analysis of professional football at club level, with new material included to reflect the development of the economics of professional football over the past ten years. Using a combination of economic reasoning and statistical and econometric analysis, the authors build upon the successes and strengths of the first edition to guide readers through the economic complexities and peculiarities of English club football. The book uses a wide range of international comparisons to help emphasise both the broader relevance as well as the unique characteristics of the English experience. Topics covered include some of the most hotly debated issues currently surrounding professional football, including player salaries, the effects of management on team performance, betting on football, racial discrimination and the performance of football referees. This edition also includes new chapters on football applications of game theory, club football around the world, and the economics of the World Cup. d o b s o n is Professor of Economics at Hull University Business School, Hull University.

stephen

g o d d a r d is Professor of Financial Economics at Bangor Business School, Bangor University.

john

The Economics of Football Second edition

Stephen Dobson and

John Goddard

 cambridge university press

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Tokyo, Mexico City Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521517140 © Stephen Dobson and John Goddard 2011 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2011 Printed in the United Kingdom at the University Press, Cambridge A catalogue record for this publication is available from the British Library Library of Congress Cataloguing in Publication data Dobson, Stephen.   The economics of football / Stephen Dobson, John Goddard. – 2nd ed.    p.  cm.   Includes bibliographical references and index.   ISBN 978-0-521-51714-0 (hardback)   1.  Soccer–Economic aspects–Great Britain.  2.  Soccer–Great Britain–   Finance.  I.  Goddard, John A.  II.  Title.   GV943.3.D63 2011   338.4′37963340941–dc22   2010040413 ISBN 978-0-521-51714-0 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.



To: My daughters Imogen and Hannah sd

To: My family and friends jg

Contents

Preface Acknowledgements List of figures List of tables

page xi xiii xiv xv

1 Introduction 1.1 The economics of professional team sports: three seminal contributions 1.2 Outline of this volume

1 2 8



2 The economic theory of professional sports leagues 2.1 The North American professional team sports model 2.2 A model of an n-team league 2.3 A model of a two-team league 2.4 Revenue sharing 2.5 Restraints on expenditure on players’ salaries

12 14 19 23 27 33



3 Competitive balance, uncertainty of outcome and home-field advantage 3.1 Measuring competitive balance and competitive inequality 3.2 Home-field advantage 3.3 Distributional properties of the goals scored by the home and away teams 3.4 Good and poor sequences, and persistence in football match results

42 42 50

4 Forecasting models for football match results 4.1 Previous literature on modelling and forecasting match results in football 4.2 A goals-based forecasting model 4.3 Probabilistic forecasts for match results in ‘scores’ format

79



59 67

79 82 88 vii

viii

Contents

4.4 A results-based forecasting model 4.5 Probabilistic forecasts for match results in ‘win-draw-lose’ format 4.6 Evaluation of the goals-based and results-based forecasting models



5 Game theory and football games 5.1 The penalty kick 5.2 A game-theoretic model of in-play strategic choice for football teams 5.3 The timings of player dismissals and goals 5.4 An empirical model for the in-play arrival rates of player dismissals and goals 5.5 Estimation results and interpretation 5.6 Stochastic simulations for in-play match result probabilities conditional on the current state of the match 6 English professional football: historical development and commercial structure 6.1 English professional football: competitive structure and team performance 6.2 Match attendances 6.3 Financial structure of English football: overview of profit and loss accounts 6.4 Gate revenues and admission prices 6.5 Broadcast revenues 6.6 Football’s labour market: players’ salaries and the transfer system 6.7 Ownership, governance and finance

95 98 100 106 107 111 119 122 124 130

139 139 150 159 162 171 179 186



7 Determinants of professional footballers’ salaries 7.1 The compensation of professional footballers 7.2 The economics of superstars 7.3 Rank-order tournaments and intra-team earnings distributions 7.4 Determinants of players’ compensation: empirical evidence

197 198 201 204 209



8 Professional footballers: employment patterns and racial discrimination 8.1 Employment mobility, migration and career structure in English football 8.2 International migration of professional footballers 8.3 Racial discrimination in professional team sports

216

9 The football manager 9.1 The role of the football manager 9.2 Measuring the managerial contribution: the production frontier approach

249 251



217 227 236

254

Contents

ix

Patterns of managerial change in English football Determinants of managerial change Estimation of hazard functions for managerial departure The effect of managerial change on team performance Managerial succession effects in English football

260 270 276 285 289

10 The football referee 10.1  The role of the football referee 10.2 Favouritism and referee behaviour 10.3 The incidence of disciplinary sanction in English Premier League football

295 296 298

11 Spectator demand for football 11.1 Econometric analysis of football attendances 11.2 Modelling the demand for attendance at English league football, 1947–1997 11.3 Explaining base attendances, and the loyalty, league position, price and goals scored coefficients

321 322

12 Gambling on football 12.1 Previous evidence on the informational efficiency of football and other sports betting markets 12.2 A forecasting model for half-time/full-time match outcomes 12.3 Comparing the model’s probabilistic forecasts with betting odds 12.4 Testing the informational efficiency of the half-time/full-time fixed-odds betting market

352



13 Football around the world: France, Germany, Brazil, Japan and China 13.1 France 13.2 Germany 13.3 Brazil 13.4 Japan 13.5 China

380 380 385 391 395 399



14 The economics of the World Cup 14.1 The World Cup 14.2 Costs and benefits of hosting a mega sporting event 14.3 Prospective economic impact studies 14.4 Retrospective economic impact studies 14.5 Intangible benefits of mega events

405 407 409 413 415 417

9.3 9.4 9.5 9.6 9.7





References Index

303

336 346

353 365 367 371

423 447

Preface

Since the early 1990s, professional football in many countries has experienced an astonishing transformation. Player salaries have risen exponentially, television contracts yield revenues on a scale unimaginable only a few years ago, many football stadia have been completely rebuilt, and the importance of commercial sponsorship and merchandising has increased beyond measure. Commercial aspects of football feature regularly in the news headlines, and the media devote pages to coverage of football finances. Football’s importance is not only economic, but also social and cultural. Several million people attend matches each season, and many millions more watch football on television and follow its fortunes through coverage in the media. At the grassroots level, football’s popularity as a participant sport generates benefits for the health of the population. At the highest level, international footballing success generates intangible benefits in the form of prestige and goodwill. Academic interest in the economic analysis of football has mirrored the growth in the sport’s popularity. In the US, economists have written and published books and scholarly articles on major league sports since the mid-1950s. Consequently, the older academic literature on sports economics is dominated by studies of sports such as baseball, basketball and (American) football. These writings shed light on a wide range of issues, including the determinants of the compensation received by sports professionals, the nature of joint production in team sports, competitive balance, uncertainty of outcome and the distribution of playing talent in sports leagues, and the contribution of the coach or manager to team performance. The common thread linking research into all of these topics is the formulation and testing of economic hypotheses using sports as a laboratory. A major attraction of sports to empirical economists is that the availability of data permits investigation of economic propositions that would be difficult to test in other areas, owing to a lack of suitable data. During the last decade of the old century and the first decade of the new, scholarly papers on the economics of football have been published with increasing regularity in academic journals. Undergraduate and postgraduate students in many universities study the economics of sports as part of their degree programmes. At xi

xii

Preface

the end of the 1990s, we felt that a monograph was needed to cover developments in the subject, and present a unifying overview of this relatively new area of academic research. We therefore decided to write the first edition of The Economics of Football, which was published by Cambridge University Press in September 2001. Since publication, we have been encouraged by the responses to the first edition we have received from scholars, students and other readers. Since the appearance of the first edition, there has been a proliferation of scholarly work on the economics of football, in Europe and many other parts of the world. Several new academic journals have been launched, dedicated to the study of sports economics, finance and management. Football has received extensive coverage in these field journals, and in mainstream journals in economics, finance and management. Several books have been published, focusing on the economics and business aspects of football. When Cambridge University Press suggested that we should consider preparing a new edition of The Economics of Football, we agreed that the time was right to revise and update the book. This second edition provides substantially revised and updated coverage of all of the key topics from the first edition. In addition, a broad range of new material reflects the growth in the scope and sophistication of the literature over the past decade. The second edition includes new chapters on football applications of game theory, football referees, football betting markets, the economics of club football around the world, and the World Cup. As before, our objective is to present a wide-ranging overview of the current state of theoretical and empirical research on the economics of football.

Acknowledgements

We would like to thank colleagues and students at the Department of Economics, Otago University; Bangor Business School, Bangor University; and the School of Business and Economics, Swansea University for their direct and sometimes unknowing help towards the development of this project. We would like to give special thanks to Rick Audas, Tunde Buraimo, Andy Cooke, Juan Carlos Cuestas, Peter Dawson, Neil Doncaster, David Forrest, Rodney Fort, Bill Gerrard, Leo Kahane, Ruud Koning, Huw Lloyd Williams, Phil Molyneux, Dorian Owen, Phil Quinn, Rob Simmons, Peter Sloane, Frank Stähler, Sarah Wale, Yizheng Wang, Leighton Vaughan Williams and John Wilson. We would also like to thank a number of staff at Cambridge University Press for their assistance during the development of this project. In particular, we are grateful to Chris Harrison (Publishing Director, Social Sciences) for his unfailing support and encouragement, and Philip Good (Assistant Editor, Economics and Business) for his advice and guidance. We are grateful to Matt Davies of Out of House Publishing Solutions Ltd for his assistance during the process of production, and Penny Harper (copy-editor) for her meticulous efforts in checking and correcting the original manuscript.

xiii

Figures

2.1 Profit-maximisation and win-percent-maximisation equilibria: two-team closed model 2.2 Profit-maximisation and win-percent-maximisation equilibria: two-team open model 2.3 Revenue sharing in a closed model: profit maximisation 2.4 Revenue sharing in a closed model: win-percent maximisation 2.5 Nash equilibrium and joint profit-maximisation equilibrium:  profit-maximisation model 2.6 Luxury tax: closed model 2.7 Luxury tax: open model 2.8 Payroll cap: closed model 2.9 Payroll cap: open model 2.10 G14 payroll cap: closed model 2.11 G14 payroll cap: open model 3.1 The Lorenz curve and Gini coefficient 6.1 Percentage shares in aggregate performance of clubs in Groups 1 to 5 6.2 Percentage shares in aggregate attendance of clubs in Groups 1 to 5 6.3 Percentage shares in aggregate gate revenue of clubs in Groups 1 to 5 7.1 Optimum investment in playing talent, rank-order tournament model

xiv

page 25 26 28 29 31 34 35 36 37 38 39 46 150 154 168 208

Tables

3.1 Percentages of home wins, draws and away wins, average numbers of goals scored by the home and away teams, and win percentages per season, English league, 1970–2009 seasons page 54 3.2 Home-team success percentages (2/1/0 points for W/D/L) by tier (division) in five-season bands, English league, 1970–2009 seasons 56 3.3 Percentages of home wins, draws and away wins, and average numbers of goals scored by home and away teams, international comparisons, 1973–2009 seasons 57 3.4 Joint and marginal percentage distributions of goals scored by home and away teams, English league, 1970–1981 seasons 60 3.5 Joint and marginal percentage distributions of goals scored by home and away teams, English league, 1982–2009 seasons 60 3.6 Percentage distribution of goals scored by the home team, conditional on the number of goals scored by the away team, English league, 1982–2009 seasons 61 3.7 Percentage distribution of goals scored by the away team, conditional on the number of goals scored by the home team, English league, 1982–2009 seasons 62 3.8 Parameter estimates for fitted double and bivariate Poisson and negative binomial distributions, home- and away-team goals data, English league, 1982–2009 seasons 66 3.9 Hypothesis tests for comparisons between fitted double and bivariate Poisson and negative binomial distributions, home- and away-team goals data, English league, 1982–2009 seasons 68 3.10  Longest runs of consecutive results, English league, 1970–2009 seasons 69 3.11 Empirical unconditional and conditional match result probabilities 70 3.12 League table, Premier League, 2009 season, and ordered probit team quality parameter estimates 72 3.13 Simulated unconditional and conditional match result probabilities 74 3.14 Tests for persistence in sequences of consecutive match results 75 4.1 Goals-based forecasting model: estimated coefficients and p-values 85 xv

xvi

List of tables

4.2 Data for calculation of average goals scored and conceded covariates, Hull City vs Tottenham Hotspur fixture 4.3 Data for calculation of goals scored and conceded in recent matches covariates, Hull City vs Tottenham Hotspur fixture 4.4 Estimated match result probabilities, Hull City vs Tottenham Hotspur fixture 4.5 Results-based forecasting model: estimated coefficients and p-values 4.6 Fitted match result and selected score probabilities, Premier League, weekend of 21–23 February 2009 4.7 Pseudo-R-square values for forecasting performance, 2009 season: goals-based forecasting model, and probabilities derived from six betting firms’ prices 5.1 Observed proportions of penalty kicks, goalkeeper dives and goals 5.2 Hypothetical goal-scoring and player-dismissal probabilities for numerical examples 5.3 Determination of the two teams’ optimal strategies for the 90th minute, home team leading by one goal after 89 minutes 5.4 Determination of the two teams’ optimal strategies for the 90th minute, scores level after 89 minutes 5.5 Hypothetical match result probabilities at the end of the first minute, conditional on score and player dismissals, for numerical examples 5.6 Determination of the two teams’ optimal strategies for the first minute 5.7 Rates of player dismissal and goal scoring conditional on current duration, English League, T1–T4, 2002–2009 seasons 5.8 Rates of player dismissal and goal scoring conditional on current difference in scores, English League, T1–T4, 2002–2009 seasons 5.9 Rates of player dismissal and goal scoring conditional on numerical disparity in players, English League, T1–T4, 2002–2009 seasons 5.10 Estimation results: player-dismissal hazard functions 5.11 Estimation results: goal-scoring hazard functions 5.12 Home-win probabilities, conditional on relative team strengths and the state of the match at various durations 5.13 Draw probabilities, conditional on relative team strengths and the state of the match at various durations 5.14 Away-win probabilities, conditional on relative team strengths and the state of the match at various durations 5.15 In-play home-win/draw/away-win probabilities: illustration 6.1 Historical performance of top English teams in league and cup competition 6.2 Incidence of giant-killings in FA Cup ties, 1974–2009 6.3 Group definitions 6.4 English league attendances, aggregate and by tier 6.5 Average revenue, wages and salaries and operating profit per season, three-season periods, English League, 1994–2008 seasons

89 91 95 97 102

104 110 114 115 116 118 118 119 120 120 125 128 132 133 134 136 144 147 148 151 160

List of tables

6.6 Financial data, leading English clubs and averages by tier, 2008 season, £m 6.7 TV and other revenue, leading English clubs and averages by tier, 2008 season, £m 6.8 English league average admission prices 6.9 English league gate revenues 6.10 Revenue from sale of broadcast rights, English Premier League, average per season, 1993–2010 seasons, £m 6.11 Average net transfer expenditure within the Premier League/Football League per season, selected three-season periods, £m 6.12 Average flows of transfer expenditure within the Premier League/ Football League per season, 2006–2008 seasons, £m 6.13 Gross transfer expenditure of Premier League and Football League clubs per season, 2001–2008 seasons, £m 6.14 Average gross transfer expenditure and average revenue per season, three-season periods, 1994–2008 seasons, £m 7.1 Average basic footballer’s salary by tier, English League, 2000 and 2006 seasons, £ 8.1 Employment totals for professional footballers by tier, Engish League, 1986–2009 8.2 Percentage distribution of professional footballers in England by age band and tier, English League, selected years 8.3 Percentage distribution of professional footballers in England by month of birth, English League, selected years 8.4 Employment totals for professional footballers by birthplace (country), English League, 1986–2009 8.5 Total numbers of professional footballers by birthplace (country) and tier, English League, selected years 8.6 Percentage distribution of footballers by birthplace (region) and location of club (region), English League, 1989 8.7 Percentage distribution of footballers by birthplace (region) and location of club (region), English League, 1999 8.8 Percentage distribution of footballers in England by birthplace (region) and location of club (region), English League, 2009 8.9 Four-year employment transition probabilities by tier, English League, 1989–1993 8.10 Four-year employment transition probabilities by tier, English League, 1993–1997 8.11 Four-year employment transition probabilities by tier, English League, 1997–2001 8.12 Four-year employment transition probabilities by tier, English League, 2001–2005 8.13 Four-year employment transition probabilities by tier, English League, 2005–2009

xvii

161 162 164 166 174 185 185 186 186 199 218 219 220 221 222 223 224 225 226 227 228 229 230

xviii

List of tables

8.14 Cross-tabulation of squad players’ home countries and countries of employment, Euro 2000 8.15 Cross-tabulation of squad players’ home countries and countries of employment, Euro 2008 8.16 Estimation results: initial divisional status 8.17 Estimation results: retention 8.18 Estimation results: divisional transition 9.1 Managerial spells ranked by duration (matches), English League, 1973–2009 seasons 9.2 Managerial spells ranked by win ratio, English League, 1973–2009 seasons 9.3 Managerial departures, by season, English League, 1973–2009 seasons 9.4 Average number of managerial departures per season, four-season bands, English League, 1974–2009 seasons 9.5 Managerial departures by month, English League, 1974–2009 seasons 9.6 Managerial departures by tier, four-season bands, English League, 1974–2009 seasons 9.7 Average duration (matches completed) of terminating managerial spells, four-season bands, English League, 1974–2009 seasons 9.8 Average duration (matches completed) and average win ratio, in terminating managerial spells by tier, English League, 1974–2009 seasons 9.9 Distribution of complete and right-censored managerial spells by duration (in matches), crude estimates of the survivor, distribution, hazard and probability functions, English League, 1973–2009 seasons 9.10 Involuntary and voluntary managerial job departure hazard functions: estimation results 9.11 The managerial succession effect: estimation results 10.1 Numbers of yellow cards incurred by the home and away teams, English Premier League, 1997–2009 seasons 10.2 Numbers of red cards incurred by the home and away teams, English Premier League, 1997–2009 seasons 10.3 Sample frequency distribution for the bivariate disciplinary points dependent variable, {Z1,j,Z2,j} 10.4 Unconditional model: fitted bivariate probabilities and observed proportions for the numbers of disciplinary ‘points’ incurred by the home and away teams 10.5 Average numbers of yellow and red cards awarded per match by team, English Premier League, 1997–2009 seasons 10.6 Average numbers of yellow and red cards and disciplinary ‘points’ awarded per match by referee, English Premier League, 1997–2009 seasons 10.7 Rule changes and changes of interpretation, by season

233 234 243 244 245 261 263 267 268 269 269 270 271

280 282 292 303 303 305

307 311 314 316

List of tables

xix

10.8 Average numbers of yellow cards, red cards and disciplinary ‘points’ awarded per match by season, English Premier League, 1997–2009 seasons 317 11.1 Stadium capacity, average attendance, capacity utilisation, 2009 season T1 clubs, 1979, 1989, 1999 and 2009 325 11.2 Attendance model: first-stage estimation results 340 11.3 Attendance model: second-stage estimation results 347 12.1 Probabilities for half-time/full-time outcomes 369 12.2 Mean returns based on bookmakers’ ‘best odds’ 370 12.3 Illustration of ‘highest expected return’ betting strategy: English Premier League, 11 May 2003 372 12.4 Returns from ‘highest expected return’ and indiscriminate betting strategies 374 12.5 Average rate of return by tier (division): chronological analysis 376 12.6 Mean expected and actual returns: all possible bets ranked by expected return 377 13.1 Historical performance of top French teams in league and cup competition 382 13.2 Average league attendances, France Ligue 1 and German Bundesliga 1, 1981–2010 (’000) 385 13.3 Revenue, costs and profitability, aggregates and breakdown, France, all Ligue 1 clubs, selected years (€m) 386 13.4 Historical performance of top German teams in league and cup competition 388 13.5 Revenue, costs and profitability, aggregates, Germany, all Bundesliga 1 clubs, selected years (€m) 391 13.6 Historical performance of top Brazilian teams in league and cup competition 393 13.7 Percentage breakdown of total revenue, twenty-one Brazilian clubs, 2004–2007 394 13.8 J. League winners and runners-up, Japan, 1993–2009 397 13.9 Average attendance, revenue and salary expenditure, Japan, J1 clubs, 1999–2008 (¥m) 399 13.10 Football League and Super League winners and runners-up, China, 1994–2009 400 14.1 History of the World Cup 408

1

Introduction

Academic interest in the economics of professional team sports dates back as far as the mid-1950s. Since then, many books and journal articles have been written on the subject. Much of the academic literature originates in the United States (US). In common with trends that are evident throughout the subject discipline of economics, empirical research on the economics of sport has become increasingly sophisticated, both theoretically and in its use of econometric methodology. Papers on the economics of sport now appear regularly in many of the leading economics journals, and most economists would agree that in view of its social, cultural and economic importance, professional sport is a legitimate area of interest for both theoretical and empirical researchers. Indeed, many would argue that the unique configurations of individual and team incentives, and the interactions between cooperative and competitive modes of behaviour that professional team sports generate, make this particularly fertile territory in which to explore the perennial questions about incentives, effort, risk and reward that lie at the heart of all areas of economic inquiry. This volume makes a contribution to the burgeoning literature on the economics of team sports, by providing a comprehensive survey of research that is focused on professional football. The spectacular recent increase in the size of football’s audience is, of course, a strong motivating factor. Such a survey will recognise and reflect not only football’s global popularity in the first part of the twentyfirst century, but also the special historical significance of England as the original birthplace of the sport. Club football played in the English Premier League and Football League provides the laboratory for most of the original, empirical research that is reported in this volume. Each chapter of this volume concentrates on a particular aspect of the economics of professional football. The previous theoretical and empirical literature that is relevant to each topic is reviewed, and new and original empirical analyses are presented. The review sections aim to convey an impression of the breadth and depth of previous academic research into the economics of professional team sports. Much has been written already about football, and much more has been written about other sports, especially in the US where attention naturally tends to 1

2

Introduction

focus on the traditional major league sports of baseball, basketball, (American) football and hockey. Though football is the main subject of this volume, due attention and emphasis is devoted to insights that have been obtained from research into other sports, wherever these turn out to be of wider relevance. As already emphasised, anyone who reads the academic literature on the economics of sport cannot fail to be struck by the sheer volume of column inches that have been devoted to this topic. Of all the articles that have been published, however, a few early contributions were particularly important in shaping the research agenda for the economics of team sports in general, and for the economics of football in particular. Many of the ideas contained in these articles are as relevant to researchers today as they were when the articles were originally published, many years ago. In Chapter 1, three such articles are highlighted and reviewed in some detail. There is, of course, an element of subjectivity in selecting such a small number of articles out of the many that have been published. Even so, a consensus seems to have evolved that regards the articles by Simon Rottenberg (1956) and Walter Neale (1964) as fundamental to the subsequent development of research on team sports in general. Both articles address various economic implications of the structural features of the markets within which professional sports teams operate. The article by Peter Sloane (1971) has also had a major influence on the developing research agenda, especially in respect of the economics of football. In Section 1.1, each of these articles is reviewed in turn, and the subsequent development of the economics of team sports as an academic discipline is outlined. The aim of Section 1.1 is to place the research that is reported in the rest of this volume into its proper context. This is followed in Section 1.2 by a summary of the contents of the remaining chapters of this volume. 1.1  The economics of professional team sports: three seminal contributions

Rottenberg: ‘The Baseball Players’ Labor Market’, Journal of Political Economy, 1956 Rottenberg is widely credited with writing the first academic analysis of the economics of professional team sports. The paper was written at a time when US professional baseball players’ contracts included a reserve clause. Once a player signed his first one-year contract with a team in Major League Baseball (MLB), he ceased to be a free agent. On expiry of his present contract, his team retained the option to renew his contract for another year.1 This served to limit players’ freedom of movement, by binding them to their present employers. Effectively, the reserve clause created a monopsony in the players’ labour market: each contracted player could negotiate with only one potential buyer of his services. The baseball authorities defended the reserve clause on the grounds that it was necessary to ensure an equal distribution of playing talent among opposing teams. Without the reserve clause, the rich teams (with the largest potential markets) would outbid the poorer ones for the best available players. This would tend to reduce uncertainty of

The economics of professional team sports

3

outcome and spectator interest in the league competition as a whole, and depress the attendances and revenues of all teams. Rottenberg’s contribution was to argue that free agency in the players’ labour market would not necessarily lead to a concentration of the best players in the richest teams. In other words, a reserve clause was not a necessary condition to ensure competitive balance. Professional team sports are intrinsically different from other businesses, in which a firm is likely to prosper if it can eliminate competition and establish a position as a monopoly supplier. In sports, it does not pay a rich team to accumulate star players to the extent that (sporting) competition is greatly diminished, because of the joint nature of ‘production’ in sports. Consequently, a team that attempts to accumulate all of the best available playing talent will find at some stage that diminishing returns begin to set in. In baseball no team can be successful unless its competitors also survive and prosper sufficiently so that the differences in the quality of play among teams are not ‘too great.’ … At some point, therefore, a first star player is worth more to poor team B than, say, a third star to rich team A. At this point, B is in a position to bid players away from A in the market. (Rottenberg, 1956, p254, 255)

If teams are rational profit maximisers, the distribution of playing talent among the teams should be more or less equal. Neither a reserve clause nor explicit collusion is necessary in order to bring about this result. It is in each team’s self-interest to ensure that it does not become too strong relative to its competitors. It follows that players will be distributed among teams so that they are put to their most ‘productive’ use; each will play for the team that is able to get the highest return from his services. But this is exactly the result which would be yielded by a free market. (Rottenberg, 1956, p256)

A reserve clause will therefore deliver almost the same distribution of playing talent between the competing teams as free agency. Whether players are free agents or not, the distribution of playing talent is determined by the incentive to maximise the capitalised value of the services supplied by individual players. If there is another team for which this capitalised value would be higher than it is for the player’s present team, then there is a price at which it is advantageous for both teams to trade the player’s contract. Rottenberg also discusses the implications of the reserve clause, and the monopsony power it confers on teams as buyers of playing services, for players’ salaries. Each player’s reservation wage (the minimum salary he would accept to play baseball) is determined primarily by the next highest salary he could earn outside baseball adjusted to reflect his valuation of the non-pecuniary costs and benefits of playing baseball. Although theoretically the team has the contractual power to impose the reservation wage on all players, Rottenberg notes that in practice this does not seem to happen. Many players earn far more from baseball than they could in alternative employment. This is attributed to the fact that players as well as teams have bargaining power in salary negotiations: in an extreme case, a player can

4

Introduction

simply threaten to withdraw his services. If a player’s reservation wage is $10,000, but he is worth $20,000 to his team, then a salary anywhere between $10,000 and $20,000 is possible, depending on the ‘shrewdness and guile of the parties in devising their bargaining strategies’ (Rottenberg, 1956, p253). Competition among sellers, however, imposes limitations on players’ bargaining power. A star player worth $40,000 to his team cannot extract a salary beyond $30,000 if a lesser player worth $20,000 is willing to accept a salary of $10,000 to fill the same position. The main effect of the reserve clause is that players receive salaries below their value to the team that employs them. In other words, it tends to direct rents away from players and towards teams. The reserve clause does not achieve its stated aim of influencing the allocation of playing talent between teams. Rottenberg concludes by considering several alternative regimes that might produce a more or less equal distribution of playing talent between teams with free agency in the players’ labour market. These include: • Revenue sharing. If all revenues are shared equally, teams have no pecuniary incentive to spend on players to enhance their own performance and revenue. An equal distribution of mediocre playing talent is the most likely outcome. • Imposition of a maximum salary. The effect on the distribution of talent depends on the ability of the teams to circumvent the maximum by offering players nonpecuniary rewards. • Allocating multiple team franchises in large cities. If reasonable equality between each team’s potential market size can be achieved, this is expected to create a more equal distribution of playing talent. Neale:  ‘The Peculiar Economics of Professional Sports’, Quarterly Journal of Economics, 1964 Neale’s analysis begins by emphasising the joint nature of production in professional sports. Heavyweight boxing is used as an example to introduce what Neale calls the ‘Louis Schmelling Paradox’. World champion Joe Louis’ earnings were higher if there was an evenly matched contender available for him to fight than if the nearest contender was relatively weak. The same point applies also in baseball. Suppose the Yankees used their wealth to buy up not only all the good players but also all of the teams in the American League: no games, no receipts, no Yankees. When, for a brief period in the late fifties, the Yankees lost the championship and opened the possibility of a non-Yankee World Series they found themselves – anomalously – facing sporting disgrace and bigger crowds. (Neale, 1964, p2)

Does this imply that professional sport is an industry in which monopoly is less profitable than competition, contradicting what is taught to students and what can be read in any Principles text? Neale addresses this paradox by distinguishing between sporting and economic competition. Sporting competition is more profitable than sporting monopoly for the reasons outlined above, but sporting

The economics of professional team sports

5

competition is not the same as economic competition. Similarly, although in law the sports team is a firm (which may be motivated by profit), it is not a firm in the economist’s sense. A single team cannot supply the entire market; if it did, it would have no opposition to play against. Teams must cooperate with each other to produce individual matches and a viable league competition, so there is joint production. The league’s organising body exerts strict controls over a wide range of matters including competition rules and schedules, player mobility and the entry and exit of clubs. In short, the league rather than the individual team is the ‘firm’ in the economist’s sense. A sports league should be regarded as analogous to a multi-plant firm, in which the individual teams are ‘plants’, subject to decisions which are taken and implemented collectively at league level. If the sports league is the ‘firm’ in the economic sense, this raises the question as to why it is unusual to observe direct competition between rival leagues operating within the same sport. Although the National League and American League do operate simultaneously in baseball, analytically they should be regarded as one larger ‘multi-league’ firm, since they come together at the end of each season to produce the World Series. Geographical division is a more common form of segmentation, though according to Neale, one that is inherently unstable. Where direct competition is precluded by geography, profit incentives tend to promote enlargement and the elimination of geographical boundaries. Competition between different sports is more common than competition between rival leagues within the same sport, though segmentation based on nation, region, season of the year or even social class is still common.2 All such forms of segmentation tend to inhibit direct head-to-head competition. Neale suggests that the general lack of competition between sports leagues arises because the cost and demand characteristics of the market for professional team sports tend to create conditions of natural monopoly, making it efficient for a single league to supply the entire market. On the cost side, Neale suggests that the long-run average cost curve is probably horizontal. Although an increase in the scale of production might entail the use of less efficient playing inputs, raising average costs, this tends to be offset by an ‘enthusiasm effect’. If the sport operates on a larger scale, public enthusiasm encourages more people to take up playing, eventually raising the supply of players at the highest level. To some extent, the enthusiasm effect makes supply and demand interdependent: if more people play the sport, more will also want to attend matches at the professional level. Finally, the existence of rival leagues would effectively break the monopsony power of teams as buyers of playing services, enhancing players’ bargaining power in salary negotiations. This would tend to make costs higher than they are when one league operates as a monopoly supplier. On the demand side, Neale suggests that baseball teams produce a number of streams of utility: directly for spectators who buy tickets for seats in the stadium and for television viewers who watch the match at home; and indirectly for anyone who enjoys following the championship race as it unfolds. The closer the

6

Introduction

competition, the greater the indirect effect. For newspapers and television companies in particular, the indirect effect is a marketable commodity that helps sell more of their product. The size of the indirect effect depends on the scale and universality of the championship, and is therefore maximised when the league is a monopoly supplier. Overall, ‘it is clear that professional sports are a natural monopoly, marked by definite peculiarities both in the structure and in the functioning of their markets’ (Neale, 1964, p14). An important implication is that the peculiar economic characteristics of professional sports leagues and their constituent teams should be recognised by legislatures, by the courts and by the general public, whenever practices such as collective decision-making or other (apparently) anticompetitive types of behaviour come under scrutiny. Sloane: ‘The Economics of Professional Football: The Football Club as a Utility Maximiser’, Scottish Journal of Political Economy, 1971 Sloane’s paper questions Neale’s conclusion that the league rather than the individual team or club is the relevant ‘firm’ (or decision-making unit) in professional team sports. In the case of English football, for example, the sport’s governing bodies merely set the rules within which clubs can freely operate. Most economic decisions, such as how much money to spend on stadium development and how many players to employ, are made by the clubs. Although the total quantity of ‘output’ (the number of matches played by each team) is regulated, this clearly reflects the clubs’ common interest. In cartels, it is not unusual for firms to reach joint decisions concerning price or production, but this does not imply that the cartel should be elevated to the theoretical status of a ‘firm’. In short, Sloane suggests that Neale’s argument tends to overemphasise mutual interdependence. ‘The fact that clubs together produce a joint product is neither a necessary nor a sufficient condition for analysing the industry as though the league was a firm’ (Sloane, 1971, p128). Having argued that the club is the relevant economic decision-maker, Sloane goes on to raise a number of key questions concerning the objectives of sports clubs. Implicit in the reasoning of both Rottenberg and Neale is an assumption of profit maximisation. Despite the ‘peculiarities’ of sports economics elucidated by Neale, the behaviour of professional sports teams is analysed within a very conventional analytical framework. While this may be reasonable in the case of US professional team sports, where many teams do have an established track record of profitability, Sloane suggests that it may not be universally applicable. Throughout the history of English football, profit-making clubs have been the exception and not the rule. Most chairmen and directors of football clubs are individuals who have achieved success in business in other fields. Their motives for investing may include a desire for power or prestige, or simple sporting enthusiasm: a wish to see the local club succeed on the field of play. In many cases, profit or pecuniary gain seems unlikely to be a significant motivating factor. If so, it may be sensible to view the objective of the football club as one of utility

The economics of professional team sports

7

maximisation subject to a financial solvency constraint. The financial solvency constraint recognises that the benevolence of any chairman or director must reach its limit at some point. Non-profit-maximising models of the firm had received considerable attention in the economics literature during the decade prior to the publication of Sloane’s article. A major drawback to the general introduction of the utility maximisation assumption in the theory of the firm is that it may be rationalised so that it is consistent with almost any type of behaviour and therefore tends to lack operational significance. (Sloane, 1971, p133)

In the case of football clubs, however, it is not too difficult to identify several plausible and easily quantifiable objectives. Sloane suggests the following: • Profit. The expectation that profit is not the sole or even the most important objective does not preclude its inclusion as one of several arguments in the utility function. • Security. Simple survival may be a major objective for many clubs. Decisions (concerning, for example, sales of players) may aim more at ensuring security than at maximising playing success. • Attendance or revenue. A capacity crowd enhances atmosphere and a sense of occasion, and may in itself be seen as a measure of success. Recently, an increasing willingness to charge whatever ticket prices the market will bear suggests that revenue (or profit) carry a heavier weight in the utility function than in earlier periods, when it was usual to charge the same price for all matches, irrespective of the level of demand. • Playing success. This is probably the most important objective of all, and one to which chairmen, directors, managers, players and spectators can all subscribe. • Health of the league. This enters the utility function in recognition of clubs’ mutual interdependence. Formally, the club’s objective is to maximise: U = u( P,A,X,π R − π 0 − T )

subject to π R ≥ π 0 + T

[1.1]

where P = playing success; A = average attendance; X = health of the league; πR = recorded profit; π0 = minimum acceptable after-tax profit; and T = taxes. It is important to note that the utility maximisation model has implications that are very different to those that follow from the profit-maximising assumptions of Rottenberg and Neale. In particular, if the weighting of P in the utility function is heavy relative to that of X and πR, the argument that diminishing returns would prevent the accumulation of playing talent in the hands of a small number of rich clubs does not necessarily hold, unless there are binding financial constraints preventing expenditure on new players. The notion that profit incentives should help maintain a reasonably even allocation of playing talent between richer and poorer teams breaks down. The case for regulation to override the ‘free market’ outcome, whether in the form of a reserve clause, revenue sharing or the taxation of transfer

8

Introduction

fees, therefore seems to be enhanced if clubs are pursuing non-profit rather than profit objectives. 1.2  Outline of this volume

Since the appearance of the pioneering work of Rottenberg, Neale and Sloane, there has been a proliferation of published academic research on the economics of team sports, in journal articles and in books. Many of these contributions are reviewed in this volume. By way of an introduction, this section contains a brief outline of the contents of each of the following chapters. Rottenberg’s argument – that market mechanisms can be relied upon to maintain a reasonable degree of competitive equality among the member teams of a sports league  – provides the motivation for a number of theoretical contributions to the sports economics literature, examining the implications for resource allocation within a professional sports league of several regulatory mechanisms, including the reserve clause, payroll caps, the reverse-order-of-finish draft, revenue sharing, and rules governing the award of franchises and league membership. According to the theoretical analysis, most of these devices promote the survival of small-market teams; but in many cases they fail to reduce competitive inequality because they do not create the necessary profit incentives. Chapter 2 reviews some of the key findings from this literature. The theoretical models of the economics of sports leagues are concerned with the degree of competitive balance or competitive inequality between the member teams of a league competition, which in turn determines the extent of uncertainty of outcome for individual match results and for the destination of the league championship. In Chapter 3, the emphasis shifts away from this theoretical analysis at the level of the league championship, towards the measurement of competitive inequality and uncertainty of outcome for individual match results. Certain other empirical patterns and regularities in football match results data are investigated, including the phenomenon of home-field advantage, and ‘streaks’ or persistence effects in sequences of consecutive match results. Uncertainty of outcome seems to be an essential ingredient for any competitive sport. If the match result were completely deterministic, what would be the point for either competitors or spectators? The observation that the result of any individual match is uncertain, however, does not immediately consign any forecasting exercise to irrelevance. If prediction is interpreted as assessment of the probabilities for home-win, draw and away-win outcomes, the results of individual football matches are highly predictable, as evidenced by the wide variation from one match to the next in the betting odds quoted by bookmakers and online betting firms for these outcomes. Chapter 4 examines the specification and performance of econometric forecasting models for match results in football, which generate probabilistic forecasts of the results of forthcoming matches, by number-crunching large volumes of past match results data and other relevant information.

Outline of this volume

9

Game theory is defined as the study of decision-making in situations of conflict and interdependence. Some economists have argued that sports such as football offer promising opportunities for the investigation of propositions of game theory, concerning the formulation by the players of optimising strategies. For example, the high-pressure ‘game’ played out between the kicker and the goalkeeper whenever a penalty kick is awarded mirrors closely the textbook conditions for a twoperson non-cooperative zero-sum simultaneous game. The kicker decides in which direction to shoot and the goalkeeper decides simultaneously in which direction to dive; and either the kicker scores, or a goal is averted because the goalkeeper saves or the kicker misses the target. Viewed more broadly, the football match in its entirety has many of the characteristics of a strategic and dynamic ‘game’. The two teams are pitched into direct opposition, and the team managers select and adjust continuously their styles of play as the match evolves. Chapter 5 reviews the theoretical and empirical literature, and presents some new empirical evidence on applications of game theory in football. The sporting attributes of professional football and its characteristics as a business have always been closely connected. Chapter 6 presents an overview of the historical development of English club football as a business, and an analysis of its contemporary economic, financial and commercial structure. The analysis covers English club football’s competitive structure, trends in spectator demand reflected in match attendances and gate revenues, the market for TV broadcast rights, the development of the labour market for playing talent, and the ownership, governance and financing of English football clubs. The level of the top professional footballers’ remuneration has raised concerns over the effect on the competitive structure and finances of football, and over the morality of such disproportionately high financial rewards accruing to footballers relative to other occupations whose contribution to society’s well-being is, arguably, much greater. Chapter 7 examines theoretical explanations that have been put forward for the exceptionally high remuneration of the leading stars in modern-day professional football, and other professional sports. The theoretical analysis of the economics of superstars notes that, especially since the arrival of pay-TV, sports stars are capable of servicing very large paying audiences simultaneously, incurring little or no incremental cost as the audience size increases. Other occupational groups, such as nurses and teachers, service strictly finite number of users. The rank-order tournament model views the remuneration of the highestpaid stars as a means of providing all professionals with incentives to invest in the development of their skills, in the hope of reaching the top of their profession and being rewarded accordingly. Chapter 8 discusses several other topics concerned with the economics of the professional footballers’ labour market. Patterns of migration, employment mobility and career development among the professional footballers employed by the ninety-two member-clubs of the Premier League and Football League are examined, including the impact of the arrival of large numbers of overseas players on

10

Introduction

the career prospects of locally born footballers. The factors influencing patterns of international migration by footballers are examined. Empirical evidence on racial discrimination in English football suggests that a form of hiring discrimination affects the opportunities for indigenous black players to progress to professional status. It seems likely, however, that any such effect has diminished over time. The job description of the football team manager includes the selection, supervision and coaching of players, and the formulation of tactics and strategies. Many football managers, especially in professional football’s lower tiers, are also responsible for the buying and selling of players, wage negotiations, and various administrative duties. Chapter 9 examines various aspects of the role and contribution to team performance of the football manager. In principle, the football manager’s contribution subdivides into a direct and an indirect component. The direct contribution is to maximise performance through astute team selection, superior tactics and powers of motivation; while the indirect contribution is to coach players so as to enhance their skills, and to strengthen the team through effective dealings in the transfer market. The indivisibility of the team effort which ultimately determines performance poses a major challenge for any researcher seeking to isolate and measure the manager’s contribution. The modern-day football manager’s position is renowned for its chronic insecurity, which raises several interesting questions for researchers concerning the relationship between managerial turnover and team performance. While it is the football manager who usually pays the ultimate price for perceived underachievement on the part of the players under his direction, the football referee often serves as a convenient scapegoat during the immediate aftermath of a poor result or performance. Football referees, who are the subject of Chapter 10, are routinely criticised by managers, players, journalists and spectators for being incompetent, inconsistent and biased. Several recent academic studies have examined whether there is any substance to claims of favouritism and bias on the part of football referees. Due to technological advances in broadcasting, the actions of referees have never been more intensely scrutinised than they are today. Split-second decisions taken by referees can have enormous financial consequences, due to the fine line between spectacular success and catastrophic failure that exists in football. Social history and sociology provide many useful insights into the causes of fluctuating football attendances. Econometric modelling of variations in the attendances of individual clubs, both season-by-season and match-by-match, has been a subject of attention for sports economists since the 1970s. Chapter 11 provides a non-technical review of the empirical literature, focusing on the issues of variable definition, model specification, estimation and interpretation that are faced by researchers in this area, and presents an analysis of the variation in the average attendances per season of English football clubs during the post-Second World War period. Research concerning the relationship between the market prices for bets on the outcomes of sporting contests, and the probabilities associated with these

Outline of this volume

11

outcomes, forms a subfield within the literature on financial market efficiency. Chapter 12 examines the economics of sports betting, with particular emphasis on the markets for betting on the outcomes of football matches. The growth of internet betting during the 1990s and 2000s has presented tremendous new opportunities for betting firms and their customers, based on the rapid information processing and transmission capabilities of internet technology. Much of the descriptive and empirical analysis of the football industry that is presented in this volume is focused on English club football. Chapter 13 widens the perspective, by examining the historical development and present-day competitive and commercial structure of football in five other countries:  France, Germany, Brazil, Japan and China. France and Germany both fail to match England in terms of the income that is generated by professional football at the highest level. Over several decades, however, both countries have outshone England in the international football arena. Brazil, also renowned for the excellence of its national football team, has traditionally exported many of its star footballers to wealthy clubs in western Europe, despite a strong indigenous football culture. In Japan and China, by contrast, there is little or no grassroots football tradition; and recent attempts to establish commercially vibrant professional football leagues in these countries have been driven from the top down. In the arena of international football, countries compete fiercely to host the World Cup, as well as other mega sporting events. Many World Cup bids in recent times have attempted to muster public support through extravagant claims concerning the economic benefits that will flow from a successful bid. Academic economists, however, tend to view such claims with extreme caution. Some economists believe that the net economic impact is either negligible, or perhaps even negative. The final chapter of this volume, Chapter 14, examines the economic evidence as to whether hosting a World Cup can be expected to yield economic benefits to the host nation, either tangible or intangible, that are capable of justifying the massive financial outlays. Notes 1 This was subject only to a rule that prevented the salary from being cut by more than 25 per cent in any one year. 2 Traditionally, English cricket and rugby union were upper- or middle-class sports, while football and rugby league were working-class sports. More recently, class divisions may have become more blurred, but they have not disappeared altogether. Cricket is played only in summer; rugby league switched from a winter to a summer schedule in the late 1990s; football and rugby union are played in winter. Rugby league still has a strong regional identity centred on Lancashire and Yorkshire. Cricket is popular throughout England, but is a minority sport in Scotland.

2

The economic theory of professional sports leagues

Introduction

As seen in Chapter 1, the idea that market mechanisms can be relied upon to maintain a reasonable degree of competitive equality among the member teams of a sports league, without the need for extensive regulation of player compensation or mobility by the sport’s governing body, was first articulated by Rottenberg (1956). In discussing the economic structure and characteristics of the North American baseball players’ labour market, Rottenberg considers the case of two teams located in different towns, one of which has a larger population (or potential market) than the other. Other things being equal the marginal revenue product of a player of a given level of ability is greater with the large-market team than it is with the small-market team. Since the marginal revenue function declines as the quantity of playing talent already held increases, however, it does not pay the large-market team to accumulate the most talented players to the point where complete competitive dominance is achieved. This argument does not depend upon contractual arrangements or the structure of player compensation. It is valid under free agency, in which case the player may be in a strong position to secure most or all of his marginal revenue product in salary negotiations, since his reservation wage is the salary he could command by signing for another team. It is also valid under a reserve clause, in which case teams may have the opportunity to drive player compensation down, towards the highest salary the player could command in employment outside the sport. Subsequently, El-Hodiri and Quirk (1971) developed a mathematical model of an n-team professional sports league that captures these and other insights. They demonstrate that perfect competitive balance, with all teams having equal playing strengths, is consistent with an assumption of profit-maximising behaviour only if there is no buying and selling of players’ contracts, or if the revenue functions of all teams are the same. In the type of model presented below, the latter would require that all teams are located in towns of equal (or similar) population size, so that each team’s potential market is the same. Since neither of these requirements is likely to be met in practice, ‘(i)t is not surprising, then, that casual empiricism 12

Introduction

13

indicates that in no professional team sport under current rules of operation is there a tendency toward equal playing strengths’ (El-Hodiri and Quirk, 1971, p1313). Variants of the El-Hodiri and Quirk (1971) model have been used to investigate a range of policy issues. Key results from this literature are presented by Fort and Quirk (1995) and Vrooman (1995, 2007, 2009), who examine the economic and incentive effects of a number of regulatory mechanisms, including the reserve clause, payroll caps, the reverse-order-of-finish draft, revenue sharing, and rules governing the award of franchises and league membership. According to the theoretical analysis, most of these devices promote the survival of small-market teams; but in many cases they fail to reduce competitive inequality, because they do not create profit incentives for team owners to adjust in the direction of greater competitive equality. Some of the devices may even create perverse incentives and tendencies towards greater competitive inequality. Késenne (2007b) provides a comprehensive survey of this literature. Chapter 2 reviews the main findings of this body of work, using a modified version of the models described by Fort and Quirk (1995), Vrooman (1995) and others. Most of the earliest studies that are reviewed above were developed with North American major league sports in mind. Section 2.1 describes some of the key characteristics of the North American model for the organisation of professional team sports leagues. One key feature of the North American model is that the labour market for playing talent is far less open than in the case of European football. Accordingly, much of the US literature on the economics of professional team sports leagues has considered models in which the total stock of playing talent is assumed to be fixed, and any reallocation of talent between the league member teams is a zero-sum activity. This ‘closed’ labour market assumption is reasonable for North American sports, which draw principally on home-grown talent and do not frequently trade players with teams in other countries. A closed model is less appropriate for football, especially following the liberalisation of the rules governing the European football players’ labour market in the mid-1990s, since when the leading clubs in particular have recruited large numbers of foreign players. In the case of football, therefore, an ‘open’ labour market assumption is appropriate. In an open model, the total stock of playing talent at the disposal of the league member teams is variable, and can be increased by hiring from an external market in playing talent. The next two sections of this chapter develop a theoretical model of resource allocation in a professional team sports league, under both closed and open labour market conditions. The implications for resource allocation and competitive inequality of profit-maximising behaviour and win-maximising behaviour on the part of team owners are considered. Section 2.2 examines the general case of an n-team league, and Section 2.3 examines the stylised case of a two-team league. For the n-team model, the explicit solutions for the amounts of talent hired by the

14

The economic theory of professional sports leagues

teams are algebraically complex. In the sports economics literature, it is common practice to obtain insights by considering the special case n = 2. The final two sections use the theoretical model to examine the effectiveness of rules that might be implemented by the sport’s governing body in an attempt to reduce competitive inequality between large-market and small-market teams, focusing specifically on revenue sharing and various forms of payroll cap. Do such arrangements help reduce competitive inequality, and perhaps make the league a more exciting and watchable proposition for spectators? Alternatively, might their effects be either neutral, or even counterproductive in the sense that they help entrench competitive inequalities that already exist? Revenue-sharing arrangements are discussed in Section 2.4; and payroll caps are examined in Section 2.5. 2.1  The North American professional team sports model

The theoretical literature on the determinants of the degree of competitive inequality in sports leagues was developed by US sports economists, with North American team sports primarily in mind. Naturally the development of this literature reflects the characteristics of the North American model for the organisation and regulation of team sports. This differs from the European model in several key aspects. In reviewing this literature, therefore, an awareness of the key features of the North American model is useful. This subsection outlines the organisational structure of three North American professional team sports: baseball, basketball and (American) football.1 Comparisons between the North American and European models for the organisation of sports leagues are drawn by Noll (2002, 2003) and Szymanski (2003). Perhaps the most fundamental difference between the North American and European models concerns the highly restricted nature of supply in North America. In all three sports leagues membership is controlled through the award of franchises by the leagues’ organising bodies. A franchise grants a territorial monopoly to the team’s owner: no other team can operate within the owner’s territory, and no owner can relocate to another town without the approval of 75 per cent of all team owners. In Major League Baseball (MLB), sixteen teams compete in the National League (NL) and fourteen in the American League (AL). In (American) football thirty-two teams make up the National Football League (NFL). In basketball there are thirty teams in the National Basketball Association (NBA). In each case, league competition takes place within a number of regionalised sections (divisions), and end-of-season play-offs determine championship outcomes. To appreciate the highly restrictive nature of the franchise system, it is worth noting that the mid-2009 estimate of the US population was approximately 307 million. The top divisions of the big five European football leagues each support 18 or 20 teams, with estimated national populations of ­approximately 53 million (England and Wales), 65 million (France), 82 million

The North American professional team sports model

15

(Germany),  60  million (Italy) and 46 million (Spain). Even more important, league membership in North America is determined exclusively through the franchise system; there is no hierarchical divisional structure and no promotion and relegation. Membership of the top tiers of European football is open to a much larger number of teams operating in the lower tiers of the respective leagues. Promotion and relegation between the tiers depends solely on competitive prowess. Profit maximisation is the prime objective of North American leagues and team owners, so profitability is the main factor influencing decisions concerning the award of franchises and relocation. There is also intense competition between municipalities to attract and retain franchise holders. Inducements take the form of offers to construct lavish new stadiums at public expense: a significant source of public subsidy for leagues and teams that are already rich in cash (see Chapter 14). The leagues have been able to maintain their monopoly positions largely because the US courts, acknowledging the peculiarities of the economics of team sports (see Chapter 1), have tended to accept the legitimacy of restrictions on the production of sporting events that would be inadmissible elsewhere. In a landmark ruling in 1922, the Supreme Court granted MLB exemption from the Sherman antitrust laws. In 1961 the Sports Broadcasting Act was passed by Congress, entitling the leagues to sell broadcasting rights collectively on behalf of their member teams (Quirk and Fort, 1992; Scully, 1995). The main role of the leagues within this framework is to implement rules aimed at furthering the collective interest of the teams in achieving joint profit maximisation. The leagues therefore impose restrictions on the behaviour of the teams in both the product and labour markets, which seek to prevent any individual team from achieving a level of competitive dominance that would be damaging to the interest that all teams share in maintaining a reasonable degree of competitive balance. In the early history of all three sports, the most important restriction of this kind was the reserve clause, described previously in Chapter 1. Having signed a contract as a professional, the player’s team retained the option to renew his contract, effectively binding the player to his present employer. The reserve clause was justified on the grounds that it was necessary to prevent the richest teams from outbidding the rest for the services of the top players; but its tendency to depress players’ compensation was a highly convenient side-effect from the team owners’ perspective. Baseball’s reserve clause, effective since 1880, was challenged successfully in the Supreme Court in 1976, on the grounds that it should be interpreted only as a one-year option clause. The Court ruled that by playing for a year without signing a new contract, a player could satisfy his obligations under the reserve clause, and subsequently become a free agent. Under the 1976 settlement, all MLB players became free agents after completing a minimum number of years of major league service. At the time of writing, players qualify as free agents after six years. In basketball, the one-year interpretation had always applied, but teams that signed a free agent had to pay compensation to his former employer. This system

16

The economic theory of professional sports leagues

was also abandoned in 1976, when moves towards the full implementation of free agency were initiated. Players became free agents after four years’ NBA service or upon expiry of their second contract if this happened sooner. At the time of writing, a player becomes a free agent at the end of his first contract (often four years), although the first team has the right to retain the player if it matches the highest offer received from another team. In (American) football, free agency was not introduced until 1993, when a one-year option clause (similar to MLB) was abandoned. The delay is attributed by Quirk and Fort (1999) to the relatively weak bargaining position of the players’ union, explained in turn by the short average duration of playing careers and the dominant role played in the sport by coaches (who tend to be even more influential than star players). From 1993 NFL players became free agents after a five-year qualifying period. At the time of writing, the qualifying period for unrestricted free agency is four years; players also qualify for restricted free agency rights after three years. In all three sports, trades involving in-contract players normally take the form of player-exchange deals, or swaps of players for draft picks (see below). Trading players for cash is unusual, though not completely unknown, and there is no North American equivalent of European football’s multi-million pound transfer system. Other restrictions on the free play of market forces in North American sports include the draft system, payroll caps, luxury taxes and revenue sharing. The reverse-order-of-finish draft system allows the weakest teams from the previous season the first pick of rookie players moving from college (or school in the case of baseball) to professional level for the first time. The NFL introduced the draft in 1936; the NBA followed suit soon after its formation in 1949; and MLB adopted the draft in 1965 (though the draft does not apply to new players arriving from overseas). Drafts are permissible under US antitrust law because they are included in collective bargaining agreements between leagues and player unions. These agreements also require minimum salaries for newly drafted players. The detail of how the draft works varies among the sports. There are seven rounds of the draft in the NFL (each team has seven selections). In MLB there are two drafts per year, in June and December. In the 1984–5 season the NBA became the first organising body to operate a payroll cap, in an attempt to offset the potentially damaging implications of free agency for competitive inequality. The total salary expenditure of each team was subject to a limit equivalent to 53 per cent of gross revenues divided by the number of teams in the league. In the 2005 collective bargaining agreement, the cap was set at 51 per cent of gross league revenues for seasons 2006–7 to 2011–12. A minimum level of salary expenditure is also defined, at 75 per cent of the salary cap. Any team failing to achieve the minimum level of expenditure is surcharged at the end of the season. The NBA cap is ‘soft’, because there are exceptions allowing teams to exceed the cap in order to retain players whose contract renewal would otherwise take the team’s salary expenditure above the cap limit.

The North American professional team sports model

17

In theory, by equalising expenditure on players’ compensation throughout the league, the payroll cap should enable the small-market teams to compete for championship success on equal terms with the large-market teams. In practice, however, the NBA salary cap has not succeeded in equalising expenditures, mainly because the exemption clause is invoked routinely by the large-market teams. Consequently total salaries regularly exceed 60 per cent of revenues, and the high-spending teams’ salary bills are typically more than twice those of the low-spending teams. Championship success in the NBA became more, rather than less, concentrated following the introduction of the cap (Quirk and Fort, 1999). However, competitive inequality in the NBA has been reduced since the 2002–3 season, due in part to the evolution of the luxury tax first introduced in 1999 (see below) into a hard cap after 2002–3. In 1994 the NFL adopted a ‘hard’ payroll cap, at 64 per cent of defined gross revenues. The NFL cap cannot be exceeded in the long run. While pro-rated upfront bonus payments can be made over the length of a player’s contract, the actual payroll in future years must be reduced to account for the forward bonus. In the 2006 collective bargaining agreement, the cap was set at 57.5 per cent of total revenues for the 2008–9 season, and 58 per cent subsequently. Although the percentage is lower than previously, a change in the definition of gross revenue (to include revenue from the sale of luxury seats) has made the size of the revenue pool larger. There is also a minimum payroll requirement, set in the range of 84–90 per cent of the cap. An attempt to introduce a payroll cap in MLB resulted in a players’ strike in 1994 and 1995, and was eventually abandoned. A luxury tax, rather than a payroll cap, has been part of each subsequent collective bargaining agreement. The luxury tax is a tax on salary expenditure exceeding a set threshold. Team payrolls are permitted to exceed the threshold, but with a liability to pay tax on the excess expenditure. The tax starts at 22.5 per cent, increasing to 30 per cent and 40 per cent on the second and third occasions the threshold is breached. During the 2000s, however, the threshold has been set sufficiently high that only the largest-market team, the New York Yankees, has been taxed regularly and in large amounts. According to figures quoted by Vrooman (2009), the Yankees contributed $121.6 billion of the total luxury tax revenue of $136.4 billion paid by all MLB teams between 2003 and 2007. The NBA luxury tax, which was introduced in 1999, is more onerous than the MLB version. Teams whose payroll exceeds a predetermined level pay one dollar for each dollar their payroll exceeds the tax level. The tax level is computed by taking 61 per cent of projected basketball-related income, subtracting projected benefits, and adjusting for whether the previous season’s basketball-related income was above or below the projection. On several occasions following its introduction the tax was not triggered; but the 2005 collective bargaining agreement guarantees that the tax is effective in every season. Five teams paid $55 million in 2006–7; eight teams paid $92.4 million in 2007–8; and seven teams paid $87.3 million in 2008–9 (Coon, 2010).

18

The economic theory of professional sports leagues

In all three sports revenue sharing plays an important part in offsetting inequalities in drawing power between teams. Broadcast rights are sold in separate packages to national and local broadcasters. Practices concerning the distribution of gate revenues vary between sports. Home and away teams in the NFL share gate revenues on a 66:34 split. Other venue revenues are not shared, while local broadcast revenue is small, and is not shared. In MLB, 31 per cent of local revenues (including gate, venue and broadcast revenues) are shared. In the NBA, local revenues are not shared. As a general principle, national broadcast revenues are shared equally between all major league member teams. Since the mid-1990s, there has been exponential growth in the value of rights, and a steady migration of the rights away from the traditional free-to-air broadcasters ABC, CBS and NBC. The beneficiaries include Fox, the group owned by Rupert Murdoch’s News Corporation, and several satellite and cable pay-TV broadcasters. The NFL deal for 2006–11, valued at $22.1 billion, assigns the primary role to ESPN (a cable broadcaster affiliated with ABC) and DirecTV (satellite). The MLB deal for 2007–13, valued at $5.6 billion, divides the broadcast rights between Fox, ESPN (cable), TBS (cable, owned by Time Warner) and DirecTV (satellite). Since 2002, the broadcast rights for NBA have been held by the cable providers ESPN and TBS. The 2008–16 deal is valued at $7.4 billion. With the leagues maintaining a stranglehold over the supply of professional team sports, it is unsurprising that the histories of the three sports are littered with attempts on the part of outsiders to set up rival competitions. Following the creation of the NL in 1876, there were several attempts to establish rival leagues, including the AL which was set up in 1901. The current NL–AL monopoly, achieved by agreement between the two leagues in 1903, has survived subsequent challenges from the Federal League (1914), the Mexican League (in the 1940s), and a threatened Pacific Coast League (which was averted in 1958, partly as a result of the moves of the Brooklyn Dodgers and New York Giants to Los Angeles and San Francisco, respectively). In basketball the NBA was created in 1949 from the remains of two rival leagues. Its most powerful challenger since has been the American Basketball Association (ABA), set up in 1967. Mounting financial difficulties eventually led to the demise of the ABA, with four of its surviving teams being incorporated into the NBA in 1976. Since the creation of the American Professional Football Association (the forerunner of the NFL) in 1920, there have been several attempts to establish rival leagues in (American) football; the most successful being the fourth American Football League (AFL), set up after the NFL had refused to award a number of expansion franchises in the late 1950s. The AFL operated alongside the NFL between 1960 and 1969, before a merger incorporating the AFL teams into the NFL realised the original aims expressed by the AFL’s founders ten years earlier. Although there is a prolific and colourful history of attempts to create rival leagues, only the AL has endured for more than a few years, and then only by

A model of an n-team league

19

operating together with the NL as a de facto joint monopoly supplier. In some instances, however, rival league proposals (whether implemented or only threatened) have been successful in forcing the established leagues to make policy changes. Clearly, there is a strong imperative in any sport to operate a competitive structure which delivers a single champion. But while the established leagues remain effectively closed to new entrants, excluding a number of cities capable of supporting potentially valuable franchises, the incentives that have previously brought so many rival league proposals to (temporary) fruition will undoubtedly remain in place. 2.2  A model of an n-team league

This section develops a theoretical model of resource allocation in a professional team sports league, for the general case where the number of competing teams, denoted n, is unspecified. In the model, it is assumed that the member teams of a sports league hire units of playing talent that are embodied in players, and that each player’s remuneration is proportional to the number of units of talent he (or she) embodies. In principle there is no limit to the quantity of talent that any team is able to deploy. While football teams are restricted to deploying only eleven players at any time, they can always deploy more talent by hiring more highly talented players. Accordingly, the model is developed by examining the team owner’s decision on the number of units of talent hired and deployed. The following notation is used to develop the model: ti = talent hired and deployed by team i T = total quantity of talent hired by all league member teams n = number of league member teams t 8 = T/n = average quantity of talent hired by all league member teams τi = ti  / t 8 = nti / T = ratio of talent hired by team i to the average quantity of talent hired by all league member teams wi = team i’s win ratio or win percent mi = market size of team i c = cost per unit of talent Ri = total revenue of team i MRi = marginal revenue of team i ARi = average revenue of team i In order to develop the model, it will be useful to begin by obtaining some general expressions for the effect of a change in ti on t 8 and on τi. First, note that t 8 = T/n, where T = t1 + t2 + … + tn. The partial derivative with respect to ti is ∂ t / ∂t i = (1 / n )[1 + ∑ ( ∂t j / ∂t i )]  j≠ i

Second, note that τi = ti / t .8 The partial derivative with respect to ti is

[2.1]

20

The economic theory of professional sports leagues

∂τ i / ∂t i = ( −t i / t 2 )( ∂ t / ∂t i ) + 1 / t = (1 / t 2 )[ t − t i ( ∂ t / ∂t i )] 

[2.2]

According to [2.1] and [2.2], the effect of a change in ti on τi depends upon the implications of the change in ti for tj, for all j≠i. In other words, the effect on τi of a change in the talent hired by team i depends upon the implications of this change for the amounts of talent that are hired by all of the other league member teams. In the model, it is assumed that team i’s revenue is dependent on three factors: (i) Team i’s market size, represented by mi; (ii) The overall quality of playing standards in the league as a whole, measured by t 8; and (iii) The quality of team i relative to the average quality of all league member teams, measured by τi. The first of these factors allows for league membership to comprise teams with differing ‘base’ levels of support. These could be due to differences in the population sizes of the teams’ home cities or towns, or other historical factors that have led to the emergence of such differences. The second factor allows for each team’s spectator demand to depend on the absolute quantity of the teams across the league as a whole. The third factor allows each team’s spectator demand to depend on its own quality relative to the league average. The specification of the total revenue function is Ri = ηm i ( t − θ t 2 )( τ i − ξτ 2i ) 

[2.3]

The inclusion in [2.3] of τi as a determinant of team i’s revenue captures the notion that supporters prefer a winning team, and are expected to attend home matches in larger numbers when the home team is successful. In the literature, it is standard practice to assume that team i’s win ratio or win percent2 in matches played against team j is determined by the relative quantities of talent hired by the two teams, or wi = ti/(ti + tj). For an n-team league, this assumption leads to a rather complex expression for team i’s win ratio over all of its league matches, which takes the form ∑ [t i /(t i + t j )] /( n − 1) . The inclusion of τi in [2.3], rather than wi, makes the j≠ i revenue function easier to manipulate. For a two-team league τi = 2wi, and the choice between τi and wi is trivial, affecting only the parameterisation of the revenue function. It is important to note that the adoption of the revenue function defined by [2.3] imposes some restrictions on the generality of the model. In particular, the assumption that the parameters η, θ and ξ are identical for all teams, and that market size is the only source of intra-team differences in revenue functions, is restrictive. If a restriction of this kind is not imposed, however, it is extremely difficult to obtain generalisations from the model concerning the effects on competitive inequality of variations in the objectives of team owners, or policy measures like revenue sharing or payroll caps (Fort, 2000; Fort and Quirk, 2004).

A model of an n-team league

21

Team i’s marginal revenue is defined as the effect on total revenue of a change in ti. A general expression for team i’s marginal revenue is obtained by partially differentiating [2.3] with respect to ti. Team i’s average revenue is the average revenue generated by each unit of talent hired by team i. A general expression for team i’s average revenue is obtained by dividing both sides of [2.3] by ti. MRi = ηm i [(1 − 2θ t )( τ i − ξτ 2i )( ∂ t / ∂t i ) + ( t − θ t 2 )(1 − 2ξτ i )( ∂τ i / ∂t i )]  ARi = ηm i ( t − θ t 2 )( τ i − ξτ 2i ) / t i

[2.4]

For simplicity, it is assumed that each team’s total cost is linear and proportional to the quantity of talent it hires, and that the teams incur no fixed costs. These assumptions produce marginal and average cost functions for the two teams that are constant, and equivalent to the market price for each unit of talent. C i = ct i [2.5] MC i = AC i = c for all i  In most variants of the theoretical model, the equilibrium allocation of talent between the league’s member teams usually depends upon the objective function of the team owners. Below, two alternatives are considered:  profit maximisation and win-percent maximisation subject to a zero-profit constraint. For convenience the latter is usually known simply as win-percent maximisation. With reference to European football, in particular, it has been argued that the latter objective function provides a more accurate characterisation of the reality than profit maximisation (Sloane, 1971; Késenne, 1996, 2007a, 2007b; Vrooman, 2000, 2007; Fort and Quirk, 2004; Dietl, Lang and Werner, 2009); see also Chapter 6, Section 6.7. The n-team closed model

In a closed model, a change in the talent hired by team i has direct implications for the quantities of talent hired by the other teams, because it is assumed that the total quantity of talent is fixed. For convenience and without any loss of generality, the units of measurement of talent can be normalised such that T = 1 and t 8 = 1/n. Equations [2.1] and [2.2] have the following implications:

∑ ( ∂t

j

/ ∂t i ) = −1

∂ t / ∂t i = 0

∂τ i / ∂t i = 1 / t = n / T = n 

[2.6]

j≠ i

Using [2.6], the equations for total revenue, marginal revenue and average revenue [2.3] and [2.4] can be rewritten as functions of mi, ti and τi ( = nti): Ri = ηm i [(1 / n ) − (θ / n2 )]( τ i − ξτ 2i ) MRi = ηm i n[(1 / n ) − (θ / n2 )](1 − 2ξτ i ) ARi = ηm i [(1 / n ) − (θ / n2 )]( τ i − ξτ 2i ) / t i 

[2.7]

The economic theory of professional sports leagues

22

With no external market in playing talent, it is reasonable to assume that the salary per unit of talent is determined endogenously, within the model, by the total level of demand for talent among all of the league’s member teams. The salary per unit of talent adjusts to ensure that each team is able to hire as much talent as it wishes at that salary, and that all of the fixed stock of talent is employed by the league’s member teams. For profit maximisation in the closed model, each team hires talent to the point at which the marginal revenue generated by the last unit of talent equals the marginal cost incurred by hiring the last unit of talent, or MRi = MCi. For win-percent maximisation in the closed model, each team hires talent to the point at which the zero-profit constraint is attained, or ARi = ACi. Each of these conditions gives rise to a system of n linear equations in ti. These equations, together with the adding-up constraint T = ∑ t j = 1, can be used to obtain the solutions for ti and c, j

under both the profit-maximisation assumption and the win-percent-­maximisation assumption. The n-team open model

In an open model in which the teams make their hiring decisions independently, a change in the quantity of the talent hired by one team has no direct implications for the quantities of talent that are hired by all of the other teams, unless the teams adjust their own decisions as to how much talent to hire in response to changes in other teams’ decisions. Equations [2.1] and [2.2] have the following implications:

∑ ( ∂t

j

/ ∂t i ) = 0

∂ t / ∂t i = 1 / n

j≠ i

∂τ i / ∂t i = (1 / t 2 )( t − t i / n ) = ( n2 / T 2 )[( T − t i ) / n] = n∑ t j / T 2 

[2.8]

j≠ i

In an open model, playing talent is purchased from an international market at a price per unit of talent which, for simplicity, is assumed to be determined by the interaction between supply and demand in the international market. The salary per unit of talent is therefore predetermined, or determined exogenously, from the perspective of the teams that purchase talent in this market. The elasticity of the supply of talent with respect to salary is infinite in the open model, and zero in the closed model. The implications of a talent supply function that lies between these two extremes are explored by Cyrenne (2009) and Fort and Winfree (2009). The total quantity of talent held by all of the domestic league’s member teams is variable in an open model with an infinitely elastic supply of talent. When one team acquires more talent, there is no direct impact on the quantities of talent held by the other teams. It is assumed that profit-maximising or win-percent-­maximising team owners take their decisions on how much talent to acquire on the basis of an assumption that other teams will stick with the amounts of talent they currently hold. In other words, each team owner takes his decision on how much talent to

A model of a two-team league

23

hold on the basis of an assumption that other team owners will not react to this decision by adjusting the amounts of talent they hold. This is known as a zero conjectural variations assumption. It gives rise to a type of equilibrium solution known as a Nash equilibrium, at which each team owner hires the quantity of talent that maximises his own objective function, while treating the quantities of talent hired by his team’s rivals as if they were fixed and beyond his control. In the profit-maximisation case, each team hires the quantity of talent that maximises its profit, conditional on the quantities of talent hired by every other team (that maximise their profits) remaining unchanged at their current levels. Since every team maximises its own profit, the quantities of talent hired are mutually consistent. The equilibrium is stable unless, for some reason, one or more of the teams decide to abandon the zero conjectural variations mode of behaviour. The term ‘Nash equilibrium’ is commonly used by economists to refer to a profit-maximisation equilibrium of this kind. However, an analogue of the Nash equilibrium also exists for the win-percent-maximisation model. Each team selects the quantity of talent that maximises its win percent (subject to the zero-profit constraint), conditional on the quantities of talent hired by every other team (that maximise their win percents) remaining unchanged at their current levels. Using [2.8], the equations for total revenue, marginal revenue and average ­revenue [2.3] and [2.4] can be rewritten as functions of mi, T, ti, tj for j≠i, and τi ( = nti/T): Ri

= ηm i [(1 / n )T − (θ / n2 )T 2 ]( τ i − ξτ 2i )

MRi = ηm i {[(1 / n ) − ( 2θ / n2 )T ]( τ i − ξτ 2i ) + n[(1 / n )T − (θ / n2 )T 2 ](1 − 2ξτ i )∑ t j / T} j≠ i

ARi = ηm i [(1 / n )T − (θ / n )T ]( τ i − ξτ ) / t i 2

2

2 i



[2.9]

For profit maximisation each team hires talent to the point at which the marginal revenue generated by the last unit of talent equals the marginal cost incurred by hiring the last unit of talent, or MRi = MCi. This condition gives rise to a system of n non-linear simultaneous equations in ti. The solution to this system of equations is the Nash equilibrium solution to the profit-maximisation model. For winpercent maximisation, each team hires talent to the point at which the zero-profit constraint is attained, or ARi = ACi. This condition also gives rise to a system of n non-linear simultaneous equations in ti, which can be solved to find the analogue of the Nash equilibrium solution for the win-percent-maximisation model. 2.3  A model of a two-team league

The previous section defined the structure of a very general model for an n-team league. For the n-team model, however, the explicit solutions for the amounts of talent hired by the teams are algebraically complex. In the sports economics literature, the standard (almost universal) practice is to present solutions for the

24

The economic theory of professional sports leagues

special case where n = 2. The notion of a two-team league is obviously counterfactual, and may therefore seem unappealing when it is encountered for the first time. However, it turns out that most of the key insights that can be obtained from the two-team model remain applicable, in an appropriately modified form, in the more realistic but less tractable case where n>2. Therefore the use of a theoretical model for a stylised two-team league should be viewed as a convenient simplification, enabling useful results to be obtained that are widely applicable. In the two-team model, team i’s win percent is assumed to be equivalent to the ratio of its own talent to the total quantity of talent hired by both teams, or wi = ti / (t1 + t2). In Section 2.2, the revenue functions [2.3], [2.4], [2.7] and [2.9] are expressed in terms of t ,8 τi, ti and tj (for j≠i). In Section 2.3, it is convenient to reparameterise the revenue functions, so as to obtain expressions in terms of T, wi and wj. In order to do so, note that T = t1 + t2, τi = nti / T = 2ti / T = 2ti / (t1 + t2), and t 8 = T/n = T/2. Accordingly, τi = 2wi, and T = 2t .8 Finally, and without any loss of generality, it is assumed that there is a disparity between the market sizes of teams 1 and 2 in the two-team model, such that m1>m2. Below, team 1 is sometimes referred to as the large-market team, and team 2 as the small-market team. The two-team closed model

In the two-team closed model, T = t1 + t2 = 1 and wi = ti / (t1 + t2) = ti. Using [2.7], the resulting expressions for total revenue, marginal revenue and average revenue are Ri = ψm i ( w i − φw 2i ) MRi = ψm i (1 − 2φw i ) ARi = ψm i (1 − φw i ) 

[2.10]

where ψ = 2η[(1/n) − (θ/n2)] and φ = 2ξ. For a team owner’s objective of profit maximisation, the solutions to the model, obtained by solving the equations MR1 = MC, MR2 = MC and t1 + t2 = 1 for t1, t2 and c, are m1 − m 2 + 2φm 2 ; 2φ(m1 + m 2 ) ψm1m 2 (2 − 2φ ) ; cπ = m1 + m 2  t1π =

m 2 − m1 + 2φm1 2φ(m1 + m 2 ) π t1 m1 − m 2 + 2φm 2 = t 2π m 2 − m1 + 2φm1 t 2π =

[2.11]

For a team owner’s objective of win-percent maximisation, the solutions, obtained by solving the equations AR1 = AC, AR2 = AC and t1 + t2 = 1 for t1, t2 and c, are m1 − m 2 + φm 2 ; φ(m1 + m 2 ) ψm1m 2 (2 − φ ) ; cw = m1 + m 2

t1w =

m 2 − m1 + φm1 φ(m1 + m 2 ) t1w m1 − m 2 + φm 2 = t 2w m 2 − m1 + φm1  t 2w =

[2.12]

A model of a two-team league

25

c

•

cw cπ

AR1

• AR2

MR2 t1 = 0, t2 = 1

MR1 t1π

w

t1

t1 = 1, t2 = 0

Figure 2.1  Profit-maximisation and win-percent-maximisation equilibria: two-team closed model

If the team owner’s objective is win-percent maximisation, the equilibrium salary per unit of talent is higher than it is if the owner’s objective is profit maximisation (cw > cπ); and competitive inequality is higher than it is if the owner’s objective is profit maximisation (tw1 /tw2 > tπ1/tπ2). Figure 2.1 compares the profit-maximisation and win-percent-maximisation equilibria in the two-team closed model. The downward-sloping MR1 shows team 1’s marginal revenue as a function of t1 represented on the horizontal axis. MR2 shows team 2’s marginal revenue. Since t1 = 1 – t2, MR2 plotted against t1 is the inverse of the same function plotted against t2, and is therefore upward-sloping. The profit-maximisation equilibrium is located at the intersection of MR1 and MR2. Team 1 hires t1π units of talent, and team 2 hires t2π = 1 – t1π, where t1π > 0.5 and t2π < 0.5. Similarly, the win-maximisation equilibrium {t1w,t2w} is located at the intersection of the downward-sloping AR1 and upward-sloping AR2 functions. In an extension of the profit-maximisation version of the closed model, Hoehn and Szymanski (1999) investigate the implications for competitive balance in the domestic league of involvement of large-market teams in European competition. While team 2’s revenue depends only on its win percent against team 1 in domestic competition, team 1’s total revenues are obtained from both domestic and European competition. In the latter, team 1 competes against a European team with a similar (large) home-town population. Team 1’s involvement in European competition provides an incentive to invest more heavily in talent than it would if it were not involved, in order to achieve a reasonable win percent in Europe and maximise profits from both competitions. The effect is to make competition more unequal in the domestic league. The higher the proportion of team 1’s total

26

The economic theory of professional sports leagues c

c

MC

t2π t1π

AC AR1( t2w )

MR1( t2π ) MR2( t1π ) t1, t2

AR2( t1w ) t2w

t1w

t1, t2

Figure 2.2  Profit-maximisation and win-percent-maximisation equilibria: two-team open model

r­ evenue that is derived from Europe, the greater is the degree of domestic competitive inequality. The two-team open model

In the two-team open model, T = t1 + t2 and wi = ti/(t1 + t2) = τi/2. Using [2.9], a simplified expression for total revenue is Ri = ηm i (T − γT 2 )(w i − φw 2i ) 

[2.13]

where γ = θ/2 and φ = 2ξ (as before). Partially differentiating Ri with respect to ti yields MRi = ηm i [(1 − 2 γT )( w i − φw 2i )( ∂T / ∂t i ) + ( T − γT 2 )(1 − 2φw i )( ∂w i / ∂t i ) 

[2.14]

Note that ∂T/∂ti = 1 and ∂wi/∂ti = tj/(t1 + t2)2 = wj / (t1 + t2) = wj / T. Substituting these results into [2.14] yields MRi = ηm i [(1 − 2γT)(w i − φw 2i )+(1 − γT)(1 − 2φw i )w j ] 

[2.15]

Using [2.13], team i’s average revenue is ARi = ηm i (T − γT 2 )(w i − φw 2i )/t i 

[2.16]

For a team owner’s objective of profit maximisation, the solutions to the model, obtained by solving the equations MR1 = MC, MR2 = MC for t1 and t2, are algebraically complex, but simply represented diagrammatically. The left-hand diagram in Figure 2.2 shows team 1’s marginal revenue function, drawn conditional on team 2 hiring tπ2 units of talent, intersecting with the (exogenously determined) horizontal marginal cost function at tπ1; and likewise, team 2’s marginal revenue function, drawn conditional on team 1 hiring tπ1 units of talent, intersecting with the horizontal marginal cost function at tπ2. For a team owner’s objective of winpercent maximisation, the solutions, obtained by solving the equations AR1 = AC and AR2 = AC for t1 and t2, are also algebraically complex. The solution is illustrated in the right-hand diagram of Figure 2.2, which has a construction similar to the left-hand diagram.

Revenue sharing

27

2.4  Revenue sharing

In this section, the theoretical model developed above is used to examine the impact of revenue sharing on competitive inequality in the two-team model. Would the redistribution of some of the revenues of the league’s stronger member teams to their weaker counterparts help to reduce competitive inequality, perhaps making the league a more exciting and watchable proposition for spectators? Or would redistribution actually make no difference to competitive inequality? Or might redistribution, as some economists have argued, even have perverse effects of increasing, rather than reducing, competitive inequality? The findings of the previous theoretical literature on this question are mixed. According to the benchmark analyses of Quirk and El Hodiri (1974) and Fort and Quirk (1995), based on a closed model with a team owner’s objective of profit maximisation, revenue sharing does not influence competitive balance, but it does tend to depress players’ salaries. If the team owner’s objective is win-percent maximisation, however, or if team owners optimise using a utility function containing arguments other than profits, then revenue sharing might assist in reducing competitive inequality (Atkinson, Stanley and Tschirhart, 1988; Késenne, 1996, 2000, 2007b, 2009; Rascher, 1997). In an analysis based on an open model, Szymanski and Késenne (2004) suggest that a revenue-sharing arrangement might have the perverse and counterintuitive effect of increasing competitive inequality. We examine this proposition in detail below. Dietl and Lang (2008) draw a similar conclusion; see also Dietl, Franck and Lang (2008), Dietl, Lang and Werner (2009) and Grossman, Dietl and Lang (2010). Easton and Rockerbie (2005) examine the conditions for a revenue-sharing arrangement to achieve majority support among the league’s member teams. The teams’ willingness to support such a measure depends upon the nature of conjectures about the responses of competitors to any team’s decision to acquire more talent. Let NRi denote the net revenue of team i after redistribution of revenues under a revenue-sharing arrangement, represented by the parameter 0 ≤ α ≤ 1. α = 1 represents no revenue sharing, and α = 0 represents equal revenue sharing, such that each team receives one-half of the total revenue. The expressions for NRi are NRi = αRi + [(1 − α )/2](R i + R j ) = [(1 + α )/2]R i + [(1 − α )/2]R j 

[2.17]

In the profit-maximisation model, the case in which there is equal revenue sharing (α = 0) can be interpreted as equivalent to the case in which quantities of talent are assigned to the two teams in a manner that maximises their joint profits. Since each team has the same net revenue function when α = 0, maximisation of this net revenue function is equivalent to joint profit maximisation. Revenue sharing in the closed model

As before, if the team owners pursue an objective of profit maximisation, each team hires talent to the point at which MNRi = MC, where MNRi denotes team i’s marginal net revenue.

28

The economic theory of professional sports leagues c MR1(α=1)

MR1(α=.5)

MR2(α=1)

MR1(α=0)

MR2(α=.5)

π

c (α = 1)

• MR2(α=0)

π

c (α = .5)

•

c π ( α = 0) t1=0, t2=1

•π t1

t1=1, t2=0

Figure 2.3  Revenue sharing in a closed model: profit maximisation

Using t2 = 1 – t1 in the closed model, note that ∂Rj/∂ti = −∂Rj/∂tj and ∂R1/∂t2 = −∂R1/∂t1. Using [2.10] and [2.17], the expressions for MNRi are MNR1 = ∂NR1 / ∂t1 = ψ{m1 [(1 + α ) / 2](1 − 2φt1 ) − m 2 [(1 − α ) / 2](1 − 2φt 2 )} MNR2 = ∂NR2 / ∂t 2 = ψ{m 2 [(1 + α ) / 2 ](1 − 2φt 2 ) − m1 [(1 − α ) / 2](1 − 2φt1 )}

[2.18]

It is straightforward to show that the solutions for t1 and t2, obtained by solving the equations MNR1 = MC and MNR2 = MC, are the same as in [2.11]. The solution for c, however, differs from [2.11]: αψm1m 2 (2 − 2φ ) [2.19]  cπ = m1 + m 2 Figure 2.3 illustrates the impact of revenue sharing in a closed model with team owners in pursuit of profit maximisation. As the parameter α decreases within the range 0 ≤ α ≤ 1, and the proportion of the home team’s revenue that is shared increases, the marginal net revenue functions of both teams shift downwards by identical amounts. The gain in (net) revenue accruing to either team as a result of hiring an additional unit of talent is reduced by revenue sharing, because part of the gain in (gross) revenue accrues to the other team. Consequently neither the allocation of playing talent between the two teams, nor the level of competitive inequality, is affected by revenue sharing. However, the equilibrium salary per unit of talent is reduced as α decreases; and in the limiting case α = 0, the equilibrium salary falls to zero. Identifying the limiting case α = 0 with joint profit maximisation, the allocation of playing talent is shown to be the same if the team owners maximise their

Revenue sharing c

AR1(α=0)

AR2(α=0)

29

AR2(α=.5)

AR1(α=.5) AR1(α=1) AR2(α=1)

t1=0, t2=1

t1w = .5 t1w t1w (α=0) (α=.5) (α=1)

t1=1, t2=0

Figure 2.4  Revenue sharing in a closed model: win-percent maximisation

profits either individually or jointly (collectively). This result is an application of the Coasian invariance proposition. However, individual action on the part of the team owners affords the players bargaining power in their salary negotiations, enabling them to achieve a salary equivalent to the teams’ marginal revenues. Collective action on the part of the team owners eliminates the players’ bargaining power, forcing the equilibrium salary down to zero. If the team owners pursue an objective of win-percent maximisation, each team hires talent to the point at which ANRi = AC, where ANRi denotes team i’s average net revenue, obtained by dividing [2.17] by ti. In this case the solutions for t1 and t2 are algebraically complex. The sensitivity of competitive balance to variation in the revenue-sharing parameter is explored in Figure 2.4. As α decreases from α = 1 towards α = 0, and the proportion of revenues that are shared increases, in the vicinity of the solution the large-market team’s average net revenue function shifts downwards, and the small-market team’s average net revenue function shifts upwards. Consequently, there is a decrease in competitive inequality. For equal revenue sharing with α = 0, the two teams’ net average revenue functions are identical, and the solution is located at tw1 = tw2 = 0.5, with perfect competitive equality. Revenue sharing in the open model

To establish the solution to the open model in the case of profit maximisation, it is necessary to identify the marginal net revenue functions, by taking the partial derivatives of each of R1 and R2 in [2.13] with respect to t1 and t2.

30

The economic theory of professional sports leagues

∂R1 / ∂t1 = ηm1 [(1 − 2 γT )( w1 − φw12 ) + (1 − γT )(1 − 2φw1 )w 2 ] ∂R2 / ∂t1 = ηm 2 [(1 − 2 γT )( w 2 − φw 22 ) − (1 − γT )(1 − 2φw 2 )w1 ] ∂R1 / ∂t 2 = ηm1 [(1 − 2 γT )( w1 − φw12 ) − (1 − γT )(1 − 2φw1 )w 2 ] ∂R2 / ∂t 2 = ηm 2 [(1 − 2 γT )( w 2 − φw 22 ) + (1 − γT )(1 − 2φw 2 )w1 ] 

[2.20]

The expressions for MNRi are MNR1 = [(1 + α ) / 2]( ∂R1 / ∂t1 ) + [(1 − α ) / 2 ]( ∂R2 / ∂t1 ) MNR2 = [(1 + α ) / 2]( ∂R2 / ∂t 2 ) + [(1 − α ) / 2 ]( ∂R1 / ∂t 2 ) 

[2.21]

The solutions for t1 and t2 are obtained by solving the simultaneous equations MNR1 = MC and MNR2 = MC. A relatively simple measure of competitive inequality is obtained by substituting [2.20] into [2.21], and using the condition MNR1 = MNR2 at the profit-maximising-equilibrium, yielding m1 (1 − 2 γT )( w1 − φw12 ) + m1 (1 − γT )(1 − 2φw1 )w 2 = m 2 (1 − 2 γT )( w 2 − φw 22 ) + m 2 (1 − γT )(1 − 2φw 2 )w1 Rearranging  1 − 2 γT   ( m1 / m 2 )( w1 − φw12 ) − ( w 2 − φw 22 )  (1 − 2φw 2 )w1 m1 = + α  (1 − 2φw1 )w 2  1 − γT   (1 − 2φw1 )w 2 m 2

[2.22]

The left-hand side of [2.22] can be interpreted as a measure of competitive inequality. Note that as w1 increases and w2 decreases, both terms in the numerator of the left-hand side increase, and both terms in the denominator decrease. Unambiguously, therefore, the left-hand side increases (decreases) as competitive inequality increases (decreases). On the right-hand side of [2.22], (1 – 2γT)/ (1 – γT)>0, and (m1/m2)(w1 – φ w21) – (w2 – φ w22) > 0. All terms on the right-hand side are positive. Competitive inequality is therefore increasing in the revenue-sharing parameter α. Competition is more equal with equal revenue sharing (α = 0) than it is with no revenue sharing (α = 1). As α decreases within the range 0 ≤ α ≤ 1, the right-hand side of [2.22] decreases, and competitive inequality decreases. The equilibrium conditions for win-percent maximisation are ANR1 = AC and ANR2 = AC, where ANRi = [(1 + α ) / 2 ]Ri /t i + [(1 − α ) / 2 ]R j / t i 

[2.23]

As before, the solutions for t1 and t2 are algebraically complex. Again, however, it is possible to derive a relatively simple measure of competitive inequality using the condition ANR1 = ANR2 at the win-percent maximisation equilibrium, yielding w1 (1 + α )( m1 / m 2 )( w1 − φw12 ) + (1 − α )( w 2 − φw 22 )  = w12 ) + (1 + α )( w 2 − φw 22 ) w 2 (1 − α )( m1 / m 2 )( w1 − φw

[2.24]

Revenue sharing

31

t2 α=0

•

•

BR1

t π2

profit maximisation

t 2w

J •

α=0.5 win-percent maximisation

N • α=1

•

α=0.5

• α=1 BR2

α=0 t1π

t1w

t1

Figure 2.5  Nash equilibrium and joint profit-maximisation equilibrium: profit-maximisation model

Note that for α = 1 (no revenue sharing), w1/w2 = (m1/m2)(w1 − φw21)/(w2 − φw22) > 1; and for α = 0 (equal revenue sharing), w1/w2 = 1. As in the case of profit maximisation, competition is more equal with equal revenue sharing (α = 0) than it is with no revenue sharing (α = 1). With equal revenue sharing, both teams have the same net revenue function, and both take the same decision concerning the quantities of talent they hire. Accordingly w1 = w2, and there is perfect competitive equality. Figure 2.5 tracks the progression from the Nash equilibrium to the joint profitmaximisation equilibrium in the profit-maximisation model. The quantities of talent hired by the two teams, t1 and t2, are represented on the horizontal and vertical axes. For the case of no revenue sharing (α = 1), BR1 and BR2 are the best-response functions of teams 1 and 2. BR1 is read clockwise from the vertical to the horizontal axis, and shows, for each possible value of t2, the profit-maximising value of t1. Similarly BR2 is read anticlockwise from the horizontal to the vertical axis, and shows, for each possible value of t1, the profit-maximising value of t2. The profit-maximising solution for both teams under the zero conjectural variations assumption is (tπ1,tπ2), represented by point N and located at the intersection of BR1 and BR2. If a revenue-sharing arrangement is introduced, the best-response functions shift towards the bottom-left-hand corner of Figure 2.5, and also tend to tilt. The shifts from α = 0 through α = 0.5 to α = 1 are such that the points of intersection also move towards the bottom-left-hand corner but, in accordance with the interpretation of [2.22], in a manner that implies a reduction in competitive inequality (represented by the rays from the origin to the intersection of the best-response functions becoming steeper). The joint profit-maximisation equilibrium, at which α = 0, is represented by point J. Figure 2.5 also tracks the progression between the

32

The economic theory of professional sports leagues

counterparts of these two equilibria in the win-percent maximisation model, over variations in the revenue-sharing parameter from α = 0 through α = 0.5 to α = 1. The Szymanski-Késenne revenue-sharing analysis

The finding that revenue sharing reduces competitive inequality in the profitmaximisation version of the open model is contrary to an analysis presented by Szymanski and Késenne (2004), henceforth SK, who draw the opposite conclusion. SK find that competitive inequality is higher in the case of equal revenue sharing (α = 0) than it is in the case of no revenue sharing (α = 1). In other words, and perhaps counterintuitively, the introduction of a revenue-sharing arrangement increases competitive inequality. SK explain this result through a tendency for revenue sharing to offset the negative external effect of team strengthening by either team on the other team’s revenue. The negative external effect of team strengthening by team 2 on team 1’s revenue is larger than the negative external effect in the reverse direction. When these effects are partially neutralised by revenue sharing, the reduction in team 2’s marginal revenue is larger than the reduction in team 1’s marginal revenue. Accordingly, the solution shifts in the direction of greater competitive inequality. A key component of the SK analysis is an assumption that revenue depends upon win percent, but not upon the quantities of talent hired by either or both teams in absolute terms. SK use a revenue function that is similar to [2.10]. Within the framework that is developed in this chapter, [2.10] is appropriate for use in a closed model, where the total quantity of talent hired by the two teams combined is assumed fixed, and is therefore omitted from the revenue function. In an open model, however, the assumption that revenue depends upon win percent only seems counterintuitive or counterfactual. Subsequently Cyrenne (2009) and Feess and Stahler (2009) develop models in which team revenues depend upon both win percent and the absolute quantities of talent. Both interpret the SK analysis as a special case, applicable only when a restricted formulation of the revenue function is adopted. If a revenue function similar to [2.10] is used in an open model, an implication is that if the quantities of talent (expressed in absolute terms) are reduced towards zero, but in a manner such that the ratio of the quantities of talent hired by the two teams is maintained at a constant value, then revenue is unaffected. This would imply that a fixture in English football’s Premier League for which the team managers (hypothetically) selected teams comprising park footballers would command the same market value as the same fixture starring talented international superstars. This seems a highly dubious proposition.3 Clearly, both absolute and relative talent are determinants of spectators’ utility, and the revenue function in an open model should include both. As has been shown in this section, when the revenue function is specified accordingly, revenue sharing always reduces competitive inequality. The negative external effect of team

Restraints on expenditure on players’ salaries

33

strengthening by either team on the other team’s revenue through the change in win percent is offset by a positive external effect emanating from the increase in the combined quantity of talent hired by both teams. When the net (overall) external effect is partially neutralised by revenue sharing, the reduction in team 2’s marginal revenue is always smaller than the reduction in team 1’s marginal revenue. Consequently the solution shifts in the direction of greater competitive equality. 2.5  Restraints on expenditure on players’ salaries

This section examines the impact on competitive inequality of three forms of restraint on expenditure on players’ salaries: first, a tax on expenditure on salaries above a specific threshold, known as a luxury tax; second, a limit on the total amount each team is permitted to spend on salaries as a proportion of the revenue of the average team, known as a payroll cap; and third, a limit on the ratio of each team’s expenditure to its own revenue, known as the G14 payroll cap. In each case, the implications for competitive inequality in the two-team closed and open models are developed, for the case of profit maximisation. Summary results are also provided for the case of win-percent maximisation, but for reasons of space the full analysis is not presented. Luxury tax: a tax on salary expenditure over a set threshold

The luxury tax is a relatively recent innovation in North American major league sports, whereby the league taxes any team’s expenditures on players’ salaries in excess of a specific tax threshold (Gustafson, 2006). The luxury tax is a more flexible mechanism for restraining salary expenditure than the payroll cap (see below), which imposes an absolute limit on salary expenditure. Gustafson and Hadley (1996) and Marburger (1997) analyse the impact of the luxury tax on salary and competitive inequality; and Van de Burg and Prinz (2005) examine a variant in which a progressive tax rate is applied. Let θ denote the threshold for salary expenditure above which the luxury tax is payable, and let τ denote the rate at which tax is levied on expenditure above θ. Let {t1π , t 2π } denote the solution when there is no luxury tax, obtained by solving MR1 = c and MR2 = c. Suppose initially the tax threshold is set at a level that makes only team 1 (the large-market team) liable to pay the tax, so that ct1π > θ . In this case, team 1’s marginal cost function increases from c to c + τ. Let {t1π , t2π } denote the solution when team 1 is liable to pay the tax but team 2 (the small-market team) is not liable, obtained by solving MR1 = c + τ and MR2 = c. Then suppose instead the tax threshold is set at a level that also makes team 2 liable to pay the tax, so that ct2π > θ . In this case, team 2’s marginal cost function also increases to c + τ. If team 1 and team 2 are both liable to pay the tax, the solution, denoted {t1π , t2π } , is obtained by solving MR1 = c + τ and MR2 = c + τ.

34

The economic theory of professional sports leagues c

~c π+ τ

cπ = c π + τ ~c π

•

•

cπ

MR2 MR1

θb cπ

θa ~c π

~t π 1

t1π = t1π

t1

Figure 2.6  Luxury tax: closed model

Figure 2.6 illustrates the analysis for the closed model, in which c is determined endogenously and t2 = 1 – t1. When there is no luxury tax, the solution is {tπ1, cπ}, located at the point where MR1 = MR2 = cπ. If the luxury tax threshold is θa, this solution is invalid because cπtπ1 > θa. The solution switches to {t1π , c π } , such that MR1 = c π + τ and MR2 = c π . At {t1π , c π }, c π t2π = c π (1 − t1π ) < θa If only the large-­ market team is liable to pay the luxury tax, therefore, competitive inequality is reduced and the equilibrium salary per unit of talent is reduced. If a lower tax threshold of θb is set, this solution becomes invalid, because c π t2π > θb . The solution switches to { t1π , c π } , such that MR1 = MR2 = c π + τ . Note that t1π = t1π , but c π < c π . If both teams are liable to pay the luxury tax, therefore, competitive inequality is the same as it is when there is no luxury tax, but the equilibrium salary per unit of talent is reduced by an amount equivalent to the marginal tax rate. Figure 2.7 illustrates the analysis for the open model, in which c is exogenous and there are no constraints on the values of t1 and t2. The solution when there is no luxury tax, {tπ1, tπ2}, is located at the intersection of BR1(c) and BR2(c). If the luxury tax threshold is θa, this solution is invalid because ctπ1 > θa. The solution switches to {t1π , t2π } , located at the intersection of BR1(c + τ) and BR2(c). At {t1π , t2π } , ct2π < θa . If only the large-market team is liable to pay the luxury tax, therefore, competitive inequality is reduced, indicated by the steeper slope of the ray at {t1π , t2π } . If a lower tax threshold of θb is set, however, this solution is also invalid because ct2π > θb . The solution switches to { t1π , t2π }, located at the intersection of BR1(c + τ) and BR2(c + τ). { t1π , t2π } is located on the same ray from the origin as {tπ1, tπ2}. If both teams are liable to pay the luxury tax, therefore, competitive inequality is the same as it is when there is no luxury tax.

Restraints on expenditure on players’ salaries

35

t2

θa/c

π π {~t , ~t2 }

•1

•

π π

{t1, t 2 }

θb/c

{t1π, t π2}

•

BR2(c) BR2(c+τ) BR1(c) BR1(c+τ)

θb/c

θa/c

t1

Figure 2.7  Luxury tax: open model

In both the closed and the open model, the luxury tax reduces competitive inequality in the case where the large-market team is taxed while the small-market team is untaxed, but the luxury tax has no effect on competitive inequality in the case where both teams are taxed. The solution when the team owners’ objective is win-percent maximisation (not illustrated in Figures 2.6 and 2.7) is established in a similar manner. In the case where team 1 is taxed but team 2 is not taxed, the solutions for t1 and t2 are obtained by solving AR1 = {θ + (c + τ)}(t1 – θ/c)}/t1 and AR2 = c. Competitive inequality is less than it is when there is no luxury tax. In the case where both teams are taxed, the solutions for t1 and t2 are obtained by solving AR1 = {θ + (c + τ)}(t1 – θ/c)}/ t1 and AR2 = {θ + (c + τ)}(t2 – θ/c)}/t2. Competitive inequality is the same as it is when there is no luxury tax. Payroll cap: a limit on each team’s total salary expenditure as a percentage of the average team’s revenue

The implications of a payroll cap for competitive inequality and player salaries are examined by Quirk and Fort (1992), Staudohar (1999) and Késenne (2000, 2007b). Recently, Dietl et al. (2008) and Dietl, Lang and Rathke (2009) have examined the social welfare effects of payroll or salary caps. Let φ denote the proportion of the average team’s revenue that defines the upper limit for each team’s salary expenditure. As before, let {tπ1, tπ2} denote the solution when there is no payroll cap, obtained by solving MR1 = c and MR2 = c. Suppose initially the payroll cap is set at a level that imposes a constraint on team 1 only, so that ctπ1 > φ(Rπ1 + Rπ2)/2, where {Rπ1, Rπ2} are the revenues associated with the unconstrained solutions {tπ1, tπ2} (with other revenue expressions similarly defined). {t1π , t2π } , the solution when team 1’s salary expenditure is constrained but team 2 is

36

The economic theory of professional sports leagues c

~ ~ ct 2 = φ a (R 1π + R π2 ) / 2

~ ~ ct1 = φ a (R 1π + R π2 ) / 2

ct 2 = φ b (R 1π + R π2 ) / 2

ct1 = φ b (R 1π + R π2 ) / 2

MR2

cπ ~c π cπ

•

•

• t1π = 0.5 ~t1π

MR1

t1π

t1

Figure 2.8  Payroll cap: closed model

unconstrained, is obtained by solving φ(R1 + R2)/(2t1) = c and MR2 = c. Suppose instead the payroll cap is set at a level that also imposes a constraint on team 2’s  1π + R  2π ) / 2 . If team 1 and team 2 are both salary expenditure, so that ct 2π > φ( R constrained, the solutions for t1 and t2, denoted {t18 , t28 }, are obtained by solving φ(R1 + R2)/(2t1) = c and φ(R1 + R2)/(2t2) = c. Figure 2.8 illustrates the analysis for the closed model. When there is no payroll cap, the solution is {tπ1, cπ}, located at the point where MR1 = MR2 = cπ. If the payroll cap is φa, this solution is invalid because cπtπ1 > φa(Rπ1 + Rπ2)/2. The solution  1π + R  2π ) /( 2t1π ) = c π and MR2 = c π . At switches to {t1π , c π } , such that φa ( R π π π π π π {t1 , c }, c t2 = c (1 − t1 ) < θa . If only the large-market team is capped, therefore, competitive inequality is reduced and the equilibrium salary per unit of talent is reduced. If a lower payroll cap of φb is set, however, this solution is also invalid π +R  π ) / 2 . The solution switches to { t1π , c π } , such that because c π t2π > φb ( R 2 1 π π π φb( R1 + R2 ) /( 2 t1 ) = c π and φb( R1π + R2π ) /( 2 t2π ) = c π . Since t2π = 1 − t1π , the solution is t1π = t2π = 0.5 . If both teams are capped, therefore, competitive inequality is eliminated altogether and there is perfect competitive balance. Figure 2.9 illustrates the analysis for the open model. The solution when there is no payroll cap, {tπ1, tπ2}, is located at the intersection of BR1 and BR2. If the payroll cap is φa, this solution is invalid because ctπ1 > φa(Rπ1 + Rπ2)/2. Team 1 must reduce its salary expenditure by hiring less talent. Team 2, which is unconstrained, reacts by increasing its quantity of talent hired. There is a leftward shift along BR2, towards  1π + R  2π ) / 2 . If only the large-market team the solution {t1π , t2π } , at which ct1π = φa( R is capped, therefore, competitive inequality is reduced, indicated by the steeper slope of the ray at {t1π , t2π } . If a lower payroll cap of φb is set, however, this solution  1π + R  2π ) / 2 . The solution switches to { t1 , t2 } , becomes invalid because ct2π > φb( R

Restraints on expenditure on players’ salaries

t2

37

~ ~ φ a (R 1π + R π2 ) /( 2c) φ b (R 1π + R π2 ) /( 2c) ~ ~ φ a (R 1π + R π2 ) /( 2c) φ b (R 1π + R π2 ) /( 2c)

φ a (R 1π + R π2 ) /( 2c) ~ ~ φ a (R 1π + R π2 ) /( 2c) {~t1π , ~t2π}

•

{t1π , t π2}

~ ~ φ b (R 1π + R π2 ) /( 2c)

• {t1π , t π2}

φ b (R 1π + R π2 ) /( 2c)

• BR1

BR2 t1

Figure 2.9  Payroll cap: open model

such that φb( R1π + R2π ) /( 2 t1π ) = c and φb( R1π + R2π ) /( 2 t2π ) = c . This implies t1π = t2π . As in the closed model, if both teams are capped, competitive inequality is eliminated altogether and there is perfect competitive balance. In both the closed model and the open model, the payroll cap reduces competitive inequality in the case where the large-market team is capped while the smallmarket team is uncapped, and eliminates competitive inequality altogether in the case where both teams are capped. The solution when the team owners’ objective is win-percent maximisation is established in a similar manner. If team 1’s salary expenditure is constrained while team 2 is unconstrained, competitive inequality is reduced in comparison with the case of no payroll cap. If both teams’ salary expenditures are constrained, competitive inequality is eliminated altogether, and the solution is the same as in the profit-maximisation model. Vrooman (1995) dissents from the proposition that payroll caps are helpful in reducing competitive inequality, interpreting most capping arrangements as a collusive attempt to control costs, rather than to redistribute playing talent among the league’s member teams. According to the invariance proposition, the allocation of playing talent that maximises total league profits is unaffected by any restrictions on salary expenditure. If such restrictions are imposed, profit-maximising team owners are expected to invent mechanisms to circumvent them and restore the optimal allocation of playing talent for profit maximisation. Such mechanisms might include player loan arrangements, whereby the team borrowing the player pays part of the loanee’s salary, enabling the parent team to retain the property rights in the player’s services while maintaining its salary expenditure within the limit imposed by the cap (Vrooman, 1995; Marburger, 2006).

38

The economic theory of professional sports leagues c AR1 MR1

AR2 MR2

cπ ~c π

•

ρaAR 2

•

cπ

ρaAR1

• ~π t1π t1

t1π = t1w

ρ bAR 2 ρ bAR1 t1

Figure 2.10  G14 payroll cap: closed model

G14 payroll cap: constraint on the ratio of each team’s salary expenditure to its own revenue

The G14 was a lobby group comprising leading football clubs from seven European countries, to provide a unified voice in negotiations with the sport’s international governing bodies. Originally formed in 2000 by fourteen clubs, the membership of the G14 was increased to eighteen clubs in 2002, but the original name was retained. In 2002 the G14 announced a voluntary agreement that its members would adhere to a limit on salary expenditure of 70 per cent of each club’s revenue, to take effect from the 2006 season. The G14 disbanded in 2008. Késenne (2003, 2007b) examines the implications of the G14 payroll cap for salaries and competitive inequality, and Dietl, Franck and Nuesch (2006) investigate the conditions under which a voluntary cap is self-enforcing. Let ρ denote the proportion of each team’s revenue that defines the upper limit for its own salary expenditure under the G14 payroll cap. As before, let {tπ1, tπ2} denote the solution when there is no G14 payroll cap, obtained by solving MR1 = c and MR2 = c. At {tπ1, tπ2}, team 2 (the small-market team) has a higher ratio of salary expenditure to total revenue than team 1 (the large-market team). Suppose initially the G14 payroll cap is set at a level that imposes a constraint on team 2 only, so that ctπ2 > ρRπ2. Let {t1π , t2π } denote the solution when team 2’s salary expenditure is capped but team 1 is uncapped, obtained by solving MR1 = c and ρR2/t2 = c. Suppose instead the G14 payroll cap is set at a level that also imposes  1π . If team 1 and team 2 are both capped, a constraint on team 1, so that ct1π > ρR the solutions for t1 and t2, denoted { t1 , t 2} , are obtained by solving ρR1/t1 = c and ρR2/t2 = c. Figure 2.10 illustrates the analysis for the closed model. When there is no G14 payroll cap, the solution is {tπ1, cπ}, located at the point where MR1 = MR2 = cπ. If the G14

Restraints on expenditure on players’ salaries

t2

ρ bR1π / c

ρaR 1π / c

{t1π, t π2}

•

ρaR π2 / c ~ ρaR π2 / c

• {~t π1 , ~t 2π}

BR2

ρ bR π2 / c

•

{t1π, t π2}

39

BR1 t1

Figure 2.11  G14 payroll cap: open model

payroll cap parameter is ρa, this solution is invalid because cπtπ2 > ρRπ2. The solution  1π or switches to {t1π , c π } , such that MR1 = c π and ρa AR2 = c π . At {t1π ,c π }, c π t1π < ρa R π c < AR1 . If only the small-market team is capped, therefore, competitive inequality is increased and the equilibrium salary per unit of talent is reduced. If a lower G14 pay 1π . roll cap parameter of ρb is set, however, this solution is invalid because c π t1π > ρ b R The solution switches to { t1π , t2π } , which satisfies the constraints ρb R1π / t1π = c π and ρb R2π / t2π = c π . If both teams are capped, therefore, competitive inequality is further increased, and the equilibrium salary per unit of talent is further reduced. At { t1π , t2π } , it can be shown that the level of competitive inequality is the same as it is when the team owners’ objective is win-percent maximisation and there is no cap. Figure 2.11 illustrates the analysis for the open model. The solution when there is no G14 payroll cap, {tπ1, tπ2}, is located at the intersection of BR1 and BR2. If the G14 payroll cap parameter is ρa, this solution is invalid because ctπ2 > ρaRπ2. Team 2 must reduce its salary expenditure by hiring less talent. Team 1, which is unconstrained, reacts by hiring more talent. There is a rightward shift along BR1, towards  2π . If only the small-market team is capped, the solution {t1π , t2π } , at which ct2π = ρa R therefore, competitive inequality is increased, indicated by the shallower slope of the ray at {t1π , t2π } . If a lower G14 payroll cap parameter of ρb is set, however, this  1π . The solution { t1π , t2π } satisfies the consolution is also invalid because ct1π > ρb R π π π π straints ρb R1 / t1 = c and ρb R2 / t2 = c . If both teams are capped, therefore, competitive inequality is further increased, indicated by the shallower slope of the ray at { t1π , t2π } . As in the closed model, if both teams are capped, the level of competitive inequality is the same as it is when the team owners’ objective is win-­percent maximisation and there is no cap. In both the closed model and the open model, therefore, the G14 payroll cap succeeds in its stated objective of reducing team owners’ total salary expenditure, but does so at the expense of an increase in competitive inequality. When both

40

The economic theory of professional sports leagues

teams’ salary expenditures are constrained, competitive inequality with a team owners’ objective of profit maximisation is the same as it is when there are no restraints on salary expenditure and the team owners’ objective is win-percent maximisation. When the team owners’ objective is win-percent maximisation, there is a range of values for ρ such that team 2’s salary expenditure is constrained while team 1 is unconstrained. Within this range, competitive inequality is higher than it is when there is no cap. There is a (lower) range of values for ρ such that both teams’ salary expenditures are constrained. Competitive inequality is the same as it is as when there is no cap. Conclusion

The notion that market mechanisms can be relied upon to maintain a reasonable degree of competitive equality among the member teams of a sports league, without the need for intervention by the sports governing body to redistribute revenue, restrict expenditure on players’ salaries, or constrain players’ employment mobility, has a long tradition in the theoretical sports economics literature. Economists tend to take a sceptical view of the effectiveness of interventions designed to produce outcomes different from those that would be delivered by free markets. Although regulatory intervention may be helpful in lowering players’ salaries, thereby boosting profitability or promoting the survival of smaller-market teams, this does not imply that intervention will always create the incentives required for adjustment in the direction of reduced competitive inequality. Some forms of intervention may even create perverse incentives and tendencies in the opposite direction. Much of the early literature on the economics of team sports leagues was written from a North American perspective, and develops models in which the total stock of playing talent is assumed fixed, so that any reallocation of talent between the league’s member teams is a zero-sum activity. In contrast with North American major league sports, which draw principally on home-grown talent, English and European football operates with a more open labour market. The total stock of playing talent at the disposal of the league’s member teams is variable, and can be increased by hiring from an external market in playing talent. One of the main objectives of this chapter has been to review and consolidate a growing body of literature that examines the adaptation of theoretical models of resource allocation in professional sports leagues originally developed based on closed labour market assumptions, to the open labour market case. Key conclusions that emerge from the analysis of revenue sharing and several forms of payroll cap are as follows. The effect of revenue sharing on competitive inequality is neutral in a closed model. In an open model, in which team revenues depend upon both the absolute and relative qualities of playing talent fielded by the teams, revenue sharing reduces competitive inequality. The effect of a luxury tax or a payroll cap on competitive inequality depends upon how the measure

Restraints on expenditure on players’ salaries

41

is pitched: does it seek to constrain the salary expenditure of all of the league’s member teams, or is it targeted more selectively? A luxury tax which targets only the largest spenders should reduce competitive inequality, but if such a tax is applied indiscriminately its effect on competitive inequality is neutral. A payroll cap which imposes a specific limit on each team’s total salary expenditure should reduce competitive inequality. In contrast, a payroll cap of the kind advocated by the G14, which limits each team’s total salary expenditure to a specific proportion of its own revenue, is likely to increase competitive inequality, by entrenching differences that already exist between the drawing power of the league’s large- and small-market member teams. Notes 1 For the early history, see Quirk and Fort (1992, 1999) and Scully (1995). For recent history, see Coon (2010) for the NBA and Vrooman (2009). This section draws upon all of these sources. 2 For sports in which every match produces a winner and a loser, the terms ‘win ratio’ and ‘win percent’, which have been used interchangeably in the academic literature, refer to the ratio of matches won to matches played. For sports such as football, in which some matches are drawn or tied, an analogue of the win ratio or win percent can be constructed by taking the ratio of total ‘points’ to matches played, where ‘points’ are awarded on a scale of 1 for a win and 0.5 for a draw. 3 If revenues depend upon relative team quality only, the joint profit-maximisation solution (α = 0) is degenerate. By reducing their absolute quantities of talent hired towards zero, the teams always increase their joint profits. Revenues are unaltered as the absolute quantities of talent are reduced, because revenues depend upon relative talent only; but costs decrease because costs are proportional to the absolute quantities of talent. As α is progressively lowered from α = 1 to α = 0, the SK revenue-sharing analysis envisages the teams adjusting from the Nash equilibrium towards the degenerate joint profit-maximising equilibrium, progressively divesting themselves of all of their playing talent.

3

Competitive balance, uncertainty of outcome and home-field advantage

Introduction

The theoretical models of the economics of sports leagues reviewed in Chapter 2 are concerned with the degree of competitive balance or competitive inequality between the member teams of a league competition, which in turn determines the extent of uncertainty of outcome for individual match results and for the destination of the league championship. In Chapter 3, the emphasis shifts away from this theoretical analysis at the level of the league championship, towards the measurement and empirical investigation of competitive inequality and uncertainty of outcome for individual match results in football. The measurement of competitive balance or competitive inequality in a sports league has been the subject of a large number of articles in the academic sports economics literature in recent years. Section 3.1 reviews this literature, with particular emphasis on studies focusing on English or European football. Section 3.2 examines the nature of home-field advantage in professional team sports. Section 3.3 investigates the statistical properties of football match results data, and examines the accuracy with which several variants of the Poisson distribution and the negative binomial distribution are able to describe the distributional properties of match results data presented in scores format. Finally, Section 3.4 presents an empirical investigation of persistence in sequences of consecutive match results. Does a winning streak help build a team’s confidence, making it more likely that further matches will also be won? Or does it lead to complacency, increasing the likelihood that the next match will be drawn or lost? A Monte Carlo simulation exercise is used to address these questions. 3.1  Measuring competitive balance and competitive inequality

In the North American sports economics literature, the measurement of competitive inequality often focuses upon the dispersion in win ratio or win percent between the member teams of a sports league. In sports where every match produces a winner and a loser, and there are no draws or ties, the cross-sectional 42

Measuring competitive balance and competitive inequality

43

dispersion in win ratios over an entire season can be measured using the standard deviation: n

σ=

∑ (w i =1

− 0.5)

2

i

n



[3.1]

In [3.1], wi is team i’s win ratio (number of wins divided by number of matches played), and n is the number of teams. The higher is the value of σ, the greater is the level of competitive inequality. One difficulty with this measure, however, is that n and the number of matches played are not always constant in the same league over time, and are usually not the same for different sports. Accordingly, observed values of σ measured for the same sport over time, or measured for different sports, are not always comparable. To deal with this difficulty, σ can be benchmarked against the standard deviation that would describe dispersion for a league with perfect competitive equality, in which (ignoring home-field advantage) every team has a probability of 0.5 of winning every match (Noll, 1988; Scully, 1989; Quirk and Fort, 1992; Fort and Quirk, 1995). The ideal standard deviation is 0.5/√m, where m is the number of matches played by each team. The relative competitive inequality measure is:  [3.2] Relative σ = σ /( 0.5 / m ) For a league of perfect competitive equality, the relative σ measure should not be significantly different from one. The higher is relative σ, the greater is the level of competitive inequality. This measure is used to measure competitive balance or competitive inequality by Vrooman (1995), Quirk and Fort (1992), Humphreys (2002), Zimbalist (2002) and Schmidt and Berri (2003), among others. Fort (2006) reviews the application of the relative σ measure to win-ratio data for MLB, the NFL, NBA and National Hockey League (NHL). Although the relative σ measure is computationally straightforward and simple to interpret, it has been subject to criticism. Since teams playing at home tend to win more often than they lose, two teams of equal playing strength are not equally likely to win (Trandel and Maxcy, 2009). This introduces an upward bias into the value of the ‘ideal’ standard deviation that is used in the denominator of [3.2], causing the relative σ measure to understate the degree of competitive inequality. Owen (2010) shows that the relative σ measure is more sensitive to changes in the number of teams and the number of matches played than is the unadjusted standard deviation, [3.1]. This may lead to misleading comparisons of competitive inequality across leagues or over time, if the numbers of teams and/or matches played are not constant. By extension, Eckard (1998) examines the effect on competitive inequality in American college football of a range of restrictions on player recruitment, eligibility and compensation that were introduced by the NCAA (National Collegiate

Competitive balance and home-field advantage

44

Athletic Association) in 1952. Pooled cross-section time-series data are used to decompose the overall variance in win ratios into a time component for each team and a cumulative component across teams:

∑ ∑ (w i

i,t

t

− 0.5)2 / nT = ∑ ∑ (w i,t − w i )2 / nT + ∑ (w i − 0.5)2 / n  i

t

i

[3.3]

where wi,t is team i’s win ratio in season t; w i = ∑ w i,t / T ; n is the number of teams; t

and T is the number of seasons. Post-1952, there was a reduction in the first term and an increase in the second term on the right-hand side of [3.3]. This suggests that the regulations made competition more unequal: differences between strong and weak teams became more entrenched, resulting in a reduction in the variation of each team’s performance over time, and an increase in the variation in average performance between teams. Eckard (2001) applies similar methods to MLB data, finding an increase in competitive balance following the introduction of free agency in 1976. Humphreys (2002) uses the competitive balance ratio (CBR) measure to identify trends in competitive inequality over time, taking account of both the timeseries variation in each team’s win ratio calculated over a number of seasons, and the cross-sectional variation in the teams’ win ratios within each season. The standard deviation of team i’s win ratio measured over T seasons is: σ i ,T =

T

T

t =1

t =1

∑ ( w i,t − w i )2 / T , where w i = ∑ w i,t / T

The standard deviation of the win ratios measured over n teams in season t is: n σ n,t = ∑ ( w i,t − 0.5 )2 / n i =1

The CBR is:

N

T

i =1

t =1

CBR = σ T / σ n , where σ T = ∑ σ i,T , σ n = ∑ σ n,t 

[3.4]

An increase in the CBR indicates a reduction in competitive inequality, driven by either an increase in ‘churning’ in the teams’ win ratios from season to season (increase in σT), or a reduction in the dispersion of the teams’ win ratios within each season (decrease in σn). For MLB, Humphreys finds CBR has increased over time. An issue that arises when applying the relative σ measure to football is how to deal with drawn matches (Cain and Haddock, 2006; Fort, 2007). A simple approach is to record a draw as half of a win, and calculate the win ratio on this basis. For English football, Szymanski (2001) reports annual results from 1977 to 1999. Buzzacchi, Szymanski and Valletti (2003) report ten-year averages for the top tier of English football, which show an increase in competitive inequality to the end of the 1980s, followed by a reduction during the 1990s. Bourg (2004) reports

Measuring competitive balance and competitive inequality

45

five-year averages for the ‘Big 5’ European leagues (England, France, Germany, Italy and Spain). Between the 1980s and 2000 there was an increase in competitive inequality in France and Germany, and a reduction in England, Spain and Italy. Kringstad and Gerrard (2007) report ten-year averages for the period 1966–2006. Competitive inequality was lower in the first ten-year period compared to the most recent period in all cases except Italy. Lenten (2008) examines the implications for competitive inequality of the introduction of an unbalanced playing schedule in the Scottish Premier League in the 2001 season. An unbalanced schedule creates biases in the teams’ win ratios, and so has implications for the measurement of competitive inequality. Koning (2000) approaches the measurement of competitive inequality by using a match-level measure of uncertainty of outcome. An ordered probit model is fitted to match results data for the top tier in Dutch football, in order to estimate a team quality coefficient for each team. The cross-sectional standard deviation of these coefficients in each season is interpreted as a measure of competitive inequality. Marques (2002) adopts a similar approach in a study of the trend in competitive inequality in Portuguese football. It appears that this method should produce results very similar to those obtained from an analysis of the trend in the dispersion of win ratios. Goossens (2006) suggests complete predictability might represent a better benchmark for the standardisation of [3.1] than perfect competitive equality. The National Measure of Seasonal Imbalance (NAMSI) takes values between zero and one, with a zero value representing the case where every team achieves a win percentage of 0.5, and a value of one representing the case of complete predictability, when the strongest team wins all of its matches, the second-strongest team wins all of its matches except those against the strongest team, and so on: n

NAMSI =

∑ (w i =1

− 0.5)

2

i

n

∑ (w i =1

− 0.5)  2

i,max

[3.5]

where wi,max is the win ratio achieved by team i when there is complete predictability. Between 1963 and 2005, the NAMSI measure indicates no significant change in competitive inequality for Germany and France, and a small but significant increase for Belgium and England. For several other countries, including Spain, Italy, the Netherlands and Denmark, there is no clear trend. Several alternative measures of dispersion have also been used to measure competitive inequality. Several US studies use the Lorenz curve and Gini coefficient (Fort and Quirk, 1995; Schmidt, 2001; Schmidt and Berri, 2001; Larsen, Fenn and Spenner, 2006). The Lorenz curve shows the variation in the cumulative win ratio of the j most successful teams, as j varies from 1 to n (where n is the total number of teams). Figure 3.1 illustrates. The teams are represented horizontally, from the

46

Competitive balance and home-field advantage

Cumulative win ratio up to team j

A

B C

O

D Teams (j=1,...,n) arranged from highest to lowest win ratio

Figure 3.1  The Lorenz curve and Gini coefficient

most to the least successful (reading from left to right) along the horizontal axis. The vertical axis shows the cumulative win ratio (the sum of the win ratios of all teams from team 1 to team j, as a function of j). If all teams have the same win ratio of 0.5, the Lorenz curve is the 45-degree line OCA. If the distribution of win ratios is skewed, the Lorenz curve is the concave curve OBA. With reference to Figure 3.1, the Gini coefficient is defined as follows: n

area of the crescent between OBA and OCA G= = area of the triangle ODA

j

∑∑w

i

j=1 i=1

n

0.5(n +1)∑ w i 

[3.6]

i=1

The minimum value G = 0 describes the case in which all teams have the same win ratio of 0.5. Since no team can win all of the league’s matches, however, the maximum theoretical value of G = 1 is unattainable. Reporting G in unadjusted form tends to understate the level of competitive inequality (Utt and Fort, 2002). In reporting results for English League football throughout this volume, we refer to football seasons by their end-year. For example, the 2008–2009 season is referred to as the 2009 season. The official nomenclature at the time of writing (during the 2010 season) for the four tiers (divisions) of English football’s Premier League and Football League is ‘Premiership’ (the Premier League) and ‘Championship’, ‘League One’ and ‘League Two’ (the three tiers of the Football League). In the rest of this chapter, and throughout this volume, these four tiers (divisions) are known as T1, T2, T3 and T4 (tiers one to four). Michie and Oughton (2004) plot Lorenz curves for T1 for selected seasons between 1950 and 2004. Goossens (2006) reports Gini coefficients for several

Measuring competitive balance and competitive inequality

47

European leagues for the period 1963–2005. The least unequal were Denmark, Sweden, Germany and Italy, and the most unequal were Portugal, the Netherlands, Greece and Spain. Intermediate cases include France, Belgium and England. The Herfindahl index (HI), defined as the sum of the squared win ratios, can also be used as a measure of competitive inequality: n

HI = ∑ w 2i i =1



[3.7]

An increase in HI signifies an increase in competitive inequality. For England, Michie and Oughton (2004) find the HI for T1 to have remained roughly unchanged between 1947 and the 1980s, and to have risen thereafter. For the period as a whole, the HI increased by around 13 per cent. However, part of the increase was due to a reduction in the number of teams from twenty-two until the 1989 season, to twenty from the 1996 season onwards (with several variations between twenty and twenty-two between the 1990 and 1995 seasons). Depken (1999) notes that HI is bounded from below by 1/n, and proposes an adjusted Herfindahl index, dHI = HI – 1/n. Variations over time in n affects both the lower bound of HI and the upper bound. Using the dHI measure, Depken finds that competitive inequality in MLB over the period 1920–96 became more stable over time. Michie and Oughton (2004) standardise HI using SHI = 100 [HI/(1/n)]. In a perfectly balanced league, SHI = 100. For the top tier of English football, SHI increased by 21 per cent between 1947 and 2004, with most of this increase having occurred after the late 1980s. For the Scottish Premier League, the patterns in SHI and the Gini coefficient for seasons 1997 to 2006 are similar (Lenten, 2008). Applied to win ratio data, the m-team concentration ratio provides a measure of competitive inequality that focuses on the performance of the top teams. Michie and Oughton (2004) report a five-team concentration ratio, denoted C5, and a standardised version, denoted C5B, in which the benchmark is a league in which all teams have an identical win ratio of 0.5: 5

C5 = ∑ w j /( 0.5n );

C5B = C5 /(5 / n ) 

[3.8]

j=1

In a similar vein, Goossens (2006) tracks the trend in the numbers of different teams achieving a top three position over five consecutive seasons for several European countries. For England, Curran, Jennings and Sedgwick (2009) report the ratio of the number of top four positions occupied by the four most successful teams over a ten-year period to the maximum number of top four positions that could be occupied by four teams (= 40), for the period 1949–2008. This measure reflects the ascendancy of Arsenal, Chelsea, Liverpool and Manchester United during the 2000s (see also Chapter 6, Section 6.1).

Competitive balance and home-field advantage

48

Groot (2008) proposes a ‘surprise index’ measure of competitive inequality, based on the realised number of surprise points and the maximum number of surprise points available if teams are perfectly balanced (every team wins its home matches or every game ends in a draw). Surprise points are earned when a lower-ranked team in the final league table either wins (two surprise points) or draws (one point) a match against a higher-ranked team. Surprise points are multiplied by the difference in rankings and aggregated. In a league with maximum competitive inequality and no surprises, the surprise index is zero: the top team wins all its matches; the second-placed team wins all its matches except those against the top team; and so on. For a highly balanced league, the surprise index approaches its maximum value of one. For the top tier in English football, for example, there is a clear upward trend in competitive inequality over the twentieth century as a whole. Measures of concentration or inequality that are used widely in industrial economics, such as the concentration ratio, the Herfindahl index and Gini coefficient, can also be used to measure the concentration of success in terms of the number of championship wins per team recorded over a number of seasons. Using the HI, Kringstad and Gerrard (2007) report an increase in concentration in England, Germany and Italy between 1966 and 2006, and a decrease in France and Spain. Szymanski and Kuypers (1999) fit Lorenz curves to data on the number of championship wins over the period 1946–98 for five countries. Lenten (2009a) uses a dynamic measure of competitive inequality, which compares the win ratios of each team in consecutive seasons, in order to produce a one-period metric of change that takes the form of a mobility gain function. This approach offers a bridge between the within-season and between-season analyses. The method is applied to data from the Australian Football League (AFL) and the National Rugby League (NRL). There was no significant change in competitive inequality in the AFL, but there was a decline in competitive inequality in the NRL during the 1950s. Hadley, Ciecka and Krautmann (2005) focus on the dynamics of final league standings, rather than win ratios, by designating MLB teams as ‘winners’ (qualifiers for the play-offs) or ‘losers’ (non-qualifiers), and estimating transition probabilities that, from one season to the next, a winner will remain a winner; a winner will become a loser; a loser will become a winner; and a loser will remain a loser. After 1994 (during the post-strike era) the likelihood of a winner remaining a winner in the following season increased by nearly threefold (while the number of teams advancing to the play-offs doubled). This suggests an increase in competitive inequality measured by transition probabilities between winning and losing states. Mizak, Neral and Stair (2007) use an index for measuring competitive inequality based on changes in team standings over time. The year-to-year average team movement in the standings is: n

C t = ∑ |ri,t − ri,t −1 |/n  i =1

[3.9]

Measuring competitive balance and competitive inequality

49

where Ct is the churn in team standings for year t, |ri,t – ri,t-1| is the absolute value of team i’s change in rank from season t–1 to season t, and n is the number of teams. The maximum possible value of Ct depends on n. Since n can vary over time, the churn index is divided by its maximum value to produce a standardised measure. The standardised churn varies between zero (no change in league standings from one year to the next) and one (maximum possible change in league standings from one year to the next). According to the adjusted churn index, there has been a decline in competitive inequality in MLB since the 1990s, especially in the AL. For football’s top tiers in England, France, Germany, Italy and Spain, Kringstad and Gerrard (2007) report Spearman rank correlation coefficients (SRC) between the teams’ final league standings in consecutive seasons. If there is no churning and the teams finish in the same order, SRC is one; if there is no relationship between league standings in consecutive seasons, SRC is close to zero. Kendall’s tau statistic, an alternative measure of rank correlation, is used in Groot’s (2008) long-term analysis of competitive inequality in European football. For the top tier in English football, Kendall’s tau increased from 0.17 in 1888 to 0.38 in 2005. Most of the decline in churning occurred after 1947; between 1888 and 1939 there was a weak trend in the opposite direction. Several authors apply the tools of time-series econometrics, such as unit root tests and structural break tests, to indicators of competitive inequality in sports leagues (Schmidt, 2001; Schmidt and Berri, 2001, 2003; Lee and Fort, 2005; Brandes and Franck, 2007; Fort and Lee, 2007; Lenten 2009b). For example, Lee and Fort (2009) search for structural breaks in regressions that describe the trend in the relative σ measure, and in an m-team concentration ratio, for English toptier football. Both competitive inequality indicators are based on league points (rather than win ratios).  The explanatory variables used in the regressions are a constant and a time trend. The analysis identifies break points in 1901, 1906, 1937, and 1995 or 1997 (or both). The analysis is consistent with the notion that competitive inequality increased following the formation of the Premier League at the start of the 1993 season. Dobson and Goddard (2004) are critical of the direct application of competitive inequality measures, such as the standard deviation of win ratios, which were developed with US major league sports in mind, to data from the top tiers of European football. Such measures fail to take into account the tiered competitive structure of the European leagues. Intra-tier variation in win ratios might say something about competitive inequality within an entire league; but such measures seem unlikely to provide a powerful indication. Most of the action is inter-rather than intra-tier, but inter-tier inequality is not considered. In England, however, all Premier League and Football League teams take part in a competition that does permit direct comparisons between the playing strengths of teams from different tiers. The FA Cup (Football Association Challenge Cup) is a sudden-death knockout tournament involving both league and non-league teams. For spectators, a major attraction is the cup’s propensity to produce shock results, such as the elimination of a Premier League team by an opponent from the lower reaches of the Football League or from non-league.

50

Competitive balance and home-field advantage

Szymanski (2001) uses FA Cup match attendance data in an effort to identify trends in competitive inequality in English football. Analysing cup attendances in matches where a corresponding league fixture (between the same teams in the same season) took place, Szymanski finds that cup attendances declined relative to league attendances. In the demand for sports literature, one version of the uncertainty of outcome hypothesis asserts an inverse relationship between match-level uncertainty and match attendance. Accordingly Szymanski interprets declining cup attendances as evidence of increasing inter-tier competitive inequality. League attendances are less affected by a rise in competitive inequality, which is primarily an inter- rather than an intra-tier phenomenon. Dobson and Goddard (2004) measure inter-tier competitive inequality directly using FA Cup match results data, rather than indirectly via a hypothesised and unsubstantiated relationship with match attendance. The empirical evidence for any relationship between match-level uncertainty of outcome and match attendance is widely recognised as being rather weak and unconvincing (see Chapter 11, Section 11.1). A statistical analysis of win probabilities in FA Cup results suggests there was an increase in competitive inequality during the 1920s and 1930s, and a further increase during the mid to late 1970s, 1980s and 1990s. Chapter 6, Section 6.1 presents some of the more recent data on ‘giant-killings’, identifying the frequency with which lower-ranked teams overcame higher-ranked opponents (from higher tiers) in FA Cup ties played between the 1970s and 2000s. 3.2  Home-field advantage

Home-field advantage, a pervasive feature of professional team sports, has been the subject of extensive academic research, reviewed previously by Courneya and Carron (1992), Nevill and Holder (1999) and Carron, Loughhead and Bray (2005). The sources of home-field advantage in any sport are difficult to identify or quantify empirically with any precision, but fall generally into four main categories:  familiarity (or unfamiliarity) with the home team’s stadium and facilities; disruption of the away team’s preparation due to the need to travel; various types of effect of the crowd on the home team (encouragement), the away team (intimidation) or match officials (pressure leading, either consciously or subconsciously, to biased decisions favouring the home team); and in certain sports, rules that may favour the home team.1 Summarising a number of studies, Nevill and Holder (1999) find that the weight of evidence suggests that the crowd is the most important source of home-field advantage, and that the influence of the crowd on the match result operates mainly through the match officials, rather than through any direct effect on the performance of the homeor away-team players. Several aggregate measures of home-field advantage are employed in the academic literature. Nevill, Newell and Gale (1996) and Attrill et al. (2008) use percentage of matches won by the home and away teams; and Jacklin (2005)

Home-field advantage

51

uses the ratio of home wins to away wins. Pollard and Pollard (2005) use the ratio of league points won to total points available to compare long-term trends in home-field advantage in several North American professional team sports with English football. Home-field advantage in most of the sports examined was greatest in the earliest years of the sport’s existence. Home-field advantage shows little evidence of any long-term trend in MLB and the NFL, but may have increased slightly in the latter in recent years. Home-field advantage in baseball is consistently lower than in the other sports examined. Home-field advantage in the NBA and in hockey (the NHL), and in English football, has declined in recent decades.2 Using cross-sectional data on seventy-two countries and six football seasons from 1999 to 2004 inclusive, Pollard (2006) compares the size of the home-field advantage effect by country. In Europe, home-field advantage is above average in several countries in the Balkans, and lower than average throughout most of northern Europe, including the Baltic, Scandinavia and the British Isles. In Latin America, home-field advantage is above average in the Andean countries Bolivia, Peru, Ecuador and Colombia, and below average in the southern countries Argentina, Paraguay and Uruguay. Pollard and Gomez (2009) report a more detailed analysis for south-west Europe (France, Italy, Portugal and Spain). Page and Page (2007) examine home-field advantage in two-leg ties played on a knockout basis in European football club competition. Using data extending back to the inception of European club competition in the mid-1950s, teams drawn to play the away leg first and the home leg second are more likely to be successful in the tie. The magnitude of this effect has diminished over time. Explanations for this effect relating to competition rules (in some cases stronger teams were seeded and guaranteed to play the second leg at home; and European ties that are level at the end of 90 minutes’ play in the second leg are extended for an extra 30 minutes, conferring an additional advantage on the home team in the second leg) are investigated, but discounted as explanations for the entire discrepancy between the performance of the teams playing at home and away in the second leg. Poulter (2009) examines home-field advantage in the Champions League over the period 2001–7. Brown et al. (2002) analyse 3,914 match results played by the 32 international teams that participated in the 1998 World Cup in France. The matches were played between January 1987 and the end of the World Cup on 12 July 1998. The impact on home-field advantage of three factors is examined: familiarity with the playing facility, the importance of the match and the distance travelled by the away team. Home-field advantage is stronger when the home team played in a familiar stadium. Home-field advantage is positively related to distance travelled by the away team. For English club football, Pollard and Pollard (2005) note that home-field advantage was several percentage points higher before the Second World War than it was when football resumed afterwards, following a seven-year wartime

52

Competitive balance and home-field advantage

break. This shift is interpreted as circumstantial evidence that familiarity may have been an important source of home-field advantage (players new to the sport when football resumed would have been equally unfamiliar with their own and their opponents’ stadia), and that crowd effects may have been unimportant (English football matches attracted record attendances in the immediate postwar seasons). Among other studies with a more specific focus, Barnett and Hilditch (1993) report that four English clubs that used artificial playing surfaces during the 1980s and early 1990s (Luton Town, Oldham Athletic, Preston North End and Queen’s Park Rangers) enjoyed a moderately enhanced home-field advantage. Clarke and Norman (1995) analyse home-field advantage at club level using 1980s data. Home-field advantage does not vary significantly by tier, but it does vary over time. London clubs had a below-average home-field advantage, and home-field advantage effects had greater leverage on winning than on goal margins. Pollard (2002) finds home advantage is somewhat reduced when a team moves to a new stadium. Using data from the 1993 season, Nevill, Newell and Gale (1996) find that home-field advantage in English and Scottish football was associated with the average attendance in each tier. More penalties were awarded to the home team and fewer home-team players were sent off in the higher tiers with large attendances. Boyko, Boyko and Boyko (2007) and Johnston (2008) report conflicting findings concerning the impact of the crowd size on home-field bias. Each of these studies also considers whether referee bias contributes to home-field advantage. Page and Page (2010) report that the magnitude of home-field advantage depends upon the referee, and that this relationship is moderated by the size of the crowd. Some referees are more prone to be influenced by the crowd than others (see also Chapter 10). Travel may contribute to home-field advantage, if players become tired after travelling long distances, often on the day of the match for lower-tier teams in particular. Anecdotally, Koyama and Reade (2010) note that Carlisle United, one of the most remotely located English clubs, won sixteen consecutive home matches during the 2008 season. However, when T3 and T4 were organised on a regional basis (Division 3 North and South, seasons 1921 to 1958 inclusive), home-field advantage was greater than it became subsequently, even though the distances travelled by away teams were smaller. Several other studies suggest distance exerts only a weak effect on home-field advantage (Pace and Carron, 1992; Nevill and Holder, 1999; Carron, Loughhead and Bray, 2005; Pollard, 2006). Other factors that have been proposed as causes of home advantage include territoriality and psychology. Defending the home ground may evoke sentiments associated with territoriality. Neave and Wolfson (2003), for example, reported higher concentrations of testosterone in players before a home match than before an away match. Several researchers have sought explanations for home-field advantage in player psychology. For example, Waters and Lovell (2002) report

Home-field advantage

53

that players expressed greater confidence when playing at home, and were more optimistic about the likely outcome. Table 3.1 presents an analysis of home-field advantage in the English league over a forty-year period from the 1970 season to the 2009 season. The tabulation shows the proportions of matches in all four tiers that resulted in home wins, draws and away wins, and the average numbers of goals scored per match by the home and away teams and in total. The final two columns report summary measures of home-field advantage, in the form of home-team success percentages. The penultimate column reports the percentage of league points that were gained by home teams, calculated using a scale of 2/1/0 (two points for a win, one for a draw and zero for a loss). This was the scoring system for league points until the end of the 1981 season. Subsequently, three league points have been awarded for a win; and from the 1982 season onwards the final column reports the equivalent home-team success percentages calculated using a scale of 3/1/0. The change in the points scoring system results in an increase of about one per cent in the home-field advantage measure. A continuous series based on a common scoring system therefore appears preferable to one that switches midway from 2/1/0 to 3/1/0. Because the 2/1/0 series gives equal weighting to every match (whereas the 3/1/0 series gives more weight to matches that are won or lost than it gives to draws); and because the 2/1/0 series is directly comparable to a win ratio or win-percent measure for American sports which do not permit draws (ties), the 2/1/0 series is our preferred home-field advantage measure. On the 2/1/0 measure, average home-field advantage for the period 1980–2003 is 61.1 per cent. Subsequently there has been a slight reduction, to an average of 58.0 per cent for the 2004–9 period. For the period 1980–2003, the corresponding figures quoted by Pollard and Pollard (2005) for North American major league sports are 53.7 per cent for MLB, 57.2 per cent for NHL, 58.0 per cent for NFL and 62.6 per cent for NBA. Table 3.2 reports average values of the 2/1/0 home-field advantage measure by tier (division), calculated over five-season intervals over the same period. In all tiers, there has been a marked improvement in the average performance of away teams, and a corresponding deterioration in the performance of home teams. The reduction in home-field advantage has been more pronounced in the lower tiers than in the higher tiers. In 1970–4, T1 had the lowest home-field advantage and T4 the highest; but by 2005–9 these positions had been reversed. A particularly striking feature of Table 3.1 is the large jump in the average number of goals scored by away teams, which coincided with the introduction of the award of three league points (rather than two) for a win, from the 1982 season onwards. The improvement in the performance of away teams since the early 1980s was initially (in the 1980s) due to an improvement in their offensive or goal-scoring capability, but has been sustained subsequently (in the 1990s and 2000s) by an improvement in their defensive capability to avoid conceding goals.

Home wins (per cent)

49.9 48.8 51.4 51.7 48.9 52.4 50.2 51.9 50.1 48.0 49.9 49.6 47.1 52.0 50.8 50.1 50.1 48.9 46.1 46.8 46.8 48.4 47.5

Season

1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992

28.6 28.3 27.6 28.4 30.2 27.9 27.7 27.9 30.9 29.6 27.9 28.0 27.4 26.3 26.0 24.3 24.6 27.4 27.3 28.6 27.3 27.6 26.9

Draws (per cent) 21.5 22.9 21.0 19.9 21.0 19.7 22.1 20.2 19.0 22.4 22.2 22.4 25.5 21.6 23.2 25.6 25.3 23.7 26.6 24.6 25.9 24.1 25.5

Away wins (per cent) 1.64 1.54 1.62 1.57 1.51 1.59 1.59 1.66 1.62 1.55 1.58 1.53 1.53 1.72 1.69 1.62 1.69 1.55 1.55 1.58 1.54 1.56 1.52

Average goals per match:  home team 1.00 0.99 0.97 0.92 0.92 0.92 0.99 0.99 0.98 1.01 0.98 0.94 1.07 1.06 1.06 1.10 1.11 1.05 1.08 1.08 1.09 1.06 1.08

Average goals per match:  away team 64.2 63.0 65.2 65.9 64.0 66.4 64.1 65.9 65.5 62.8 63.8 63.6 60.8 65.2 63.8 62.3 62.4 62.6 59.8 61.1 60.4 62.2 61.0

Home-team win per cent (2/1/0 pts) — — — — — — — — — — — — 61.9 66.6 65.1 63.4 63.5 63.9 60.7 62.3 61.5 63.4 62.1

Home-team win per cent (3/1/0 pts)

Table 3.1 Percentages of home wins, draws and away wins, average numbers of goals scored by the home and away teams, and win percentages per season, English league, 1970–2009 seasons

46.5 45.6 46.4 45.0 46.4 47.9 45.0 45.5 46.5 46.7 44.3 45.2 44.3 43.3 46.4 43.4 43.0

26.4 27.4 27.5 29.6 28.1 27.8 28.0 27.1 27.4 26.5 27.0 27.9 28.6 29.5 24.7 26.5 27.5

Source: Rothmans/Sky Sports Football Yearbook

1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

27.1 27.0 26.1 25.3 25.5 24.3 27.0 27.4 26.2 26.8 28.7 26.9 27.1 27.2 29.0 30.2 29.5

1.58 1.53 1.51 1.48 1.47 1.51 1.46 1.46 1.50 1.54 1.48 1.50 1.46 1.42 1.43 1.41 1.43

1.12 1.14 1.08 1.06 1.03 1.05 1.08 1.07 1.07 1.09 1.15 1.10 1.10 1.07 1.08 1.12 1.11

59.7 59.3 60.1 59.8 60.4 61.8 59.0 59.1 60.1 59.9 57.8 59.1 58.6 58.1 58.7 56.6 56.8

60.7 60.2 61.2 60.9 61.5 63.0 59.9 60.0 61.2 60.9 58.5 60.1 59.5 59.0 59.5 57.2 57.5

56

Competitive balance and home-field advantage

Table 3.2 Home-team success percentages (2/1/0 points for W/D/L) by tier (division) in five-season bands, English league, 1970–2009 seasons Seasons 1970–1974 1975–1979 1980–1984 1985–1989 1990–1994 1995–1999 2000–2004 2005–2009

T1

T2

T3

T4

All tiers

62.5 63.5 63.5 61.1 60.1 59.9 59.8 59.8

64.9 64.2 63.2 62.3 61.1 60.8 59.0 58.1

63.7 66.0 63.9 61.3 60.9 60.2 58.4 57.6

66.4 65.6 63.2 61.8 59.8 60.0 59.9 56.1

64.4 64.9 63.4 61.6 60.5 60.2 59.2 57.7

Source: Rothmans/Sky Sports Football Yearbook

Inspection of Table 3.1 raises the question whether the long-term erosion of the importance of home-field advantage is attributable solely to changes in incentives arising from the introduction of three rather than two league points for a win (Jacklin, 2005; Dilger and Geyer, 2009; Moschini, 2010), or whether it reflects changes in the underlying ‘technology’ defining the processes which generate match results. Such changes might include improvements in training methods enabling players to perform more consistently away from home; improvements in the quality of transportation making away travel less onerous; or improvements in professionalism, making footballing ability a more decisive influence on match results, or making psychological effects on players or officials deriving from the attitude of the crowd less decisive (Smith, 2003). Arguing along similar lines, Koyama and Reade (2010) suggest that an increase in the opportunity for supporters to scrutinise players’ performances away from home, resulting from the increasing scope of TV coverage, has raised incentives for players to perform to their maximum ability in all matches. Because England’s adoption of three-points-for-a-win pre-dated the ­implementation of the same change in a number of other leading football nations by more than a decade, some international comparisons of home- and away-team win ratios and goal-scoring records should shed some light on this matter. Table 3.3 summarises the relevant data for teams in the top tiers of England, France, Germany, Scotland and Spain, for seasons 1973 to 2009 inclusive. For England the data are aggregated into three nine-season and two five-season periods (seasons 1973–1981, 1982–1990, 1991–1999, 2000–2004 and 2005–2009, inclusive). For the other four countries, the data are similarly aggregated, except for the 1991–9 period, which is split into two subperiods at the point of introduction of three-points-for-a-win: the 1995 season in France and Scotland, and the 1996 season in Germany and Spain.

50.0 48.6 45.6 46.8 47.2

57.0 55.1 51.7 49.2 50.1 45.3

54.3 50.9 45.4 44.9 50.1 46.0

France 1973–1981 1982–1990 1991–1994 1995–1999* 2000–2004* 2005–2009*

Germany 1973–1981 1982–1990 1991–1995 1996–1999* 2000–2004* 2005–2009*

Home wins (per cent)

England 1973–1981 1982–1990* 1991–1999* 2000–2004* 2005–2009*

Seasons

25.5 27.7 31.2 29.3 24.4 25.6

25.1 27.4 31.7 31.0 27.1 31.3

28.0 26.1 28.6 25.9 25.4

Draws (per cent)

20.1 21.5 23.4 25.8 25.5 28.4

18.0 17.4 16.6 19.8 22.8 23.4

21.9 25.3 25.8 27.3 27.5

Away wins (per cent)

2.29 2.18 1.76 1.73 1.72 1.62

1.92 1.67 1.45 1.47 1.46 1.32

1.58 1.59 1.51 1.54 1.47

Average goals per match:  home team

1.32 1.26 1.19 1.22 1.16 1.22

1.01 0.87 0.76 0.87 0.93 0.90

1.00 1.06 1.09 1.13 1.05

Average goals per match:  away team

0.671 0.648 0.610 0.596 0.623 0.588

0.696 0.688 0.676 0.647 0.636 0.609

0.641 0.617 0.599 0.598 0.598

Home-team win ratio

Table 3.3 Percentages of home wins, draws and away wins, and average numbers of goals scored by home and away teams, international comparisons, 1973–2009 seasons

61.6 53.6 50.4 47.9 48.2 46.9

Spain 1973–1981 1982–1990 1991–1995 1996–1999* 2000–2004* 2005–2009* 25.1 26.9 28.4 27.1 26.9 24.9

24.7 25.3 29.3 27.3 22.5 23.3

Draws (per cent)

Note: * denotes three league points awarded for a win.

46.7 45.4 40.7 43.4 45.0 44.6

Home wins (per cent)

Scotland 1973–1981 1982–1990 1991–1994 1995–1999* 2000–2004* 2005–2009*

Seasons

Table 3.3 (cont.)

13.3 19.5 21.2 25.0 24.9 28.2

28.5 29.3 30.0 29.2 32.5 32.0

Away wins (per cent)

1.74 1.57 1.51 1.60 1.58 1.49

1.62 1.53 1.36 1.51 1.57 1.46

Average goals per match:  home team

0.79 0.88 0.94 1.09 1.10 1.13

1.21 1.14 1.11 1.16 1.23 1.15

Average goals per match:  away team

0.742 0.671 0.646 0.615 0.616 0.594

0.591 0.581 0.554 0.571 0.562 0.563

Home-team win ratio

Distributional properties of goals scored

59

The results for France, Germany and Spain indicate that long-term decline in the size of home-field advantage is an international phenomenon, and has progressed further in each of these three countries than in England. This partly reflects the fact that home-field advantage counted for more in these three countries than it did in England in the 1970s. Since then a process of international convergence has been underway. In France and Spain, the short-term impact of the introduction of three-points-for-a-win in the mid-1990s was the same as in England at the start of the 1980s: an immediate increase in the average number of goals scored by the away team, and a corresponding increase in the proportion of matches finishing in away wins. In Germany most of the erosion of the importance of home-field advantage appears to have occurred during the 1970s and 1980s, before the introduction of three-points-for-a-win. The proportion of away wins was higher in Scotland than in any of the other four countries throughout the period covered by Table 3.3. Although there has been some erosion of home-field advantage and a corresponding improvement in the performance of away teams, the shift has been smaller than in any of the other four countries. The relatively strong performance of away teams may reflect a high level of competitive imbalance in the Scottish league: home advantage is less important in matches between teams that are highly unequal. The Scottish data may also be affected by a series of changes to the league and divisional structure during the 1970s, 1980s and 1990s, which had implications for competitive balance. The introduction of three-points-for-a-win in the 1995 season coincided with a reduction in the number of teams in the top division from twelve to ten. Other things being equal this would be expected to reduce competitive inequality, and increase the importance of home-field advantage. This latter effect appears to have dominated the three-points-for-a-win effect, since the home-team win ratio was higher in 1995–9 than it was in 1991–4. 3.3  Distributional properties of the goals scored by the home and away teams

Section 3.3 investigates the statistical properties of football match results data, and examines the use of several variants of the Poisson distribution and the negative binomial distribution that are able to describe the distributional properties of match results data presented in scores format. The analysis begins by reporting, in Tables 3.4 and 3.5, the percentage distributions of the numbers of goals scored in each match by the home and away teams based on league match results between the 1970 and 2009 seasons (inclusive). Table 3.4 reports the results for the twelve seasons prior to the introduction of three-points-for-a-win, from 1970 to 1981, inclusive; and Table 3.5 reports the results for the twenty-eight seasons subsequently, from 1982 to 2009, inclusive. For example, Table 3.5 indicates that 8.1 per cent of matches during the 1982– 2009 period finished as 0–0 draws, 10.9 per cent finished as 1–0 wins for the home team and 7.8 per cent finished as 0–1 wins for the away team. A 1–1 draw was the

60

Competitive balance and home-field advantage

Table 3.4 Joint and marginal percentage distributions of goals scored by home and away teams, English league, 1970–1981 seasons Goals scored by the away team

Goals scored by the home team

0

1

0 1 2 3 4 5 6+

9.3 11.8 9.2 5.0 2.1 0.7 0.3

6.8 13.2 9.3 4.7 1.8 0.6 0.2

Total

38.3

36.6

2

3

4

5

6+

Total

3.3 5.1 5.1 2.4 1.0 0.4 0.2

1.2 1.9 1.4 0.9 0.3 0.1 0.0

0.3 0.5 0.3 0.2 0.1 0.0 0.0

0.1 0.2 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0

20.8 32.6 25.5 13.2 5.3 1.9 0.7

17.4

5.9

1.4

0.3

0.1

100.0

Source: Rothmans Football Yearbook

Table 3.5 Joint and marginal percentage distributions of goals scored by home and away teams, English league, 1982–2009 seasons Goals scored by the away team

Goals scored by the home team

0

1

2

3

4

5

6+

Total

0 1 2 3 4 5 6+

8.1 10.9 8.1 4.2 1.7 0.6 0.2

7.8 12.8 9.4 4.4 1.7 0.6 0.2

4.1 6.4 5.1 2.5 0.9 0.3 0.1

1.5 2.3 1.7 1.0 0.4 0.1 0.0

0.5 0.7 0.4 0.3 0.1 0.0 0.0

0.1 0.2 0.1 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0

22.1 33.2 25.0 12.5 4.9 1.6 0.6

Total

33.9

36.9

19.4

7.1

2.0

0.5

0.1

100.0

Source: Rothmans/Sky Sports Football Yearbook

most common outcome, in 12.8 per cent of all matches. The comparison between Tables 3.4 and 3.5 suggests that the change from two to three-points-for-a-win had the desired effect of encouraging attacking play, particularly by away teams. The proportion of matches that finished 0–0 was higher in 1971–82 (9.3 per cent) than in 1982–2009. Similarly among other low-scoring results, the proportions of 1–0 home wins and 1–1 draws were higher in 1970–81 (11.8 per cent and 13.2 per cent) than in 1982–2009. There was, however, a smaller proportion of 0–1 away wins in 1970–81 (6.8 per cent) than in 1982–2009.

Distributional properties of goals scored

61

Table 3.6 Percentage distribution of goals scored by the home team, conditional on the number of goals scored by the away team, English league, 1982–2009 seasons Goals scored by the away team

Goals scored by the home team

0 1 2 3 4 5 6+ Average

0

1

2

3

4

5

6+

24.0 32.2 23.9 12.3 5.0 1.8 0.7 1.51

21.0 34.6 25.5 12.0 4.7 1.6 0.7 1.52

20.8 32.8 26.5 13.1 4.7 1.6 0.5 1.55

21.4 32.5 24.2 14.0 6.0 1.5 0.4 1.57

23.5 33.3 21.9 13.3 5.5 1.9 0.7 1.53

25.3 33.9 26.1 8.9 3.9 1.2 0.8 1.39

25.9 33.3 22.2 9.9 8.6 0.0 0.0 1.42

Source: Rothmans/Sky Sports Football Yearbook

The final columns and rows of Tables 3.4 and 3.5 show the marginal probability distributions of goals per match scored by the home and away teams respectively, calculated by summing horizontally across the other columns and vertically down the other rows of each table. For example, Table 3.5 indicates that the home team failed to score in 22.1 per cent of all matches played in 1982–2009, and the home team scored once in 33.2 per cent of all matches. Similarly, the away team failed to score in 33.9 per cent of all matches, and scored once in 36.9 per cent of these matches. For away teams in particular, there has been a marked change in the shape of the marginal probability distribution of goals scored. The modal (most frequent) number of away goals scored changed from zero in 1970–81, to one in 1982–2009. Tables 3.6 and 3.7 show the conditional distributions for the numbers of goals scored by the home and away team. To save space, only the results for the 1982– 2009 period are included. The conditioning is on the number of goals scored by the opposing team. The conditional distributions can be used to identify whether there is interdependence between the numbers of goals scored by the home and away teams in each match, or whether the numbers of goals scored by the two teams can be considered as (approximately) independent of each other. For example, the first column of Table 3.6 shows, for matches in which the away team failed to score, the proportions of occasions on which the home team scored 0, 1, 2, 3 goals, and so on. In 24.0 per cent of matches in which the away team and so on failed to score, therefore, the home team also failed to score; in 32.2 per cent of matches in which the away team failed to score, the home team scored once; and so on. The second column shows the same for matches in which the away team scored once. In Table 3.7, the conditioning is reversed. The first row shows, for

62

Competitive balance and home-field advantage

Table 3.7 Percentage distribution of goals scored by the away team, conditional on the number of goals scored by the home team, English league, 1982–2009 seasons Goals scored by the away team

Goals scored by the home team

0 1 2 3 4 5 6+

0

1

2

3

4

5

6+

Average

36.8 32.8 32.4 33.5 34.5 37.2 38.4

35.1 38.5 37.7 35.4 35.3 35.1 38.9

18.3 19.2 20.6 20.4 18.7 18.8 15.1

6.9 7.0 6.9 8.0 8.6 6.4 4.9

2.1 2.0 1.7 2.1 2.2 2.2 2.2

0.5 0.5 0.5 0.3 0.4 0.3 0.5

0.2 0.1 0.1 0.1 0.2 0.0 0.0

1.05 1.09 1.10 1.11 1.11 1.02 0.95

Source: Rothmans/Sky Sports Football Yearbook

matches in which the home team failed to score, the proportions of occasions on which the away team scored 0, 1, 2, 3 goals, and so on. The second row shows the same for matches in which the home team scored once. If the numbers of goals scored by the home team and the away team are independent, then the number of away goals should not affect the conditional probabilities for the number of home goals. This implies the probability distributions in each column of Table 3.6 should look similar to each other (and similar to the marginal distribution for the number of home goals in the final column of Table 3.5). Likewise, the number of home goals should not affect the probabilities for the number of away goals, so the probability distributions in each row of Table 3.7 should also look similar to one another (and similar to the marginal distribution for the number of away goals in the final row of Table 3.5). In fact, the probabilities do not satisfy this condition for independence. In Table 3.7, for example, when the home team scored 0, the most frequent score for the away team was 0 (36.8 per cent of matches when the home team scored 0). When the home team scored 0, the away team scored 1 in 35.1 per cent of matches. When the home team scored 1, however, the most frequent score for the away team was also 1 (38.5 per cent of matches when the home team scored 1). When the home team scored 1, the away team scored 0 in only 32.8 per cent of matches. The conditional mean scores reported in the final column of Table 3.7 indicate that the (conditional) average number of away goals was an increasing function of the number of home goals over the range 0 to 3 home goals. Similarly, according to the bottom row of Table 3.6, the (conditional) average number of home goals was an increasing function of the number of away goals over the range 0 to 3 away goals.

Distributional properties of goals scored

63

In common with the results presented by Dixon and Coles (1997), these tabulations suggest that the greatest degree of interdependence occurs in low-­scoring games, since the largest discrepancies between the probabilities in adjacent rows or columns are towards the top-left-hand corners of Tables 3.6 and 3.7. Nevertheless, it is apparent that the shapes of the conditional probability distributions do vary to some extent over the full range of values for the conditioning variable, and that the numbers of goals scored by the home and away teams are therefore interdependent. This section concludes by presenting an analysis of the statistical properties of the goals data for seasons 1982–2009 that are summarised in Tables 3.5–3.7. This analysis involves using theoretical probability distributions to describe the data on the goals scored by the home and away teams. The two candidate distributions are the Poisson distribution and the negative binomial distribution. For each of these two distributions, we consider three variants, as follows. First, by treating the goals scored by the home and away teams in each match as independent, the data can be described by fitting two separate univariate distributions to the data for home teams and away teams individually. This approach, which produces a double Poisson distribution or double negative binomial distribution, does not take account of any possible dependence between the goals scored by the two teams. Second, zero-inflated variants of both the Poisson distribution and the negative binomial distributions are available, to allow for departure from the basic shapes of these theoretical distributions in the case of the ‘zero’ outcome, which in the bivariate case is the 0–0 draw. In a wide range of applications, it has been found that the theoretical distributions can have a tendency to generate probabilities that understate the observed proportion of zero outcomes. A zero-inflated adjustment involves increasing the theoretical probability for the zero outcome by an amount sufficient to bring this probability into line with the observed proportion. The theoretical probabilities for all other outcomes are deflated pro rata by the amounts required to maintain the condition that the probabilities add up to one. By extension, inflated adjustments can also be applied to the probabilities for other outcomes if required. In the case of goals data, a case has been made for applying diagonal-inflated adjustments to the probabilities for the most commonly observed drawn results of 0–0, 1–1 and 2–2 (Karlis and Ntzoufras, 2003). Third, by relaxing the independence assumption, the data can be described by fitting bivariate distributions to the data for the home teams and away teams jointly. An explicit formula exists for the joint probability function of the bivariate Poisson distribution. No such formula exists in the case of the bivariate negative binomial distribution; but it is possible to create a ‘synthetic’ bivariate distribution from two univariate distributions, using a copula function. The two sets of univariate probabilities are treated as inputs to the copula function, which generates the bivariate probabilities with one or more additional parameters introduced to describe the dependence. The Frank copula requires a single additional parameter.

64

Competitive balance and home-field advantage

This procedure for creating a bivariate distribution can be applied to a wide range of univariate distributions, including both the Poisson and the negative binomial. In order to facilitate direct comparisons between these two distributions as candidates for describing the goals data, a ‘synthetic’ bivariate Poisson distribution generated via a copula function is used below, rather than the theoretical bivariate Poisson distribution.3 The technical details are as follows. Let S1 and S2 denote the numbers of goals scored by the home and away teams expressed as random variables, and let s1 = 0,1,2, … and s2 = 0,1,2, … denote the realised values of S1 and S2. f1(s1) = P(S1 = s1) denotes the probability that the home team scores s1 goals, for s1 = 0,1,2, … , known as the marginal probability function for S1. Similarly, f2(s2) = P(S2 = s2) denotes the probability that the away team scores s2 goals, known as the marginal probability function for S2. The formulae for fi(si) in each case, together with the corresponding expressions for the expected value of Si and the variance of Si, are as follows: Poisson distribution: f i (s i ) = exp( − λ i,j )λ si,ji /s i! Expected value and variance: E(Si ) = λ i var(Si ) = λ i 

[3.10]

Negative binomial distribution: f i (s i ) = [Γ (ρi + s i )/{s i!Γ (ρi )}]{ρi /(λ i + ρi )}ρi {λ i /(λ i + ρi )}si Expected value and variance: E(Si ) = λ i

var(Si ) = λ i (1 + κ i λ i )

where κ i = 1/ρi 

[3.11]

where exp( ) denotes the exponential function and Γ( ) denotes the gamma function. The distinction between the Poisson distribution and the negative binomial distribution is found in the ancillary parameter ρi≥0, which allows for greater flexibility in the dispersion of Si across matches than is allowed by the Poisson distribution. Note that for ρi = 0, var(Si) = λi. In this limiting case, the negative binomial distribution is the same as the Poisson distribution. For ρi>0, however, var(Si)>λi. In this general case, the negative binomial distribution allows for overdispersion. In the sample data, the degree of overdispersion is small but positive. The sample mean values of S1 and S2 are 1.5259 and 1.0838, and the sample variances are 1.5839 and 1.1038. The sample correlation coefficient between S1 and S2 of 0.0104 is significantly different from zero at the 0.01 level. As indicated above, dependence between S1 and S2 is addressed by creating a ‘synthetic’ bivariate distribution from the two univariate distributions. Let Fi(si) denote the univariate distribution functions for Si corresponding to fi(si). In other words, F1(s1) = P(S1≤s1) expresses the probability that the home team scores s1 or fewer goals, for all possible values of s1 ( = 0,1,2, …). Similarly, F2(s2) = P(S2≤s2) is the probability that the away team scores s2 or fewer goals. The bivariate joint distribution function is defined as follows:

Distributional properties of goals scored

65

G[F1 (s1 ),F2 (s 2 )] = P(S1 ≤ s1 ,S2 ≤ s 2 ) =

1  {exp[ϕF1 (s1 )] − 1}{exp[ϕF2 (s 2 )] − 1} ln 1 +  ϕ  exp(ϕ ) − 1



[3.12]

The bivariate joint distribution function G[F1(s1),F2(s2)] expresses the probability that the home team scores s1 or fewer goals and the away team scores s2 or fewer goals. The ancillary parameter ϕ determines the nature of any correlation between S1 and S2: for ϕ0 the correlation is negative. G[F1(s1),F2(s2)] is undefined for ϕ = 0, but in this case it is conventional to write G[F1(s1),F2(s2)] = F1(s1)F2(s2). The bivariate joint probability function corresponding to G[F1(s1),F2(s2)] expresses the probability that the home team scores (exactly) s1 goals and the away team scores (exactly) s2 goals. The bivariate joint probability function f(s1,s2) = P(S1=s1,S2=s2) is obtained iteratively, as follows: f(0,0) = G[F1 (0),F2 (0)] f(s1 ,0) = G[F1 (s1 ),F2 (0)] − G[F1 (s1 − 1),F2 (0)] f(0,s 2 ) = G[F1 (0),F2 (s2 )] − G[F1 (0),F2 (s2 − 1)] f(s1 ,s 2 ) = G[F1 (s1 ),F2 (s 2 )] − G[F1 (s1 − 1),F2 (s 2 )] − G[F1 (s1 ),F2 (s 2 − 1)] + G[F1 (s1 − 1),F2 (s 2 − 1)]

for s1 = 1,2, for s 2 = 1,2, for s1 ,s 2 =1,2, [3.13] 

Finally, the diagonal-inflated adjustment for 0–0, 1–1 and 2–2 draws is applied by introducing three additional parameters, π0, π1 and π2, adjusting the joint probabilities as follows:   = P(S = 0,S = 0) = (1 − π )P(S = 0,S = 0) + π (1 − π − π ) f(0,0) 1

2

0

1

2

0

1

2

 ) f(1,1 f(2,2)

 1 = 1,S2 = 1) = (1 − π 0 )P(S1 = 1,S2 = 1) + π 0 π1 = P(S  1 = 2,S2 = 2) = (1 − π 0 )P(S1 = 2,S2 = 2) + π 0 π 2 = P(S  ,s ) = P(S  1 = s1 ,S2 = s 2 ) = (1 − π 0 )P(S1 = s1 ,S2 = s 2 ) f(s 1 2 for{s1 ,s 2 } ≠ {0,0},{1,1}or{2,2}



[3.14]

Table 3.8 reports the parameter estimates obtained by fitting 16 alternative specifications to the home and away teams’ goals data for the 59,922 English league matches played during the 28 seasons from 1982 to 2009 (inclusive). The four specifications used for the probability functions are double Poisson, bivariate Poisson, double negative binomial and bivariate negative binomial. Four variants are reported in each of these four cases: (i) unadjusted; (ii) zero-inflated adjustment for 0–0 draws only; (iii) diagonal-inflated adjustments for 0–0 and 1–1 draws; and (iv) diagonal-inflated adjustments for 0–0, 1–1 and 2–2 draws. As a descriptive measure of the quality of each fitted model, the final column of Table 3.8 reports pseudo R-square, the geometric mean of the probabilities assigned by the fitted

bivariate Poisson bivariate Poisson 0–0 bivariate Poisson 0–0,1–1 bivariate Poisson 0–0,1–1,2–2

double nb double nb 0–0 double nb 0–0,1–1 double nb 0–0,1–1,2–2

bivariate nb bivariate nb 0–0 bivariate nb 0–0,1–1 bivariate nb 0–0,1–1,2–2

5. 6. 7. 8.

9. 10. 11. 12.

13. 14. 15. 16.

1.5258 1.5360 1.5446 1.5430

1.5259 1.5388 1.5467 1.5445

1.5258 1.5418 1.5507 1.5504

1.5259 1.5424 1.5504 1.5498

λ1

Note: nb denotes negative binomial distribution.

double Poisson double Poisson 0–0 double Poisson 0–0,1–1 double Poisson 0–0,1–1,2–2

1. 2. 3. 4.

Specification and code number

1.0838 1.0910 1.0938 1.0905

1.0838 1.0929 1.0952 1.0915

1.0839 1.0951 1.0984 1.0972

1.0838 1.0955 1.0982 1.0969

λ2

.0065 .0194 .0230

.0084 .0208 .0241

.0103 .0224 .0244

.0106 .0222 .0238

π0

.5803 .5197

.5469 .4997

.4474 .4201

.4502 .4268

π1

.1405

.1376

.0630

.0608

π2

−.1305 −.0573 −.0410 −.0302

−.1287 −.0151 .0076 .0167

ϕ

.0244 .0177 .0197 .0228

.0244 .0159 .0183 .0219

κ1

.0166 .0100 .0180 .0223

.0166 .0082 .0168 .0215

κ2

.054309 .054315 .054337 .054342

.054299 .054314 .054337 .054342

.054286 .054306 .054324 .054326

.054276 .054306 .054324 .054325

Pseudo R-square

Table 3.8 Parameter estimates for fitted double and bivariate Poisson and negative binomial distributions, home- and away-team goals data, English league, 1982–2009 seasons

Sequences and persistence in match results

67

model to the actual outcome of every match. A higher pseudo R-square indicates a closer fit. Table 3.9 reports the results of likelihood ratio tests for various comparisons between the sixteen specifications. Panels 1a/b compare the double Poisson and double negative binomial with their inflated-adjusted variants, by testing the contribution to the model of the parameters π0, π1 and π2. The inflated adjustments for 0–0, 1–1 and 2–2 draws are added and tested sequentially. The inflated adjustment for 2–2 draws does not improve the quality of the double Poisson specification inflated-adjusted for 0–0 and 1–1 draws significantly; but the same adjustment does improve the corresponding double negative binomial specification significantly. Panels 2a/b repeat these comparisons for the bivariate Poisson and bivariate negative binomial specifications respectively, with similar results. Panels 3a/b compare the double Poisson and double negative binomial specifications with the corresponding bivariate specifications, by testing the contribution to the model of the parameter ϕ. In the absence of the inflated adjustments, ϕ makes a significant contribution; but if the inflated-adjustment parameters are included, ϕ becomes insignificant. The contributions to the model of ϕ on the one hand, and π0, π1 and π2 on the other hand, are similar in the sense that the former operates primarily to increase the probabilities for closely contested matches (and reduce the probabilities for large differences in scores), while the latter operates specifically upon the draw probabilities. The results reported in Table 3.9 suggest the specific adjustments to the draw probabilities are more effective in improving the quality of the fitted model than the adjustment that allows for dependence by means of the copula function. Finally, Panels 4a/b present direct comparisons of the corresponding Poisson and negative binomial specifications, by testing the contribution to the model of the overdispersion parameters κ1 and κ2 (or, equivalently, ρ1 and ρ2). These parameters make a significant contribution in every case, indicating that the negative binomial specification outperforms the Poisson. Based on these hypothesis test results, specification 12, the double negative binomial with inflated-adjusted probabilities for 0–0, 1–1 and 2–2 draws, provides the best representation of the goals data. 3.4  Good and poor sequences, and persistence in football match results

A question of enduring fascination to sports fans concerns the nature of persistence in sequences of consecutive match results. Does a sequence of wins tend to build a team’s confidence and morale, increasing the probability that the next match will also be won? Or does it tend to create pressures or breed complacency, increasing the likelihood that the next match will be drawn or lost? Does a sequence of losses tend to sap confidence or morale, increasing the probability of a further loss in the next match? Or does it tend to inspire greater effort, increasing the likelihood that the next match will be won or drawn? These questions are examined by

 2  3  4

 6  7  8

 5  6  7  8

 9 10 11 12

Panel 1a 1 2 3

Panel 2a 5 6 7

Panel 3a 1 2 3 4

Panel 4a 1 2 3 4

48.1 16.2 25.5 33.7

22.1 0.2 0.1 0.3

41.4 38.4 2.3

63.2 38.5 2.1

Chi-square

2 2 2 2

1 1 1 1

1 1 1

1 1 1

Degrees of freedom

.000 .000 .000 .000

.000 .655 .806 .610

.000 .000 .128

.000 .000 .145

p-value

Panel 4b  5  6  7  8

Panel 3b  9 10 11 12

Panel 2b 13 14 15

Panel 1b  9 10 11

Null

13 14 15 16

13 14 15 16

14 15 16

10 11 12

Alternative

Specifications under null and alternative hypotheses

48.2 18.7 26.9 34.2

22.2 2.7 1.4 0.8

11.8 46.6 9.7

31.3 47.9 10.3

Chi-square

2 2 2 2

1 1 1 1

1 1 1

1 1 1

Degrees of freedom

.000 .000 .000 .000

.000 .100 .237 .383

.001 .000 .002

.000 .000 .001

p-value

Note: The model specifications under the null and alternative hypotheses that are compared in each test are identified by their code numbers, as listed in Table 3.8. Panels 1a and 2a report tests for the significance of the zero-inflated parameters in the double Poisson and bivariate Poisson specifications. Panels 3a and 3b report tests for the interdependence parameter in the bivariate Poisson and bivariate negative binomial specifications. Panels 4a and 4b report tests for the significance of the overdispersion parameter in the double and bivariate binomial specifications.

Alternative

Null

Specifications under null and alternative hypotheses

Table 3.9 Hypothesis tests for comparisons between fitted double and bivariate Poisson and negative binomial distributions, home- and away-team goals data, English league, 1982–2009 seasons

Sequences and persistence in match results

69

Table 3.10 Longest runs of consecutive results, English league, 1970–2009 seasons Matches without a loss Arsenal Nottm Forest Chelsea Reading Bristol Rovers Liverpool Arsenal Leeds Utd

49 42 40 33 32 31 30 30

Consecutive losses Sunderland Walsall Brighton & Hove Albion Brighton & Hove Albion Carlisle Utd Barnet MK Dons Stoke City West Bromwich Albion

17 15 12 12 12 11 11 11 11

End-month

Consecutive wins

End-month

Oct-04 Nov-78 Oct-05 Feb-06 Jan-74 Mar-88 Oct-02 Feb-74

Arsenal Newcastle Utd Reading Charlton Athletic Fulham Liverpool Luton Town Manchester Utd

End-month

Matches without a win

End-month

Aug-03 Feb-89 Jan-73 Oct-02 Dec-03 Oct-93 Mar-04 Aug-85 Dec-95

Derby County Cambridge Utd Hull City Oxford Utd Newport County Rochdale

Aug-08 Apr-84 Nov-89 Aug-88 Jan-71 Aug-74

14 13 13 12 12 12 12 12

36 31 27 27 25 25

Aug-02 Oct-92 Oct-85 Mar-00 Oct-00 Oct-90 Apr-02 Aug-00

Source: Rothmans/Sky Sports Football Yearbook

Dobson and Goddard (2003), using English league match results data for seasons 1970–1999 (inclusive). This section presents an update of this earlier study, using data to the end of the 2009 season. Table 3.10 reports the longest sequences of consecutive results in the league match results data set between the 1970 and 2009 seasons inclusive, based on four criteria:  (i) matches without a win; (ii) matches without a loss; (iii) consecutive wins; and (iv) consecutive losses. For the purposes of counting sequences of consecutive results, breaks between seasons are ignored. Table 3.11 reports empirical unconditional and conditional match result probabilities, where conditioning is on the duration of various preceding sequences of consecutive similar results. The first row reports the unconditional home and away probabilities for a win (columns (1) and (2)), a win or draw ((3) and (4)), a loss ((5) and (6)) and a loss or draw ((7) and (8)). Of the 81,258 matches in the data set, 38,775 were home wins, 22,426 were draws and 20,057 were away wins. Therefore 0.477 = 38775/81258 is the unconditional home win probability (column (1)), and so on. Subsequent rows of Table 3.11 report the conditional probabilities that each result represents a ‘reversal’ of a previous sequence of consecutive ‘identical’

70

Competitive balance and home-field advantage

Table 3.11 Empirical unconditional and conditional match result probabilities Probability of a win, conditional on n = number of previous consecutive matches without a win

Probability of a win or draw, conditional on n = number of previous consecutive losses

Probability of a loss, conditional on n = number of previous consecutive matches without a loss

Probability of a loss or draw, conditional on n = number of previous consecutive wins

n

Home (1)

Away (2)

Home (3)

Away (4)

Home (5)

Away (6)

Home (7)

Away (8)

 0  1  2  3  4  5  7 10 15 20

0.477 0.465 0.451 0.438 0.433 0.422 0.409 0.396 0.344 0.346

0.247 0.236 0.228 0.219 0.216 0.212 0.202 0.190 0.177 0.163

0.753 0.731 0.715 0.695 0.686 0.670 0.611 — — —

0.523 0.494 0.474 0.456 0.442 0.415 0.413 — — —

0.247 0.232 0.222 0.210 0.199 0.191 0.168 0.132 0.114 0.086

0.477 0.464 0.449 0.438 0.423 0.406 0.387 0.344 0.303 0.294

0.523 0.496 0.478 0.460 0.451 0.424 0.382 — — —

0.753 0.738 0.716 0.693 0.663 0.646 0.583 — — —

Source: Rothmans/Sky Sports Football Yearbook

results, conditioning on the type and duration of the sequence. Two types of reversal are considered. First, a sequence of wins and draws is reversed by a loss; and a sequence of losses is reversed by a win or draw. Second, a sequence of wins is reversed by a draw or loss; and a sequence of draws and losses is reversed by a win. These two types of reversal are ‘WD|L reversals’ and ‘W|DL reversals’, respectively. Columns (3) to (6) of Table 3.11 show the conditional probabilities for WD|L reversals; and columns (1), (2), (7) and (8) show the conditional probabilities for W|DL reversals. For the purpose of calculating these probabilities, the results of any cup, European or friendly matches played within a sequence of league matches are ignored. So too are the venues (home or away) of the matches comprising the sequence of prior matches. The conditional probabilities themselves, however, are specific to the venue of match in question. For example, the conditioning for the home win probabilities in column (1) is on the number of previous consecutive matches without a win (the number of previous matches drawn or lost). The home team had failed to win its four most recent matches in 15,260 of the 81,258 matches in the data set. This figure includes cases in which the sequence without a win was longer than four matches. In 6,610 of

Sequences and persistence in match results

71

these 15,260 matches, the match result was a home win, implying a W|DL reversal. Therefore 0.433 = 6,610/15,260 is the home win probability conditional on the home team having played at least four consecutive matches without a win, prior to the match in question.4 Table 3.11 shows that the conditional probabilities of a good result (however defined) tend to decline with the duration of an unsuccessful spell, and the conditional probabilities of a poor result decline with the duration of a successful spell. Without further investigation, however, it would be incorrect to attribute this pattern to a positive persistence effect. The pattern in the conditional probabilities might be explained by the variation between teams in their relative quality or playing strength. The calculation of the win probability conditional on a long spell without a win, for example, is based mainly on the experience of weaker teams, whose win probability is below average because they are weak, but not specifically because they have not won recently. In other words, the pattern in the conditional probabilities reported in Table 3.11 might be explained by a team heterogeneity effect. Therefore any test for persistence in sequences of match results needs to control for heterogeneous team strengths. Below, a Monte Carlo analysis is used to test for persistence effects. In the absence of any persistence effects, it is assumed that the following statistical model would accurately represent the distribution of match results in each season in each tier. According to this model, the result of the match between home team i and away team j is generated as follows: Home win(k = 2) if Draw (k = 1) if Away win (k = 0) if

µ 2 < y*i,j + ε i,j µ1 < y*i,j + ε i,j < µ 2 y*i,j + ε i,j < µ1 

[3.15]

where y*i,j = αi  – αj; αi and αj are parameters reflecting the quality or playing strengths of team i and team j; μ1 and μ2 are additional parameters, known as ‘cut-off parameters’; and εi,j ~ N(0,1) is a random disturbance term, which follows a standard Normal distribution (with zero mean and variance of one). The disturbance term represents the unsystematic or random element in the result of the match between teams i and j. Table 3.12 illustrates the correspondence between the final league table and the estimated parameters of [3.15] for T1 (the Premier League) in the 2009 season. The ordering of the teams reflects the final league table, obtained by awarding three league points for a win and one for a draw. Table 3.12 also reports each team’s win percent, obtained by awarding 1 for each win and 0.5 for each draw, and dividing the total by 38 (the number of matches played by each team). Table 3.12 also reports each team’s α ˆ i for the 2009 season, with the parameter for the bottom-placed team, West Bromwich Albion, set to zero.

72

Competitive balance and home-field advantage

Table 3.12 League table, Premier League, 2009 season, and ordered probit team quality parameter estimates Won

Drawn

Lost

League points

Win ratio

αˆ i

28 25 25 20 17 17 14 14 14 15 12 12 11 10 10 9 8 7 7 8

 6 11 8 12 12 11 11 9 9 5 9 9 8 11 11 9 11 13 11 8

4 2 5 6 9 10 13 15 15 18 17 17 19 17 17 20 19 18 20 22

90 86 83 72 63 62 53 51 51 50 45 45 41 41 41 36 35 34 32 32

.8158 .8026 .7632 .6842 .6053 .5921 .5132 .4868 .4868 .4605 .4342 .4342 .3947 .4079 .4079 .3553 .3553 .3553 .3289 .3158

1.6534 1.4863 1.3943 1.1348 .8941 .8372 .6379 .5685 .5622 .4771 .3757 .3944 .2242 .3004 .2744 .1556 .1808 .1809 .0685 .0000

Manchester United Liverpool Chelsea Arsenal Everton Aston Villa Fulham Tottenham Hotspur West Ham United Manchester City Wigan Athletic Stoke City Bolton Wanderers Portsmouth Blackburn Rovers Sunderland Hull City Newcastle United Middlesbrough West Bromwich Albion

Cut-off parameters:  ˆμ1 = –.7119  μˆ 2 = .0250

Illustrative fitted match result probabilities Home win Liverpool v Middlesbrough Middlesbrough v Liverpool Aston Villa v Blackburn Rovers Blackburn Rovers v Aston Villa Manchester City v Wigan Athletic Wigan Athletic v Manchester City All matches (average)

0.673 0.309 0.563 0.417 0.501 0.480 0.455

Draw

Away win

0.209 0.285 0.252 0.284 0.269 0.274 0.255

0.118 0.406 0.185 0.299 0.230 0.246 0.290

The estimates of μ1 and μ2 are shown at the foot of Table 3.12, together with illustrative fitted match result probabilities. The latter are calculated using: ˆ 2 − ˆy i,j ) P(home win) = 1 − Φ(µ *

P(draw)

*

*

ˆ 2 − yˆ i,j ) − Φ(µ ˆ 1 − yˆ i,j ) = Φ( µ *

ˆ 1 − yˆ i,j ) P(away win) = Φ(µ



[3.16]

Sequences and persistence in match results

73

where Φ is the distribution function for the standard Normal distribution; and * ˆi − α ˆ j . The values of the cut-off parameters μˆ 1 and μˆ 2 allow for home-field yˆi,j = α advantage. The examples illustrate the implications of variations in  αˆ i and αˆ j for the home win, draw and away win probabilities. The Monte Carlo simulations enable comparisons to be drawn between the observed numbers of reversals in the data set (as defined above), and the numbers of reversals that should be obtained if [3.15] is the statistical model that describes correctly the distribution of match results if there is no persistence effect. Two test statistics are used to test for persistence effects: the first is based on the number of WD|L reversals; and the second is based on the number of W|DL reversals. In each case, the test statistic is τ = total number of match results divided by total number of reversals. If the observed value of τ is similar to its expected value obtained from the Monte Carlo simulations, the null hypothesis of no persistence cannot be rejected. If the observed τ is significantly higher than its expected value, reversals occur less frequently than they should occur if the null hypothesis is true. In this case the null hypothesis is rejected in favour of an alternative hypothesis of positive persistence. Conversely, if the observed τ is significantly lower than its expected value, reversals occur more frequently than they should when the null hypothesis is true. In this case the null hypothesis is rejected in favour of an alternative hypothesis of negative persistence. The approach is similar in principle to the well-known runs test (Mood, 1940), which investigates the randomness of sequences of positive or negative increments to a time series. Mood used analytic methods to derive asymptotic sampling distributions for the numbers of ‘runs’ (sequences of consecutive positive or negative increments) expected under the randomness assumption, based on the binomial distribution. In the present case, simulation rather than analytic methods are used, because the expected numbers of reversals depend on the degree of inequality in the team strength parameters within each tier, and therefore vary between tiers and between seasons. The greater is the degree of inequality, the easier it is for a strong team to sustain a sequence of good results (and the harder it is for a weak team to break a sequence of poor results), and so the smaller is the expected number of reversals. Fort and Rosenman (1999) apply the runs test directly to sequences of match results in MLB to test for the presence of ‘streaks’. Since there are no draws, match results are binary and the runs test is directly applicable. Each team is tested separately. The test controls for the quality of the team being tested (via the overall win percentage), but in contrast to the present analysis there is no control for variation in the quality of the opposition team. To generate the expected mean durations of sequences of consecutive results under the null hypothesis of zero persistence, 160 sets of ordered probit estimates of the parameters of [3.15] are obtained. Using the actual fixture calendars as originally completed, a computer program then generates a complete set of simulated match results for the full 40-season period, under the assumption of zero

74

Competitive balance and home-field advantage

Table 3.13 Simulated unconditional and conditional match result probabilities Probability of a win, conditional on n = number of previous consecut­ive matches without a win

Probability of a win or draw, conditional on n = number of previous consecutive losses

Probability of a loss, conditional on n = number of previous consecut­ive matches without a loss

Probability of a loss or draw, conditional on n = number of previous consecutive wins

n

Home (1)

Away (2)

Home (3)

Away (4)

Home (5)

Away (6)

Home (7)

Away (8)

0 1 2 3 4 5 7 10 15 20

0.477 0.461 0.444 0.428 0.415 0.403 0.382 0.356 0.317 0.284

0.247 0.230 0.217 0.206 0.197 0.189 0.175 0.158 0.135 0.116

0.753 0.731 0.707 0.684 0.663 0.642 0.598 0.537 ­— —

0.523 0.489 0.462 0.439 0.417 0.396 0.357 0.303 — —

0.247 0.231 0.218 0.206 0.195 0.185 0.167 0.145 0.120 0.102

0.477 0.462 0.444 0.427 0.411 0.396 0.368 0.333 0.290 0.258

0.523 0.488 0.455 0.425 0.397 0.373 0.333 0.288 — —

0.753 0.730 0.701 0.671 0.644 0.618 0.573 0.518 — —

persistence, by substituting randomly drawn values of εi,j ~ N(0,1) into [3.15]. This exercise is repeated 5,000 times, in order to generate 5,000 sets of simulated match results each of which covers the entire 40-season period. Table 3.13 reports match result probabilities conditional on each result representing a reversal of a previous sequence of consecutive results, calculated from the Monte Carlo simulations based on an assumption of no persistence. A comparison between these simulated conditional probabilities and the observed conditional probabilities reported in Table 3.11 (and allowing for occasional random variation in the latter) confirms that the actual probability of a reversal occurring is higher than the simulated probability under assumptions of no persistence. In order to test the null hypothesis that there is no persistence effect, for each of the 5,000 sets of simulated match results the test statistic τ (=number of matches ÷ number of reversals) is calculated for each of the two types of reversal. By examining the sampling distributions of the two sets of 5,000 simulated τ, critical values are established, leading to the acceptance or rejection of the null hypothesis of no persistence. The persistence tests are carried out using the data for all forty seasons from 1970 to 2009, and using the same data subdivided into eight subperiods of five seasons each: seasons 1970–1974, 1975–1979 and so on through to 2005–2009. Table 3.14 reports the results of these tests. The upper panel shows the results for WD|L reversals, and the lower panel shows the results for W|DL reversals.

2.182 2.200 2.151 2.149 2.175 2.178 2.165 2.211 2.229

matches played to W|DL reversals 2.219 2.220 2.223 2.248 2.251 2.258 2.202 2.206 2.215 2.192 2.196 2.205 2.216 2.221 2.228 2.220 2.225 2.232 2.249 2.253 2.262 2.261 2.266 2.274 2.276 2.281 2.289

Sequences of wins or sequences without a win: ratio of 1970–2009 2.199 2.203 2.204 1970–1974 2.193 2.201 2.205 1975–1979 2.151 2.158 2.162 1980–1984 2.138 2.147 2.151 1985–1989 2.162 2.170 2.174 1990–1994 2.166 2.174 2.178 1995–1999 2.192 2.201 2.206 2000–2004 2.204 2.213 2.217 2005–2009 2.217 2.227 2.230

p99.5 2.197 2.228 2.184 2.153 2.203 2.173 2.205 2.216 2.215

p97.5

Sequences without a loss or sequences of losses: ratio of matches played to WD|L reversals 1970–2009 2.194 2.197 2.198 2.213 2.215 2.217 1970–1974 2.191 2.198 2.202 2.245 2.250 2.258 1975–1979 2.147 2.155 2.159 2.201 2.205 2.213 1980–1984 2.135 2.142 2.146 2.187 2.191 2.198 1985–1989 2.160 2.168 2.171 2.213 2.217 2.225 1990–1994 2.163 2.171 2.175 2.216 2.220 2.228 1995–1999 2.187 2.196 2.200 2.242 2.246 2.255 2000–2004 2.198 2.205 2.208 2.252 2.257 2.265 2005–2009 2.207 2.215 2.219 2.262 2.266 2.275

p95.0

τ

p5.0

p0.5

p2.5

Actual

Monte Carlo simulations

Table 3.14 Tests for persistence in sequences of consecutive match results

.0000 .0428 .0104 .0836 .1112 .0948 .0000 .0368 .0792

.0556 .7284 .7480 .3152 .3988 .0764 .2216 .2964 .0528

p-value

76

Competitive balance and home-field advantage

The columns headed p0.5, p2.5, p5.0, p95.0, p97.5, p99.5 show the 0.5, 2.5, 5, 95, 97.5 and 99.5 percentiles of the sampling distributions of the test statistic τ under the null hypothesis of no persistence, obtained from the Monte Carlo simulations.5 Accordingly, a 95 per cent confidence interval for τ under the null hypothesis of no persistence, based on the results for WD|L reversals, is given by (2.197, 2.215). The null hypothesis is rejected at a significance level of 5 per cent if τ falls outside this range. Similarly, a 99 per cent confidence interval for τ is given by (2.194, 2.217). The null hypothesis is rejected at a significance level of 1 per cent if τ falls outside this range. The final two columns of Table 3.14 report the actual values of τ, and the corresponding p-values. The p-value is the minimum significance level at which the null hypothesis of no persistence can be rejected. In the results based on computations over the entire forty-season period, for WD|L reversals, τ = 2.197 falls just inside the lower bound of the 95 per cent confidence interval, but outside the lower bound of the 90 per cent confidence interval (p-value = .0556). The null hypothesis of no persistence cannot be rejected at the 5 per cent significance level; but the null is rejected at the 10 per cent level. For W|DL reversals, however, τ = 2.182 falls outside the lower bounds of both the 95 per cent and the 99 per cent confidence intervals (p-value = .0000). In this case the null hypothesis of zero persistence is rejected, in favour of an alternative of negative persistence, at any significance level. W|DL reversals occur more frequently than is expected if the null hypothesis is true. In the results based on computations for five-season subperiods, the pattern is similar. For WD|L reversals, the null hypothesis of no persistence is not rejected at the 5 per cent level for any of the eight five-year subperiods. The null hypothesis is rejected at the 10 per cent level for two of the eight periods. For W|DL reversals, in contrast, the null hypothesis of no persistence is not rejected at the 5 per cent level for four of the eight five-year subperiods. The null hypothesis is rejected at the 10 per cent level for seven of the eight sub­periods. In all cases where the null is rejected, τ is lower than is expected if the null hypothesis is true. The number of reversals is therefore higher than is expected if the null hypothesis is true. Overall the results indicate that sequences of match results are subject to statistically significant, negative persistence effects. On average, sequences of consecutive wins and sequences of consecutive matches without a win tend to end sooner than they would if there were no statistical association between the results of consecutive matches after controlling for heterogeneous team strengths. There is, however, an element of asymmetry in the pattern. The average duration of sequences of matches unbeaten is higher than the average duration of sequences without a win; and the average duration of sequences of losses is higher than the average duration of sequences of wins. Accordingly, the evidence of a negative persistence effect in the data on W|DL reversals is stronger than it is in the data on WD|L reversals.

Sequences and persistence in match results

77

Finally, Dobson and Goddard (2003) point out that the procedure described above is valid if the assumption of no variation in the team strength parameters within each season is correct. A difficulty arises, however, if this assumption is incorrect, because the actual and expected numbers of reversals are sensitive to these parameters. If there is within-season variation in the team strength parameters αi in [3.15], the expected numbers of reversals are somewhat lower than in the case where there is no variation, and the persistence test described above is biased towards detection of a positive persistence effect. This suggests that rejection of the null hypothesis of no persistence in favour of an alternative of negative persistence is a particularly strong result. If there is within-season variation in the team strength parameters, this test tends to be biased in the opposite direction. Conclusion

Chapter 3 has investigated a number of empirical regularities in football match results data. The problem of measuring competitive balance or competitive inequality within a sports league has attracted considerable attention in the academic sports economics literature in recent years. Researchers have applied several measures of concentration or inequality, some of which are borrowed from industrial economics, to sports teams’ win ratio or league points data. Popular measures include unadjusted and adjusted standard deviations, the Lorenz curve and the Gini coefficient, the Herfindahl index, and various concentration ratios. Some studies measure competitive inequality directly, by means of an analysis of the probabilities for individual match results. The sources of home-field advantage in any sport are difficult to identify or quantify empirically, but can be classified broadly as follows: familiarity with the home team’s stadium and facilities; disruption to the away team’s preparation due to the need to travel; crowd effects on either the home team (encouragement) or the away team (intimidation) or the match officials (pressure for decisions favouring the home team); and (in some sports) rules favouring the home team. English football has witnessed a reduction in the importance of home-field advantage between the 1970s and the 2000s, which appears to be partially but not entirely explained by the switch from the award of two to three league points for a win in the early 1980s. Several variants of the Poisson distribution and the negative binomial distribution provide a good description of the distributional properties of football match results data presented in scores format. The greater flexibility of the negative binomial distribution in allowing for overdispersion is useful in describing the unconditional distributions of goals scored by the home and away teams (unconditional in the sense that controls for team quality are not included). Positive correlation between the goals scored by the home and away teams may be represented by means of either bivariate distributions, which include a correlation parameter; or

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Competitive balance and home-field advantage

diagonal-inflated distributions, which make adjustments to the probabilities of low-scoring draws. Finally, the phenomenon of persistence in sequences of consecutive football match results is investigated by means of a Monte Carlo analysis, which involves comparing the actual numbers of ‘reversals’ of sequences of consecutive results, with the numbers expected if there were no persistence. A comparison between the simulation results and forty years of English match results data provides evidence of a negative persistence effect. Notes 1 For example, regulations in baseball concerning the order in which the home and away teams’ innings take place. 2 Beyond team sports, Balmer, Nevill and Williams (2001) report a highly significant homefield advantage in the Olympic Games, affecting event groups that were either subjectively judged or reliant on subjective decisions (boxing and gymnastics). In contrast, little or no home-field advantage was observed in two objectively judged event groups (athletics and weightlifting). The nature of the officiating system was found to be key to both the existence and extent of home-field advantage. 3 In Chapter 4, however, a forecasting model for match results and goals is developed, based on the explicit formula for the bivariate Poisson distribution. 4 The conditional probabilities in the other columns of the upper panel of Table 3.11 are calculated in the same way. The probabilities are not reported in cases where there were fewer than fifty sequences of the required duration on which to base the calculation. This limit is breached for sequences of consecutive wins and consecutive losses (columns (3), (4), (7) and (8)) of duration greater than (about) eight matches. 5 In the simulations for WD|L reversals for the period 1970–2009, for example, the first row of Table 3.14 shows that 0.5 per cent of the simulated τ were below 2.194 (and 99.5 per cent of the simulated τ were above 2.194); 2.5 per cent of the simulated τ were below 2.197 (and 97.5 per cent were above); and so on. At the opposite end of the range of values for τ, 97.5 per cent of the simulated τ were below 2.215 (and 2.5 per cent were above); 99.5 per cent of the simulated τ were below 2.217 (and 0.5 per cent were above); and so on.

4

Forecasting models for football match results

Introduction

Chapter 4 describes the estimation and application of goals-based and resultsbased forecasting models for match outcomes in football, recorded in the form of either goals scored and conceded by the two teams, or in the form of ‘windraw-lose’ match results. Both types of forecasting model are estimated by fitting regression models to past match results data. A diagonal-inflated bivariate Poisson regression is used for the goals-based model, and an ordered probit regression is used for the results-based model. Both models draw on an extensive set of covariates, reflecting past goal-scoring performance and match results over the preceding 24 calendar months, the significance of the match for end-of-­season championship, promotion or relegation outcomes, the current involvement of the teams in the FA Cup or European tournaments, the average attendances attracted by both teams, and the geographical distance between the home stadia of the two teams. Section 4.1 reviews the previous academic literature on modelling the outcomes of football matches. Section 4.2 describes the specification and estimation of a goals-based match results forecasting model. Section 4.3 describes the use of the goals-based model to generate out-of-sample forecasts, in probabilistic form, for either goals or ‘win-draw-lose’ match results. Sections 4.4 and 4.5 describe the estimation and application of a results-based forecasting model. Finally Section 4.6 draws some comparisons between the forecasting performance of the goalsbased and results-based models, and between the probabilities generated by these models and a set of implied probabilities derived from the quoted odds (prices) of a selection of high-street and internet bookmakers for fixed-odds betting on match results. 4.1  Previous literature on modelling and forecasting match results in football

There are two distinct strands of empirical literature on modelling the outcomes of matches in football. The first approach, favoured by many applied statisticians, 79

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involves modelling the numbers of goals scored and conceded in each match directly. Once such a model has been estimated, forecasts of win-draw-lose match results may be derived indirectly, by aggregating the estimated probabilities assigned to appropriate permutations of goals scored and conceded by the two teams. A second approach, favoured by some applied econometricians, involves modelling win-draw-lose results directly, using discrete choice regression models such as ordered probit or ordered logit. A win-draw-lose match results data set is effectively ‘nested’ within a goals data set: the result of a match is established from the goals scored by the two teams, but the match result by itself does not indicate the numbers of goals scored. Therefore any direct comparison between the forecasting capabilities of the two types of model must be based on forecasts of match results:  while goals-based models can forecast goals and results, results-based models forecast results only. One possible prior hypothesis is that a goals-based model should outperform a results-based model, because the former draws on a more extensive data set than the latter. On the other hand, given that league points are awarded for results and not for goals (with goals relevant only for separating teams with equal points totals), insofar as they determine league points, wins of 1–0 or 6–3 are of equal value. Therefore goals data might contain more noise than results data. In a goals-based model, the choice of distributional assumptions and the treatment of the problem of interdependence between the goals scored by the two teams are complex issues, which are avoided when discrete choice regression is used to model match results directly. Accordingly, a results-based model might be expected to outperform a goals-based model, on the grounds that the model selection and specification issues are more straightforward. In the academic literature, a number of studies model match results data for football. Early contributions by Moroney (1956) and Reep, Pollard and Benjamin (1971) use the Poisson and negative binomial distributions to model the distributions of the numbers of goals scored per game, along similar lines to the analysis that is reported in Chapter 3, Section 3.3. The aggregated approach adopted, however, precludes the generation of specific forecasts for individual matches based on information about the respective strengths of the two teams concerned. By comparing final league placings with experts’ pre-season forecasts, Hill (1974) demonstrates that individual match results do nevertheless have a predictable element, and are not determined solely by chance. Maher (1982) develops a model in which the home- and away-team scores follow independent Poisson distributions, with means which are the product of parameters reflecting the attacking and defensive capabilities of the two teams. If H denotes the goals scored by home team i and A the goals scored by away team j, the respective probability functions are: P(H = h) = exp( − α iβ j ) (α iβ j )h /h! and P(A = a) = exp( − γ i δ j ) (γ i δ j )a /a ! where αi and βj reflect the attacking capability of team i at home and the defensive capability of team j away, and γi and δj reflect the defensive capability of team i at

Literature on modelling and forecasting results

81

home and the attacking capability of team j away. Tests show that γi and δi can be regarded as proportional to βi and αi respectively, so it is only necessary to estimate one set of attacking and one set of defensive parameters for each team. This can be done ex post, after the full set of match results has been observed, using maximum likelihood methods. The model does not predict scores or results ex ante. Although goodness-of-fit tests show that the model provides a reasonably accurate approximation to the data, separate examination of the observed and expected distributions of the difference between the scores of the two teams reveals a tendency to underestimate the proportion of drawn matches. This is attributed to interdependence between the scores of the home and away teams, and is corrected by modelling scores using a bivariate Poisson distribution. The marginal distributions are the same as before, but allowance is also made for positive correlation between the home- and away-team scores in each match. Dixon and Coles (1997) employ Maher’s (1982) modelling approach for different ends: they seek to develop a forecasting model capable of generating ex ante match outcome probabilities. Instead of using the bivariate Poisson distribution, the marginal Poisson probabilities for the scores of both teams in lowscoring games (H≤1 and A≤1) are adjusted directly to allow for interdependence, which, as already seen, appears to be greatest towards the top-left-hand corners of Tables 3.4 and 3.5. For forecasting purposes, estimation of the vectors of αi and βj must be based on historical data only. This is achieved using a pseudo­likelihood function, in which the attacking and defensive parameters are estimated from past scores, weighted by a factor that declines exponentially over time. Each team’s parameters are updated from match to match, as the scores from the most recently completed matches enter the estimation. Graham and Stott (2008) apply a similar estimation strategy to an ordered probit regression for match results. Dynamic team-strength parameters for each team are estimated using a likelihood function in which the contribution of past results decays exponentially, with the rate of decay determined by maximising the model’s predictive capability in a holdout sample. Dixon and Pope (2004) compare probabilistic forecasts obtained from the Dixon-Coles model with probabilities inferred from UK bookmakers’ prices for fixed-odds betting. Using a forecasting approach similar to that of Dixon-Coles, Rue and Salvesen (2000) allow the attacking and defensive parameters for all teams to vary randomly over time. The estimates of these parameters are updated as new data on match outcomes are obtained. Markov chain Monte Carlo iterative simulation techniques are used for inference. Crowder et al. (2002) propose a procedure for updating the team strength parameters that is computationally less demanding than the method proposed by Rue and Salvesen. Koning’s (2000) approach to the modelling of match results describes a collection of match results retrospectively, instead of generating forecasts or estimated probabilities prospectively. Koning advocates modelling results directly, rather than indirectly through scores, partly on grounds of simplicity: fewer parameters

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Forecasting models for football match results

are required, the estimation procedures are more straightforward, and the specified ordered probit model lends itself quite easily to the inclusion of dynamics or other explanatory variables. Karlis and Ntzoufras (2003) apply a variety of bivariate Poisson models to the task of modelling goal scoring in football matches. In addition to the double and bivariate Poisson distributions, and diagonal-inflated versions of the latter, a Poisson difference distribution is also considered, in which the dependent variable is the difference between the scores of the home and away teams. Using data from Italy’s Serie A from a single season, Karlis and Ntzoufras estimate an unconditional model, and a model in which the expectations of the goals scored by each team are conditional on a limited number of team characteristics. Bittner et al. (2007) compare the use of the negative binomial distribution and several generalised extreme value distributions (Weibull, Gumbel and Frechet) to describe the distribution of goals scored per match. The outcome for each match is interpreted as the product of a self-affirmation process, in which the probability that either team scores within each microscopic interval within the match (for example, within each minute) depends on the number of goals it has scored previously. The form of the adaptation relation, which describes the evolution of the scoring probabilities over time, determines the shape of the distribution for the total number of goals per match. The adaptation relation accommodates various types of feedback effect:  for example, a team that has scored previously draws encouragement and is more likely to score again; or a team that is leading plays defensively in order to protect its lead, and is less likely to score again. Assumptions concerning the adaptation relation are identified that generate a negative binomial distribution or a generalised extreme value distribution for the total goals scored per match.1 The next four sections describe the specification and estimation of forecasting models for match results expressed in either ‘win-draw-lose’ format, or ‘scores’ format, and the application of the estimated models to obtain probabilistic forecasts for scores or results in out-of-sample matches. The two types of forecasting model are referred to as the goals-based model, which is described in Sections 4.2 and 4.3; and the results-based model, described in Sections 4.4 and 4.5. An early prototype of the results-based model is reported in Dobson and Goddard (2001) and is developed subsequently in Goddard and Asimakopoulos (2004). Goddard (2005) draws comparisons between the forecasting performance of goals-based and results-based models with specifications similar to those reported in this chapter. 4.2  A goals-based forecasting model

The bivariate Poisson distribution provides a convenient representation of a data set in which each observation (match) generates two discrete goals-scored variables, for the home and away teams, respectively. Let λ1,i,j denote the mathematical expectation of the number of goals scored by the home team in the fixture

A goals-based forecasting model

83

between home team i and away team j. Similarly, let λ2,i,j denote the mathematical expectation of the number of goals scored by the away team in the same fixture. In the model, it is assumed that λ1,i,j and λ2,i,j are both linear functions of a set of covariates, which are defined using data that are available before the match is played. Let, SHi,0(=CAj,0) and CHi,0(=SAj,0) denote the goals scored and the goals conceded by home team i, respectively (identical to the goals conceded and the goals scored by away team j). Following Holgate (1964), the bivariate Poisson joint probability function for SHi,0 and CHi,0 takes the form: P(SHi,0 = s,C Hi,0 = c) = exp( − λ1,i,j − λ 2,i,j + λ 3,i,j ) ×

min(s,c)

∑

k /{(s − k)!(c − k)!k!} (λ1,i,j − λ 3,i,j )s − k (λ 2,i,j − λ 3,i,j )c − k λ 3,i,j

k=0

for s = 0,1,2,3,4 … and c = 0,1,2,3,4 …



[4.1]

where exp( ) denotes the exponential function:  exp(x) = ex = 2.71828x; and k! denotes ‘k-factorial’:  0! = 1, 1! = 1, 2! = 2×1, 3! = 3×2×1, 4! = 4×3×2×1, and so on. This joint probability function can be interpreted as the product of three univariate Poisson probability functions with means λ1,i,j–λ3,i,j, λ2,i,j–λ3,i,j and λ3,i,j, respectively. λ1,i,j, the expected number of goals scored by the home team, depends on covariates reflecting the propensities of home team i to score and away team j to concede goals. Similarly λ2,i,j, the expected number of goals scored by the away team, depends on covariates reflecting the propensities of away team j to score and home team i to concede goals. Finally, λ3,i,j = η λ1,i,j λ 2,i,j is the covariance between SHi,0 and CHi,0. η is an additional parameter to be estimated, for which a positive value (η>0) is expected. Preliminary experimentation with the estimation of [4.1] indicated a tendency for the bivariate Poisson regression to underestimate slightly the probabilities for low-scoring draws. Accordingly, [4.1] can be modified by introducing additional parameters, which inflate the (unadjusted) probabilities of low-scoring draws, and deflate all of the other (unadjusted) probabilities, so that the adjusted probabilities sum to one. Experimentation suggested that inflation of the probabilities of 0–0, 1–1 and 2–2 draws is justified. The diagonal-inflated formulation of the bivariate Poisson probability function, containing three additional parameters π, θ1 and θ2, is as follows:   H = s,C H = c) P(S i,0 i,0 = (1 − π 0 )P(SHi,0 = s,C Hi,0 = c) + π 0 (1 − π1 − π 2 ) for{s,c} = {0,0} H H H H  P(S = s,C = c) = (1 − π )P(S = s,C = c) + π π for{s,c} = {1,1} i,0

i,0

0

i,0

i,0

0

1

 H = s,C H = c) = (1 − π )P(SH = s,C H = c) + π π P(S 0 0 2 i,0 i,0 i,0 i,0 H H H H  P(Si,0 = s,C i,0 = c) = (1 − π 0 )P(Si,0 = s,C i,0 = c)

for{s,c} = {2,2} for{s,c} ≠ {0,0},{1,1},{2,2} [4.2]

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Forecasting models for football match results

where P �(SHi,0 = s, CHi,0 = c) denotes the adjusted probability (and P(SHi,0 = s, CHi,0 = c) denotes the unadjusted probability) that the home team scores s goals and ­concedes c goals. The full list of covariate definitions used in the calculation of λ1,i,j and λ2,i,j is as follows. d d d Fi,y,s = fi,y,s /ni,y, where fi,y,s = team i’s total goals scored in matches played 0–12 months (y = 0) or 12–24 months (y = 1) before current match; within the current season (s = 0) or previous season (s = 1) or two seasons ago (s = 2); in the team’s current tier (d = 0) or one (d = ±1) or two (d = ±2) tiers above or below the current tier; and ni,y = team i’s total matches played 0–12 months (y = 0) or 12–24 months (y = 1) before current match. d d d Ai,y,s = ai,y,s /ni,y, where ai,y,s = team i’s total goals conceded, defined for the same y,s,d as above; ni,y defined as above. SHi,k = goals scored in k’th most recent home match by team i, for k = 1, …,9. CHi,k = goals conceded in k’th most recent home match by team i, for k = 1, …,9. SAi,k, CAi,k = goals scored and conceded in k’th most recent away match by team i, for k = 1, … 4. H S j,k, CHj,k = goals scored and conceded in k’th most recent home match by team j, for k = 1, … 4. SAj,k, CAj,k = goals scored and conceded in k’th most recent away match by team j, for k = 1, … 9. SIGHi,j = 1 if match is significant for championship, promotion or relegation issues for home team i but not for away team j; 0 otherwise. SIGAi,j = 1 if match is significant for away team j but not for home team i; 0 otherwise. CUPi = 1 if team i is eliminated from the FA Cup; 0 otherwise. EUINi = 1 if team i is involved in European competition during the current season, and has not yet been eliminated; 0 otherwise. EUOUTi = 1 if team i has been involved in European competition during the current season, and has been eliminated; 0 otherwise. DISTi,j = natural logarithm of the geographical distance between the grounds of home team i and away team j. APi,s = residual for team i from a cross-sectional regression of the natural logarithm of average home attendance on final league position (defined on a scale of 92 for the top team in T1 to 1 for the bottom team in T4) s seasons before the present season, for s = 1,2. d9700, d0104 and d0508 are 0–1 dummy variables identifying matches played in seasons 1997–2000, 2001–2004 and 2005–2008, respectively. CUPj, EUINj, EUOUTj, APj,s are defined as above, for team j.

Table 4.1 reports the numerical values of the estimated coefficients in the linear equations for λ1,i,j and λ2,i,j, and the four additional parameters η, π0, π1 and π2 ,

.3576 .5175 .3629 .2326 .2125 .1318 .0995 .1286 .1958 .1532 .1544 −.0324 .4277 .2797 .3622 .4805 .0634 .1108 .3049 −.0852 .0781 .1096 .1997 .2965

.000 .000 .000 .000 .003 .005 .019 .617 .004 .001 .000 .693 .000 .000 .000 .000 .153 .020 .000 .494 .062 .020 .004 .103

SHi,1 SHi,2 SHi,3 SHi,4 SHi,5 SHi,6 SHi,7 SHi,8 SHi,9 SAi,1 SAi,2 SAi,3 SAi,4 CHj,1 CHj,2 CHj,3 CHj,4 CAj,1 CAj,2 CAj,3 CAj,4 CAj,5 CAj,6 CAj,7 CAj,8 CAj,9

p-val. Covar.

.0141 .0064 .0117 .0107 .0017 .0053 .0020 .0022 .0163 .0149 .0020 .0214 −.0011 .0111 .0086 .0143 .0123 .0147 .0083 .0101 .0036 .0029 .0027 .0103 .0084 .0057

Coeff. .016 .270 .044 .066 .767 .353 .735 .707 .005 .029 .763 .002 .866 .107 .206 .038 .069 .013 .156 .084 .533 .623 .645 .074 .148 .322

p-val. SIGHi,j SIGAi,j CUPi CUPj EUINi EUINj EUOUTi EUOUTj ΔAPi,1 APi,2 ΔAPj,1 APj,2 DISTi,j d9700 d0104 d0508 const.

Covar.

  .0927 −.1369 −.0996   .0468   .2102   .1650 −.1905 −.0568   .0649   .1183 −.1111 −.1446   .0327   .0055   .0036 −.0406 −.2220

Coeff. .035 .000 .000 .066 .000 .000 .000 .172 .055 .000 .001 .000 .000 .776 .853 .038 .008

0 Fj,0,0 F+1 j,0,1 0 Fj,0,1 F−1 j,0,1 F+1 j,1,1 0 Fj,1,1 F−1 j,1,1 F+2 j,1,2 F+1 j,1,2 0 Fj,1,2 F−1 j,1,2 F−2 j,1,2 0 Ai,0,0 A+1 i,0,1 0 Ai,0,1 A−1 i,0,1 A+1 i,1,1 0 Ai,1,1 A−1 i,1,1 A+2 i,1,2 A+1 i,1,2 0 Ai,1,2 A−1 i,1,2 A−2 i,1,2

.3426 .2807 .4005 .6204 .1208 .1456 .2354 −.0566 .1694 .1641 .1853 .1076 .3121 .3455 .1922 .1073 .0513 .0317 .0406 .1710 .1356 .1249 .0979 .0188

p-val. Covar. Coeff. .000 .000 .000 .000 .001 .000 .000 .546 .000 .000 .002 .498 .000 .000 .000 .005 .393 .423 .251 .458 .017 .002 .004 .787

p-val. CHi,1 CHi,2 CHi,3 CHi,4 CHi,5 CHi,6 CHi,7 CHi,8 CHi,9 CAi,1 CAi,2 CAi,3 CAi,4 SHj,1 SHj,2 SHj,3 SHj,4 SAj,1 SAj,2 SAj,3 SAj,4 SAj,5 SAj,6 SAj,7 SAj,8 SAj,9

.0119 .0036 .0175 .0030 .0002 −.0123 .0101 −.0004 −.0010 .0064 .0081 .0080 .0050 .0061 .0121 .0091 .0018 .0213 .0032 .0084 −.0012 −.0026 .0120 .0085 .0138 .0025

Covar. Coeff. .042 .533 .003 .609 .969 .032 .080 .949 .865 .197 .103 .106 .321 .214 .014 .065 .721 .000 .580 .146 .828 .653 .038 .135 .016 .664

SIGHi,j SIGAi,j CUPi CUPj EUINi EUINj EUOUTi EUOUTj ΔAPi,1 APi,2 ΔAPj,1 APj,2 DISTi,j d9700 d0104 d0508 const.

p-val. Covar.

Equation for λ2,i,j (expectation of away goals)

Ancillary parameters:  ˆη = .0403 (p-value = .000) πˆ 0  = .0224 (p-value = .000) πˆ 1 = .5816 (p-value = .000) πˆ 2 = .1623 (p-value = .000)

0 Fi,0,0 F+1 i,0,1 0 Fi,0,1 F−1 i,0,1 F+1 i,1,1 0 Fi,1,1 F−1 i,1,1 F+2 i,1,2 F+1 i,1,2 0 Fi,1,2 F−1 i,1,2 F−2 i,1,2 0 Aj,0,0 A+1 j,0,1 0 Aj,0,1 A−1 j,0,1 A+1 j,1,1 0 Aj,1,1 A−1 j,1,1 A+2 j,1,2 A+1 j,1,2 0 Aj,1,2 A−1 j,1,2 A−2 j,1,2

Covar. Coeff.

Equation for λ1,i,j (expectation of home goals)

Table 4.1 Goals-based forecasting model: estimated coefficients and p-values

−.0928 .1077 .0202 −.0141 −.0729 −.0322 .1453 .0769 −.1690 −.1396 .0840 .0842 −.0266 .0101 .0212 −.0358 −.1105

Coeff.

.004 .004 .343 .514 .013 .356 .000 .050 .000 .000 .003 .000 .000 .541 .201 .032 .123

p-val.

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Forecasting models for football match results

estimated using data for seasons 1993 to 2008, inclusive. The coefficient values are estimated using 32,552 match result observations for all matches played in T1–T4 of the Premier League and the Football League. In addition to the match results from these sixteen seasons, data from the two preceding seasons (1991 and 1992), and data from the non-league division immediately below T4 (known as the Conference, to and from which either zero, one or two T4 teams were relegated and promoted per season), are used in the construction of the covariates used in the estimation. In the goals-based model, the average goals scored and goals conceded varid d ables Fi,y,s and Ai,y,s (for team i and their counterparts for team j), calculated over the 24 months prior to the current match, are the main indicators of attacking d d and defensive capability, or team quality. Positive coefficients on Fi,y,s and Ai,y,s are expected. It is assumed that team i’s propensity to score is captured by its +1

0 d + ∑ Fi,0,1 average scoring rate over the previous 12 months, Fi,0,0 , and its average d = -1

+1

+2

d = -1

d = -2

d d scoring rate between 12 and 24 months ago,  ∑ Fi,1,1 . The individual + ∑ Fi,1,2

components of these sums make separate contributions to the attacking and defensive capability measures. For example, if the current-season scoring rate is a better indicator of the team’s current attacking capability than the previous-season scoring rate in the same division within the same 0 12-month period, the coefficient on Fi,0,0 should (and does) exceed the coeffi0 d d d cient on Fi,0,1. Each of the sets of covariates, Ai,y,s , Fj,y,s and Aj,y,s plays a similar role in identifying the attaching and defensive capabilities of team i and team j, using data from preceding matches. The estimated coefficients on all of these variables are predominantly correctly signed and well defined. The recent goals scored and conceded variables SHi,k, SAi,k, CHi,k and CAi,k (and their counterparts for team j) allow for the inclusion of goals data from the few most recent matches of both teams. The possibility of short-term persistence in team performance suggests these variables may have particular relevance in helping predict the outcome of the current match, over and above their contribution to d d d d the average goals scored and conceded covariates Fi,y,s , Ai,y,s , Fj,y,s and Aj,y,s . In general, however, the estimated coefficients on the recent goals scored and conceded covariates tend to be rather erratic. Data on the home team’s recent home performance are found to be more useful as predictors than data on its recent away performance; and similarly the away team’s recent away performance is more useful than its recent home performance. Accordingly, data are included from the home team’s last nine home matches and last four away matches, and from the away team’s last four home matches and last nine away matches. The identification of matches with significance for end-of-season championship, promotion and relegation issues is relevant if match outcomes are affected by incentives. If a match is significant for one team and insignificant for the other, the

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teams may contribute different levels of effort. Of several alternative definitions of significance that were considered, the chosen algorithm produces the match significance dummies with the most explanatory power. A match is significant if it is possible (before the match is played) for the team in question to qualify automatically for entry into European club competition the following season (for teams near the top of T1) or be promoted or relegated (for teams near the bottom of T1, and for teams in T2, T3 and T4), assuming all other teams currently in contention for the same end-of-season outcome take one point on average from each of their remaining fixtures. The signs and significance of the estimated coefficients on SIGHi,j and SIGAi,j are predominantly consistent with incentive effects as described above. The FA Cup is a sudden-death knockout tournament involving both league and non-league teams. Teams from T3 and T4 enter the cup in the first round, and teams from T1 and T2 enter in the third round. The final is played at the end of the league season. Early elimination from the cup might have implications for a team’s performance in subsequent league matches, though the direction of the effect is uncertain. A team eliminated from the cup may be able to concentrate its efforts on the league, suggesting an improvement in league performance. Alternatively, elimination may reduce confidence (while progress fosters team spirit), suggesting a decline in league performance. The signs and significance of the estimated coefficients on CUPi and CUPj suggest that the second of these two effects dominates. Teams that finish in the top few positions in T1, and teams that are successful in the two major domestic cup tournaments (the FA Cup and the League Cup), are eligible to compete in European club competition during the following season. Until the end of the 1999 season, there were three European club tournaments; but subsequently this number was reduced to two, known (until the end of the 2009 season) as the Champions League and the UEFA Cup. Between the 1993 and 2009 seasons, the number of English participants in the two or three European club tournaments was never less than five and never more than nine. The proportion of matches that involve teams that participated in European club competition in the same season is therefore small; though the matches concerned, involving the most successful teams, are naturally the subject of disproportionate media scrutiny. The signs and significance of the estimated coefficients on EUINi, EUOUTi, EUINj and EUOUTj suggest that current involvement in European competition has a positive effect on league performance; while involvement earlier in the current season (curtailed by elimination prior to the date of the current league fixture) has an effect that is less pronounced, but still positive. The coefficients on DISTi,j indicate that geographical distance is a significant influence on match outcomes. The signs and significance of the estimated coefficients on DISTi,j suggest home advantage is stronger in matches between teams whose home stadia are located long distances apart, and weaker in matches between teams whose stadia are located near one another. The greater intensity of

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competition in local derbies may have some effect in offsetting home-field advantage, while the psychological or practical difficulties of long-distance travel for teams and supporters may increase home-field advantage in matches between teams from distant cities. Finally, the covariates APi,s and APj,s are positive for teams that tend to attract higher-than-average home attendances after controlling for league position (and negative in the opposite case). These covariates allow for a ‘big team’ effect on match outcomes: regardless of the values of other controls, ‘big’ teams are more likely (and ‘small’ teams less likely) to win, either through the direct influence of the crowd on the outcome, or because teams with a larger revenue base have more resources to spend on players. To reduce the effect of temporary variation in the attendance-performance relationship, the values of these variables for the two preceding seasons are included in the model. Since the values over successive seasons tend to be highly correlated, ΔAPi,1 = APi,1–APi,2 (and its counterpart for team j) is used in place of APi,1 (and APj,1). 4.3  Probabilistic forecasts for match results in ‘scores’ format

For each fixture for which match result probabilities are required, the model evaluates the mathematical expectations of the goals scored by the home and away teams. These are obtained using a linear combination of a set of covariate values based on past match results and other data for the two teams, and a set of coefficients that are estimated using all observations in the match results database and reported in Table 4.1. Once the mathematical expectations of the goals scored by the home and away teams have been calculated, these expectations are substituted into a modified version of the bivariate Poisson joint probability function in order to obtain probabilities for each specific match result. For expositional purposes, it is convenient to break down the task of calculating the probabilities for a forthcoming fixture into a number of steps, as follows: 1. Calculation of the numerical values of the model’s covariates for the fixture for which probabilities are required. 2. Calculation of the expectations of the numbers of goals scored by the home and away teams. 3. Conversion of the expectations of goals scored into a set of probabilities for each specific match result. The structure and layout of Section 4.3 follows these three steps. Calculation of the numerical values of the model’s covariates

The calculation of the numerical values for each of the covariates will be explained using (as an illustration) the T1 (Premier League) Hull City vs Tottenham Hotspur

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Table 4.2 Data for calculation of average goals scored and conceded covariates, Hull City vs Tottenham Hotspur fixture Tier

Matches played

Goals for

Goals against

Match result ‘points’

Hull City 2009 season, before 23/02/09 2008 season, after 23/02/08 2008 season, before or on 23/02/08 2007 season, after 23/02/07

T1 T2 T2 T2

25 13 33 13

31 24 41 18

46 10 37 19

11.0 8.5 18.5 6.0

Tottenham Hotspur 2009 season, before 23/02/09 2008 season, after 23/02/08 2008 season, before or on 23/02/08 2007 season, after 23/02/07

T1 T1 T1 T1

25 12 26 11

26 18 48 25

31 20 41 15

9.5 5.5 12.0 8.5

Note: Match result ‘points’ are awarded 1 for a win, 0.5 for a draw, 0 for a loss. Source: Sky Sports Football Yearbook

fixture from the 2009 season, played on 23 February 2009. It is helpful to note that all i-subscripts on variables refer to Hull City, and all j-subscripts refer to Tottenham Hotspur. (i) Average goals scored and conceded over past 12 months d d The covariates Fi,y,s and Ai,y,s (and their counterparts for team j) are the model’s d main team quality controls. For the Hull–Tottenham fixture, Fi,y,s (averages of the goals scored by Hull over the past 24 months, partitioned by time period, d season and division) and Aj,y,s (averages of the goals conceded by Tottenham over the past 24 months, partitioned in the same way) are used in the equad tion for λ1,i,j. Similarly, Fj,y,s (averages of the goals scored by Tottenham) d and Ai,y,s (averages of the goals conceded by Hull) are used in the equation for λ2,i,j. Table 4.2 reports the data for the calculation of the average goals scored and conceded covariates for the Hull–Tottenham fixture. Using these data, Hull’s covariate values are as follows: F0 = 31 /( 25 + 13) = 0.8158 A 0 = 46 /( 25 + 13) = 1.2105 i,0,0

i,0,0

-1 Fi,0,1 = 24 /( 25 + 13) = 0.6316 A -1i,0,1 = 10 /( 25 + 13) = 0.2632 -1 Fi,1,1 = 41 /(33 + 13) = 0.8913 A -1i,1,1 = 37 /(33 + 13) = 0.8043 -1 Fi,1,2 = 18 /(33 + 13) = 0.3913 A -1i,1,2 = 19 /(33 + 13) = 0.4130

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Tottenham’s covariate values are as follows: 0 Fj,0,0 = 26 /( 25 + 12 ) = 0.7027 0 Fj,0,1 = 18 /( 25 + 12 ) = 0.4865 0 Fi,1,1 = 48 /( 26 + 11) = 1.2973 0 Fj,1,2 = 25 /( 26 + 11) = 0.6757

A 0j,0,0 A 0j,0,1 A 0j,1,1 A 0j,1,2

= 31 /( 25 + 12 ) = 0.8378 = 20 /( 25 + 12 ) = 0.5405 = 41 /( 26 + 11) = 1.1081 = 15 /( 26 + 11) = 0.4054



d d d d Zero values are assigned to Fi,y,s , Ai,y,s , Fj,y,s and Aj,y,s for all permutations of values for d, y and s that are not applicable for the current fixture. Hull’s goals scored ratio (average goals scored per match) over the 12 months 0 -1 prior to the Hull–Tottenham fixture is Fi,0,0 + Fi,0,1 = 1.4474. Similarly, Hull’s goals scored ratio over the period 12–24 months prior to the Hull–Tottenham fixture is -1 -1 d d d d Fi,1,1 + Fi,1,2 = 1.2826 . Effectively, the definitions of Fi,y,s (and of Ai,y,s , Fj,y,s and Aj,y,s ) partition these ratios into components relating to the current season (s = 0), the previous season (s = 1) and two seasons ago (s = 2), and into components relating to the team’s current tier (d = 0), one tier above or below the team’s current tier (d = ±1) and two tiers above or below the team’s current tier (d = ±2). The partitioning enables each component of the team’s goals ratios to make different contributions to the evaluation of the expectations of the goals scored and conceded for the current fixture. For example, the coefficients that are reported in Table 4.1 attach more weight to goals scored in the current season than to goals scored in the previous season, or to goals scored two seasons ago. Goals scored in a higher tier carry more weight than goals scored in the team’s current tier, which in turn carry more weight than goals scored in a lower tier.

(ii)  Goals scored and conceded in the two teams’ most recent matches The covariates SHi,m and CHi,m (goals scored and conceded in home team i’s m’th most recent home match), SAi,n and CAi,n (goals scored and conceded in home team i’s n’th most recent away match), and their counterparts for away team j, allow for the inclusion of each team’s few most recent home and away results in the calculation of the expectations of the goals scored and conceded by both teams in the d d current fixture. These covariates also contribute towards the values of Fi,y,s , Ai,y,s (and their counterparts for team j), and are to some extent correlated with these covariates. By including the goals scored and conceded in each of the teams’ most recent matches as separate covariates, however, greater flexibility is achieved in the use of past match results data to predict future results. Experimentation indicated that data from the home team’s recent home matches are more useful as predictors than data from its recent away matches; and similarly data from the away team’s recent away matches are more useful than data from its recent home matches. Accordingly, data from the home team’s nine most recent home matches, and from the home team’s last four most recent away matches are used. Similarly, data from the away team’s four most recent home matches, and from the away team’s nine most recent away matches are used.

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Table 4.3 Data for calculation of goals scored and conceded in recent matches covariates, Hull City vs Tottenham Hotspur fixture Hull City

Tottenham Hotspur

Last nine home results (most recent first)

Last four away results

Last four home results

Last nine away results

D 2–2 L 1–3 L 0–1 L 1–4 W 2–1 D 2–2 L 0–1 L 0–3 W 1–0

D 0–0 L 0–2 L 0–2 L 1–5 — — — — —

D 0–0 W 3–1 D 1–1 D 0–0 — — — — —

L 2–3 L 0–1 L 0–2 L 1–2 W 2–0 L 1–2 W 2–1 D 4–4 L 1–2

Source: Rothmans/Sky Sports Football Yearbook

For the Hull–Tottenham fixture, SHi,k and SAi,k (goals scored by Hull in recent home and away matches) and CHj,k and CAj,k (goals conceded by Tottenham) are used in the equation for λ1,i,j. Similarly, CHi,k and CAi,k (goals conceded by Hull) and SHj,k and SAj,k (goals scored by Tottenham) are used in the equation for λ2,i,j. Table 4.3 reports the data for the calculation of the goals scored and conceded in recent matches covariates for the Hull–Tottenham fixture. Using these data, the covariate values are as follows: Hull City:        SHi,1 = 2, CHi,1 = 2; SHi,2 = 1, CHi,2 = 3; … ; SHi,9 = 1, CHi,9 = 0 SAi,1 = 0, CAi,1 = 0; SAi,2 = 0, CAi,2 = 2; … ; SAi,4 = 1, CAi,4 = 5 Tottenham Hotspur:   SHj,1 = 0, CHj,1 = 0; SHj,2 = 3, CHj,2 = 1; … ; SHj,4 = 0, CHj,4 = 0 SAj,1 = 2, CAj,1 = 3; SAj,2 = 0, CAj,2 = 1; … ; SAj,9 = 1, CAj,9 = 2 (iii)  Significance of the match for end-of-season outcomes The covariates SIGHi,j and SIGAi,j control for the likelihood that match outcomes are affected by incentives: if a fixture is significant for one team and insignificant for the other, the incentive differential is likely to influence the match result. The algorithm used to assess whether or not a fixture is significant is as follows: the fixture is significant if it is still possible (before the match is played) for the team in question to win the championship or be promoted or relegated, assuming that all other teams currently in contention for the same outcome take one point on average from each of their remaining fixtures. In T1, the teams that finish fifth and higher qualify automatically to play in European club competition in the following season, and the teams that finish eighteenth and lower are relegated. Therefore for the Hull–Tottenham fixture,

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the algorithm assesses whether it is still possible for either team to finish fifth (or higher) or eighteenth (or lower), assuming the teams currently in those positions take one point from each of their remaining fixtures. On the morning of 23 February 2009, Hull were thirteenth in T1 with 29 points from 25 matches; Arsenal were fifth with 45 points from 26 matches; Tottenham were sixteenth with 25 points from 25 matches; and Blackburn were eighteenth with 23 points from 25 matches (with 38 matches to be played in total by each team). The algorithm establishes that the Hull–Tottenham fixture is significant for both teams. Therefore SIGHi,j = 0 and SIGAi,j = 0. (iv)  Involvement of teams in FA Cup and European competition Early elimination from the FA Cup or from Europe may have implications for a team’s results in subsequent league matches in either direction. On the one hand, a team eliminated from the cup or from Europe may be able to concentrate its efforts on the league, suggesting an improvement in league results. On the other hand, elimination may cause loss of confidence, suggesting a deterioration in league results. On 23 February 2009, Hull were currently involved in the fifth round of the FA Cup; but Tottenham had already been eliminated. Hull did not participate in European competition during the 2009 season; but on 23 February 2009 Tottenham were currently involved in the third round of the UEFA Cup.2 Accordingly, for the Hull–Tottenham fixture: CUPi = 0; CUPj = 1; EUINi = 0; EUOUTi = 0; EUINj = 1; EUOUTj = 0 (v)  Geographical distance The greater intensity of competition in local derbies may have some effect in offsetting home-field advantage in such matches, while the difficulties of longdistance travel for the away team and its supporters may have the effect of increasing home-field advantage in matches between teams from opposite ends of the country. The geographical distance (as the crow flies, and based on map references) between the grounds of Hull City and Tottenham Hotspur is 152 miles. The covariate DISTi,j is the natural logarithm of this number:  DISTi,j = ln(152) = 5.0239. (vi)  Average attendance relative to league position over previous two seasons The covariates APi,s and APj,s are positive for teams that tend to attract higherthan-average home attendances after controlling for league position (and negative in the opposite case). These covariates allow for a ‘big team’ effect on match outcomes: regardless of the values of other controls, ‘big’ teams may be more likely (and ‘small’ teams less likely) to win, either through the direct influence of the crowd on the match result, or because teams with a larger revenue base have more resources to spend on players. To reduce the effect of temporary variation in the attendance-performance relationship, the values of these variables for the two preceding seasons are included in the model.

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To calculate these covariates for the Hull–Tottenham fixture, cross-sectional regressions of the natural logarithm of each team’s average home attendance (denoted LNATT) on each team’s final league position (denoted POS) are estimated, using data for all 116 teams that played in the Premier League, the Football League and the top non-league division during the 2007 season, and again during the 2008 season. The estimation results are as follows: 2007 season: LNATT = 7.0624 + 0.0311 POS + RESID 2008 season: LNATT = 6.9694 + 0.0323 POS + RESID APi,1 and APi,2 are the values of the residuals (denoted RESID) from these regressions for Hull for the 2007 and 2008 seasons, respectively. Similarly, APj,1 and APj,2 are the values of the residuals for Tottenham for the same two seasons. The data for the calculation of these covariates for the Hull–Tottenham fixture are as follows: Hull City:      2007 season average attendance = 18,758; position = 76      2008 season average attendance = 18,025; position = 94 Tottenham Hotspur: 2007 season average attendance = 35,739; position = 112 2008 season average attendance = 35,967; position = 106 The covariate values for the Hull–Tottenham fixture are as follows: APi,1  = ln(18025) – 6.9694 – 0.0323 × 94 = –0.2060 APi,2  = ln(18758) – 7.0624 – 0.0311 × 76 = 0.4134 ΔAPi,1 = –0.2060 – 0.4134 = –0.6194 APj,1  = ln(35967) – 6.9694 – 0.0323 × 106 = 0.0972 APj,2   = ln(35739) – 7.0624 – 0.0311 × 112 = –0.0616 ΔAPj,1 = 0.0978 – –0.0622 = 0.1600 Calculation of the mathematical expectations of the goals scored by the home and away teams

Once the numerical values of all covariates have been calculated, the expectations of the goals scored by the home and away teams (λ1,i,j and λ2,i,j) are obtained by substituting the covariate values into the two linear equations whose coefficients are reported in Table 4.1. The mathematical expectations of the goals scored by the home and away teams are obtained by combining these coefficients with the numerical values of the covariates for the fixture in question. In total, there are sixty-three covariates (and a constant term and dummy variables for three four-season periods) on the righthand sides of each of these equations. Algebraic expressions for the equations for λ1,i,j and λ2,i,j are as follows:

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Expectation of home team’s goals: 0 0 -1 +1 λ1,i,j = (α 0 + α 66 d0508) + α1Fi,0,0 + α 2 Fi,0,1 + α 3Fi,0,1 + α 4 Fi,0 ,1 + … + α 63 DISTi,j



Expectation of away team’s goals: 0 0 -1 +1 λ 2,i,j = (β0 + β66 d0508) + β1Fj,0,0 + β2 Fj,0,1 + β3Fj,0,1 + β 4 Fj,0 ,1 + … + β63 DISTi,j



For the Hull–Tottenham fixture: λ1,i,j = [ −0.2220 + ( −0.0406 × 1)] + ( 0.3576 × 0.8158) + ( 0.5175 × 0 ) + ( 0..3629 × 0 ) + ( 0.2326 × 0.6316 ) +  + ( 0.0327 × 5.0239) = 1.3347 λ 2,i,j = [ −0.1105 + ( −0.0358 × 1)] + ( 0.3426 × 0.7027 ) + ( 0.2807 × 0 ) + ( 0.3982 × 0.4005) + ( 0.6204 × 0 ) +  + ( −0.0266 × 5.0239) = 1.5198



Conversion of expectations of goals scored into match result probabilities

The estimated coefficients reported in Table 4.1 are used in conjunction with equations [4.1] and [4.2] to convert the numerical values of λ1,i,j and λ2,i,j into a grid containing probabilities for individual scores. For the Hull–Tottenham fixture, λ1,i,j = 1.3347 and λ2,i,j = 1.5198. The ancillary parameters are η = 0.0403, π0 = 0.0224, π1 = 0.5816, π2 = 0.1623. This implies: λ 3,i,j = η λ1,i,j λ 2,i,j = 0.0403 × 1.3347 × 1.5198 = 0.0572 − λ1,i,j − λ 2,i,j + λ 3,i,j = −2.7974 exp( − λ1,i,j − λ 2,i,j + λ 3,i,j ) = exp( −2.7974 ) = 0.0610 λ1,i,j − λ 3,i,j = 1.2776 λ 2,i,j − λ 3,i,j = 1.4627 To illustrate the application of equations [4.1] and [4.2], the calculation of the adjusted bivariate Poisson probability for a score of Hull 2 Tottenham 3 is shown in full below. Using [4.1], the unadjusted bivariate Poisson probability is: P(SHi,0 = 2, C Hi,0 = 3) = exp( − λ1,i,j − λ 2,i,j + λ 3,i,j ) ×

min( 2 ,3 )

∑ k=0

k /{( 2 − k )!(3 − k )! k !} ( λ1,i,j − λ 3,i,j )2 − k (λ 2,i,j − λ 3,i,j )3 − k λ 3,i,j 2

= 0.0610 × ∑ 1.27762 − k1.46273 − k 0.0572k /{( 2 − k )!(3 − k )! k !} k=0

= 0.0610 × [1.27762 × 1.46273 × 0.05720 /{2 !×3 !× 0 !} + 1.27761 × 1.46272 × 0.05721 /{1!× 2 !×1!} + 1.27760 × 1.46271 × 0.05722 /{0 !×1!× 2 !}]] = 0.0309 Using [4.2], the adjusted bivariate Poisson probability is:  (SH = 2, C H = 3) = (1 − π )P(SH = s, C H = c ) = (1 − 0.0224 ) × 0.0309 = 0.0301 P 0 i,0 i,0 i,0 i,0



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Table 4.4 Estimated match result probabilities, Hull City vs Tottenham Hotspur fixture Away goals → Home goals ↓ 0 1 2 3 4 5 6 7

0

1

2

3

4

5

6

7

.0663 .0756 .0472 .0196 .0061 .0015 .0003 .0001

.0894 .1281 .0740 .0317 .0102 .0026 .0006 .0001

.0670 .0875 .0615 .0255 .0084 .0022 .0005 .0001

.0325 .0443 .0301 .0136 .0046 .0012 .0003 .0001

.0120 .0168 .0117 .0055 .0019 .0005 .0001 —

.0035 .0051 .0037 .0017 .0006 .0002 — —

.0009 .0013 .0009 .0005 .0002 — — —

.0002 .0003 .0002 .0001 — — — —

Table 4.4 shows the full set of adjusted bivariate Poisson probabilities for the Hull–Tottenham fixture. 4.4  A results-based forecasting model

The description of the results-based forecasting model starts by introducing the notation that is used for the dependent variable. Each match represents one observation in the data set, and the dependent variable can be defined, without any loss of generality, for the match between home team i and away team j. Let RHi,k denote the result of team i’s k’th most recent home match from team i’s perspective, coded 1 for a win, 0.5 for a draw and 0 for a defeat. k = 0 refers to the current match (the match between home team i and away team j); and integer values of k>0 refer to team i’s previous home matches (k = 1 is team i’s last home match, before the match with team j; k = 2 is team i’s last-but-one home match; and so on). In an ordered probit regression model, match results in win-draw-lose format are used as the dependent variable. Accordingly, the dependent variable in the ordered probit regression model is RHi,0. Let RAj,0 denote the result of team j’s k’th most recent away match, defined in the same way but from team j’s perspective. Accordingly, RAj,0 = 1 − RHi,0. It is assumed that the result of the match between team i and team j depends upon an unobserved or latent variable denoted yi,j* ; and an independent and identically distributed disturbance term, εi,j, which follows the standard Normal distribution. Home win: RHi,0 = 1 if µ 2 < y*i,j + ε i,j Draw: RHi,0 = 0.5 if µ1 < y*i,j + ε i,j < µ 2 Away win: RHi,0 = 0 if y*i,j + ε i,j < µ1

[4.3]

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The latent variable yi,j* is assumed to be a linear function of a set of covariates, which are defined using data that are available before the match is played. The full list of covariate definitions used in the calculation of yi,j* is as follows. d d d = pi,y,s /ni,y, where pi,y,s = team i’s total ‘points’ score (calculated by awarding Pi,y,s 1 ‘point’ for a win, 0.5 ‘points’ for a draw and 0 ‘points’ for a loss) in matches played 0–12 months (y = 0) or 12–24 months (y = 1) before the current match; within the current season (s = 0) or previous season (s = 1) or two seasons ago (s = 2); in the team’s current tier (d = 0) or one (d = ±1) or two (d = ±2) tiers above or below the current tier; and ni,y = team i’s total matches played 0–12 months (y = 0) or 12–24 months (y = 1) before the current match. d d d Pj,y,s = pj,y,s /nj,y, where pj,y,s is team j’s total ‘points’ score, and nj,y = team j’s total matches played (both defined as above). RHi,k = result of team i’s k’th most recent home match (coded 1 for a win by team i, 0.5 for a draw and 0 for a loss) for k = 1, …,9. RAi,k = result of team i’s k’th most recent away match (coded 1 for a win by team i, 0.5 for a draw and 0 for a loss) for k = 1, …,4. H R j,k defined as above for team j, for k = 1, …,4. RAj,k defined as above for team j, for k = 1, …,9. SIGHi,j, SIGAi,j, CUPi, CUPj, EUINi, EUOUTi, EUINj, EUOUTj, DISTi,j, APi,s, APj,s, d9700, d0104, d0508 are all as defined in Section 4.2.

Table 4.5 reports the numerical values of the estimated coefficients in the linear equation for yi,j* , estimated using data for the seasons 1993–2008, inclusive. d In the results-based model, the average match results ‘points’ variable Pi,y,s for d team i, and its counterpart Pj,y,s for team j, calculated over the 24 months prior to the current match, are the principal indicators of team quality. These covariates are similarly defined, and play a similar role, to the goals scored and conceded covariates, SHi,m, CHi,m, SAi,n and CAi,n, in the goals-based model. The indexing of these variables allows for separate contributions to the team quality measures from ‘points’ gained in matches played: 0–12 months (y = 0) or 12–24 months (y = 1) before the current match; within the current season (s = 0) or previous season (s = 1) or two seasons ago (s = 2); and in the team’s current tier (d = 0) or one (d = ±1) or two (d = ±2) tiers above or below the current tier. d d Positive coefficients on Pi,y,s and negative coefficients on Pj,y,s are expected. It is assumed that the quality of team i is captured by its average ‘points’ score over the +1

0 d + ∑ Pi,0,1 , previous 12 months, equivalent to its win ratio over this period, Pi,0,0 d = -1

and its average ‘points’ score or win ratio between 12 and 24 months ago, +1

+2

d = -1

d = -2

d d . The individual components of these sums make separate contri+ ∑ Pi,1,2 ∑ Pi,1,1

butions to the team quality measures. For example, if the current-season win ratio is a better indicator of the team’s current quality than the previous-season’s win 0 ratio in the same division within the same 12-month period, the coefficient on Pi,0,0

p-value .000 .000 .000 .000 .000 .000 .000 .561 .072 .003 .000 .707 .000 .000 .000 .000 .000 .000 .003 .076 .001 .000 .002 .261

Coefficient

1.6727 1.9362 1.1905 .7283 .8169 .6193 .4572 .4563 .3555 .3723 .3975 .0757 −1.2529 −1.1888 −.7697 −.4493 −.9749 −.6081 −.3275 −1.4198 −.6729 −.5134 −.3185 −.2332

Cut-off parameters:  ˆμ1 = –.3650 μˆ 2 = .3901

0 Pi,0,0 P+1 i,0,1 0 Pi,0,1 P−1 i,0,1 P+1 i,1,1 0 Pi,1,1 P−1 i,1,1 P+2 i,1,2 P+1 i,1,2 0 Pi,1,2 P−1 i,1,2 P−2 i,1,2 0 Pj,0,0 P+1 j,0,1 0 Pj,0,1 P−1 j,0,1 P+1 j,1,1 0 Pj,1,1 P−1 j,1,1 P+2 j,1,2 P+1 j,1,2 0 Pj,1,2 P−1 j,1,2 P−2 j,1,2

Covariate RHi,1 RHi,2 RHi,3 RHi,4 RHi,5 RHi,6 RHi,7 RHi,8 RHi,9 RAi,1 RAi,2 RAi,3 RAi,4 RHj,1 RHj,2 RHj,3 RHj,4 RHj,1 RAj,2 RAj,3 RAj,4 RAj,5 RAj,6 RAj,7 RAj,8 RAj,9

Covariate .0150 .0197 .0407 .0236 −.0050 −.0341 .0186 −.0123 .0148 .0036 .0202 .0286 −.0065 −.0384 −.0204 −.0271 −.0210 −.0498 −.0008 −.0315 −.0248 −.0088 −.0048 −.0235 −.0166 −.0478

Coefficient .349 .218 .011 .141 .756 .033 .245 .440 .355 .825 .208 .074 .687 .017 .205 .093 .192 .002 .961 .049 .121 .580 .763 .141 .299 .003

p-value

Table 4.5 Results-based forecasting model: estimated coefficients and p-values

SIGHi,j SIGAi,j CUPi CUPj EUINi EUOUTj EUINi EUOUTj ΔAPi,1 APi,2 ΔAPj,1 APj,2 DISTi,j d9700 d0104 d0508

Covariate .1222 −.1416 −.0643 .0318 .1607 .0714 −.1564 −.0034 .1935 .1565 −.1374 −.1558 .0437 .0110 −.0121 −.0472

Coefficient

.002 .000 .007 .184 .000 .095 .000 .935 .000 .000 .000 .000 .000 .544 .507 .010

p-value

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Forecasting models for football match results

0 should (and does) exceed the coefficient on Pi,0,1 . Predominantly, the estimated d d coefficients on the covariates Pi,y,s and Pj,y,s are correctly signed and well defined. d d Preliminary experimentation indicated that the coefficients on {Pi,y,s , Pj,y,s } were highly significant for y = 0,1 (data from matches played 0–12 months and 12–24 months before the current match); but not for y = 2 (24–36 months before the current match). The recent match results variables RHi,k and RAi,k, and their counterparts RHj,k and A R j,k for team j, allow for the inclusion of match results data from the most recent matches of both teams. The possibility of short-term persistence in team performance suggests these variables may have particular relevance in helping predict the outcome of the current match, over and above their contribution to the covariates d d {Pi,y,s , Pj,y,s }. In general, the estimated coefficients on the recent match results covariates tend to be rather erratic. Experimentation indicated that data on the home team’s recent home performance are more useful as predictors than data on its recent away performance; and similarly the away team’s recent away performance is more useful than its recent home performance. Statistically significant estimated coefficients are obtained for some (but not all) values of k≤9 for RHi,k and RAj,k, and for some n≤4 for RAi,k and RHj,k. Accordingly, data are included from the home team’s last nine home matches and last four away matches, and from the away team’s last four home matches and last nine away matches. The remaining covariates SIGHi,j, SIGAi,j, CUPi, CUPj, EUINi, EUOUTi, EUINj, EUOUTj, DISTi,j, APi,s, APj,s play the same role in the results-based forecasting model as in the goals-based model; and the patterns in the signs and significance of the coefficients on these covariates in Table 4.5 are similar to those in Table 4.1. See Section 4.2 for commentary on the contribution of these covariates to the model.

4.5  Probabilistic forecasts for match results in ‘win-draw-lose’ format

Section 4.5 provides a summary description of the use of the results-based forecasting model introduced in Section 4.4 to obtain probabilistic forecasts for match results in ‘win-draw-lose’ format. The method is similar in principle to the method for the goals-based model that is described in detail in Section 4.3 (and many of the covariate definitions are the same). Accordingly, the following description of the method for the results-based model is relatively concise. As before, the method is illustrated using the T1 Hull City vs Tottenham Hotspur fixture played on 23 February 2009. For each fixture for which ‘win-draw-lose’ probabilities are required, the model evaluates the latent variable yi,j* in [4.3]. yi,j* is a linear combination of a set of covariate values based on past match results and other data for the two teams, and a set of estimated coefficients.

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d In the results-based model, the past match results ‘points’ covariates Pi,y,s and P are the main team quality controls. Using the data reported in Table 4.2, the covariate values are as follows: 0 HullCity : Pi,0,0 = 11 /( 25 + 13) = 0.2895 -1 Pi,0,1 = 8.5 /( 25 + 13) = 0.22237 -1 Pi,1,1 = 18.5 /(33 + 13) = 0.4022 -1 Pi,1,2 = 6 /(33 + 13) = 0.1304 d j,y,s

0 Tottenham Hotspur: Pj,0,0 0 Pj,0,1 0 Pj,1,1 0 Pj,1,2

= 9.5 /( 25 + 12 ) = 0.2568 = 5.5 /( 25 + 12 ) = 0.1486 = 12 /( 26 + 11) = 0.3243 = 8.5 /( 26 + 11) = 0.2297

d d and Pj,y,s for all permutations of values for d, y and Zero values are assigned to Pi,y,s s that are not applicable for the current fixture. The covariates RHi,m and RAi,n (results of home team i’s m’th most recent home match for m = 1 … 9 and n’th most recent away match for n = 1 … 4), and their counterparts for away team j, allow each team’s few most recent home and away results to enter the calculation of yi,j* individually. Using the data reported in Table 4.3, the covariate values are as follows: HullCity: RH = 0.5;RH = 0;RH = 0;…;RH = 1 i,1

R = 0.5;R A i,1

i,2

A i,2

i,3

= 0;…;R

i,9

A i,4

=0

Tottenham Hotspur: RHj,1 = 0.5;RHj,2 = 1;…;RHj,4 = 0.5 RAj,1 = 0;RAj,2 = 0;RAj,3 = 0;…;RAj,9 = 0 The values for all of the remaining covariates SIGHi,j, SIGAi,j, CUPi, CUPj, EUINi, EUOUTi, EUINj, EUOUTj, DISTi,j, APi,s, APj,s are the same as those reported in Section 4.3, and the calculations are not repeated here. Once the numerical values of all covariates have been calculated, the latent variable yi,j* is evaluated by substituting the covariate values into the linear equation whose coefficients are reported in Table 4.5: 0 0 +1 -1 y*i,j = γ 1Pi,0,0 + γ 2 Pi,0,1 + γ 3 Pi,0,1 + γ 4 Pi,0,1 + … + γ 39 DISTi,j + γ 42 d0508 For the Hull–Tottenham fixture: y*i,j = (1.6727 × 0.2895) + (1.9362 × 0 ) + (1.1905 × 0 ) + ( 0.7283 × 0.2237)) +  + ( 0.0437 × 5.0239) + ( −0.0472 × 1) = 0.0100



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Forecasting models for football match results

To obtain the ‘win-draw-lose’ probabilities, the evaluated yi,j* and the estimated cut-off parameters μˆ 1 and μˆ 2 are substituted into a rearranged formulation of [4.3], as follows: ˆ 2 − yˆi,j* ) ˆ 2 − yˆi,j* ) = 1 − Φ (µ Home win probability = pi,jH = P(εi,j > µ ˆ 1 − yˆi,j* < εi,j < µ ˆ 1 − yˆi,j* ) ˆ 2 − yˆi,j* ) − Φ (µ ˆ 2 − yˆi,j* ) = Φ (µ = pi,jD = P(µ Draw probability ˆ 1 − yˆi,j* ) ˆ 1 − yˆi,j* ) = Φ (µ Away win probability = pi,jA = P(εi,j < µ [4.4]  where Φ( ) is the distribution function for the standard Normal distribution. For the Hull–Tottenham fixture, the match result probabilities in ‘win-draw-lose’ format are as follows: pH = 1 − Φ( 0.3901 − 0.0100 ) = 0.3519 i,j

pDi,j = Φ( 0.3901 − 0.0100 ) − Φ( −0.3650 − 0.0100 ) = 0.2942 pAi,j = Φ( −0.3650 − 0.0100 ) = 0.3538 4.6  Evaluation of the goals-based and results-based forecasting models

Section 4.6 provides an evaluation of the forecasting performance of the goals-based and results-based models. Table 4.6 reports the match result probabilities produced by both models for all ten T1 matches played over the same weekend as the 2009 season Hull City vs Tottenham Hotspur fixture (21–23 February 2009), together with probabilities for selected scores produced by the goals-based forecasting model. Table 4.6 also reports the averages of the implied match result probabilities calculated from the prices for fixed-odds betting quoted by six high-street and internet bookmakers. Let OHi,j denote a bookmaker’s odds for a home win in the match between team i and team j, quoted in decimal form. For example, OHi,j = 4 implies a bet of £1 placed on a home win pays £4 (£3 winnings plus return of £1 stake) if the bet wins. A fair bet would have expected winnings of zero, which is the case in this example if the probability of a home win is (1/OHi,j) = 1/4. Invariably, however, bookmakers’ odds contain a margin for costs and profit. This implies a deflation adjustment is required to calculate a set of bookmakers’ implied probabilities that sum to one. Let ODi,j and OAi,j denote the decimal odds for a draw and an away win. The implied probability for a home win is: oHi,j = (1/OHi,j )/{(1/OHi,j ) + (1/ODi,j ) + (1/O Ai,j )} 

[4.5]

The implied probabilities for a draw and an away win, denoted oDi,j and oAi,j, are similarly defined. Table 4.6 provides an indication of the typical degree of variation in the probabilities that are generated by the goals-based and result-based forecasting models, and the bookmakers’ implied probabilities. For several fixtures, such as Stoke vs Portsmouth, Middlesbrough vs Wigan, Fulham vs West Bromwich Albion and Newcastle vs Everton, the two forecasting models and the

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101

bookmakers were in close agreement. For other fixtures, however, there are some significant divergences. As shown above, the two forecasting models diverge in their assessment of the probabilities for the Hull vs Tottenham fixture. In this case the bookmakers’ implied probabilities split the difference between those of the models. For the evenly balanced Aston Villa vs Chelsea fixture, the bookmakers took a more pessimistic view than the models of the home team’s prospects. The bookmakers’ view was justified by the match result. For the highly unbalanced Manchester United vs Blackburn fixture, the home team were even stronger favourites according to the models than they were according to the bookmakers. The home team duly won the match, though only by a narrow margin. A convenient summary measure of forecasting performance over any number of matches, which can be applied to a set of probabilities generated by a forecasting model or to a set of bookmakers’ implied probabilities, is pseudo-R2, defined as the geometric mean of the probabilities assigned to the actual result of each matches played during the forecast period. Let πi denote the probability that was assigned to the actual result of match i, and let n denote the number of matches for which forecasts were generated. Equivalent formulae for pseudo-R2 are as follows: pseudo-R2 = (π1π 2 … π n )1/n

n

or

pseudo-R2 = exp[(1/n)∑ ln(π i )] 

[4.6]

i=1

Table 4.7 reports ten sets of pseudo-R2 values, each calculated over all matches played during the 2009 season. This measure is evaluated for the match results probabilities generated by the goals-based and results-based models, and for a ‘model consensus’ set defined as the averages of the probabilities generated by these two models. The pseudo-R2 measure is also evaluated for each of the six sets of bookmakers’ implied probabilities, and for a ‘bookmaker consensus’ set defined as the averages of the six sets of bookmaker probabilities. The results are reported separately by tier, and for all four tiers combined. The overall forecasting performance of the forecasting models and the bookmakers is rather similar, but there is some variation in the pattern by tier. For T1 and T3, the results-based model and the model consensus record higher pseudoR2 values than any of the six bookmakers. The performance of the goals-based model falls somewhere in the middle of the range for the six bookmakers. For T2 and T4, all six bookmakers record higher pseudo-R2 values than the forecasting models. Overall the bookmakers hold a narrow advantage, but the differences in forecasting performance appear to be very small. Chapter 12 presents a more detailed evaluation of the informational efficiency of the six bookmakers’ betting odds, and examines whether forecasting models of the kind developed in Chapter 4 can be employed to ‘beat the bookmaker’ and generate a positive return on fixed-odds betting.

.1026 .0646 .0811 .0271 .0351

Selected match scores probabilities: goals-based model 1–0 .1439 .0968 .1038 2–0 .1402 .0579 .0589 2–1 .0891 .0770 .0749 3–0 .0910 .0231 .0223 3–1 .0600 .0317 .0293 .1471 .1644 .0754 .1225 .0585

.3794 .2896 .3310

Implied match result probabilities: averages of six bookmakers Home .6555 .2958 .3959 .7452 Draw .2266 .2882 .2880 .1770 Away .1179 .4160 .3161 .0778

.3747 .2903 .3350

Stoke Portsmouth 17th 13th

.4099 .2911 .2990

Man Utd Blackburn 1st 18th

21/02

.8100 .1388 .0512

Bolton West Ham 14th 8th

21/02

Match result probabilities: results-based model Home .7462 .3771 .3260 Draw .1757 .2936 .2934 Away .0782 .3292 .3805

Aston Villa Chelsea 3rd 4th

21/02

.7729 .1727 .0544

Arsenal Sunderland 5th 10th

Home team Away team Home pos. Away pos.

21/02

Match result probabilities: goals-based model Home .6819 .3436 .3385 Draw .2175 .2901 .2982 Away .1006 .3663 .3633

21/02

Date

.1420 .0784 .0751 .0289 .0288

.3892 .2990 .3218

.3927 .2927 .3147

.3956 .3225 .2819

Middlesbro’ Wigan 20th 7th

21/02

.1138 .1009 .0966 .0596 .0589

.5223 .2714 .2063

.5507 .2606 .1888

.5674 .2490 .1836

Fulham WBA 11th 19th

22/02

.1254 .1063 .0951 .0601 .0555

.5989 .2528 .1483

.6527 .2217 .1255

.5647 .2563 .1790

Liverpool Man City 2nd 9th

22/02

.0930 .0510 .0709 .0187 .0268

.3281 .2888 .3831

.3047 .2917 .4036

.3066 .2915 .4018

Newcastle Everton 15th 6th

22/02

Table 4.6 Fitted match result and selected score probabilities, Premier League, weekend of 21–23 February 2009

.0756 .0472 .0740 .0196 .0317

.3325 .2830 .3845

.3519 .2942 .3538

.3131 .2717 .4152

Hull Tottenham 12th 16th

23/02

0–0

Match result

0–1

.0867 .1376 .0547 .1007 .0626 .0801 .0260 .0343 2–1

.0972 .1406 .0511 .1085 .0643 .0782 .0254 .0320 2–1

.0716 .0778 .0209 .0278 .0059 .0142 .0008 .0021

Source: Sky Sports Football Yearbook; www.football-data.co.uk

.0796 .1011 .0319 .0435 .0128 .0270 .0025 .0055

0–0 1–1 2–2 0–1 0–2 1–2 0–3 1–3 2–2

.0872 .1377 .0545 .0957 .0562 .0757 .0220 .0306 0–0

.1342 .1437 .0395 .1134 .0501 .0600 .0147 .0184 2–0

.0699 .1186 .0498 .0576 .0258 .0489 .0077 .0151 1–1

.0798 .1216 .0461 .0619 .0258 .0469 .0072 .0135 0–0

.0905 .1380 .0528 .1101 .0714 .0838 .0309 .0375 1–2

.0663 .1281 .0615 .0894 .0660 .0875 .0325 .0443

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Table 4.7 Pseudo-R-square values for forecasting performance, 2009 season: goalsbased forecasting model, and probabilities derived from six betting firms’ prices T1

T2

T3

T4

All

Forecasting models Goals-based Results-based Model consensus (average)

0.3827 0.3839 0.3836

0.3444 0.3440 0.3445

0.3533 0.3538 0.3539

0.3429 0.3429 0.3434

0.3533 0.3535 0.3538

Bookmakers Bet365 Bet&Win Gamebookers Ladbrokes Sporting Bet William Hill Bookmaker consensus (average)

0.3834 0.3822 0.3826 0.3809 0.3823 0.3835 0.3826

0.3473 0.3467 0.3476 0.3473 0.3467 0.3484 0.3475

0.3535 0.3533 0.3535 0.3531 0.3530 0.3535 0.3536

0.3450 0.3450 0.3455 0.3445 0.3453 0.3453 0.3452

0.3548 0.3544 0.3549 0.3541 0.3544 0.3553 0.3549

Conclusion

Chapter 4 has developed goals-based and results-based forecasting models for match outcomes recorded in the form of either goals scored and conceded by the two teams, or in the form of ‘win-draw-lose’ match results. Both types of forecasting model are estimated by fitting regression models to past match results data. A diagonal-inflated bivariate Poisson regression is used for the goals-based model, and an ordered probit regression is used for the results-based model. Both models draw on an extensive set of covariates, reflecting past goal-scoring performance and match results over the preceding 24 calendar months, the significance of the match for end-of-season championship, promotion or relegation outcomes, the current involvement of the teams in the FA Cup or European tournaments, the average attendances attracted by both teams, and the geographical distance between the home stadia of the two teams. The use of the fitted models to generate out-of-sample probabilistic forecasts for future match results in goals or results format has been described in some detail, and illustrative match result forecasts for a full round of Premier League (T1) matches played during the 2009 season have been presented. Comparisons between the forecasting performance of the models on the one hand, and a selection of highstreet and internet bookmakers on the other hand, indicate that the differences in forecasting capability are small. The contribution of the forecasting models developed in this chapter to the design of a betting strategy is examined in more detail in Chapter 12.

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Notes 1 Bittner et al. (2009) report further evidence on the tails of the probability distributions of goals scored by the home and away teams, which are modelled most effectively using extreme value distributions. See also, Hever, Miller and Rubner (2010) and Ribeiro et al. (2010). 2 Having drawn their FA Cup fifth round match against Sheffield United, Hull went on to win the fifth round replay, but were eliminated by Arsenal in the sixth round. Tottenham were eliminated by Manchester United in the fourth round. Having lost the away leg of their UEFA Cup third round tie against Shakhtar Donetsk, Tottenham were eliminated four days after the Hull fixture after being held to a draw by Shakhtar in the home leg.

5

Game theory and football games

Introduction

Game theory is the study, by mathematicians, economists and decision scientists, of decision-making in situations of conflict and interdependence. Most games played in real life are complex, with multiple strategies, incomplete information and pay-offs that might not be explicitly specified. By contrast, sports sometimes give rise to situations in which the structure of a ‘game’ (using the term in the technical sense) is simple and clearly defined. Accordingly, some economists have argued that sports such as football, and others, offer a highly promising arena for the empirical investigation of the propositions of game theory. In football, the ‘game’ between the kicker and the goalkeeper that is played out each time a penalty kick is awarded and taken approximates rather closely to the simple and highly stylised examples typically used to develop the principles of game theory in economics textbooks. The kicker must decide in which direction to shoot and the goalkeeper must decide in which direction to dive. Each decides simultaneously, before knowing the other’s selection. The reward structure is zero-sum: either the kicker scores; or a goal is prevented because the goalkeeper saves or the kicker shoots high or wide. Section 5.1 of this chapter examines theoretical and empirical research on the strategic choices of kickers and goalkeepers during those few intense and highly charged moments that elapse between the referee’s decision to award a penalty, and its execution. Viewed more generally, the football match in its entirety has many of the characteristics of a strategic and dynamic ‘game’ (again, using the term in its technical sense). In every match, the two teams are pitched into direct opposition for a period of play of 90 minutes’ notional duration.1 Each team starts the match with one goalkeeper and ten outfield players. Team managers or coaches are at liberty to deploy their outfield players in any formation of their choosing, and to adjust their team’s formation and style of play at any stage of the match. The immediate objectives of the two teams throughout the match are symmetric: each team attempts to score goals and prevent its opponent from scoring. Accordingly there is a high level of interdependence:  both teams’ strategies have implications for both teams’ chances of scoring and conceding goals. 106

The penalty kick

107

The payoff structure is other than zero-sum, however, for two reasons. First, if the scores at the end of the match are unequal, three league points are awarded to the winning team and none to the losing team. If the scores are level, one point is awarded to each team. Second, a player who commits serious foul play may be dismissed while the match is in progress. No replacement is permitted, and play resumes with the dismissed player’s team at a numerical disadvantage in players. A dismissal also results in the player’s suspension from up to three future matches; in this case, replacements are permitted. However, a suspension still imposes a cost upon the team concerned, which is obliged to select from a smaller or weaker pool of players. The corresponding gain accrues to the team’s future opponents and not its current opponent. The remaining sections of this chapter examine the extent to which the in-play strategic behaviour of football teams (during the course of each match) can be rationalised in accordance with game-theoretic principles of optimising strategic behaviour by independent agents when payoffs are interdependent and non-zerosum. A theoretical model of strategic choice is described and subjected to empirical scrutiny, using data on the timings of player dismissals and goals scored in more than 16,000 English league matches played between the 2002 and 2009 seasons. Section 5.2 describes a game-theoretic model of strategic behaviour for football teams, in which the teams choose between an offensive or defensive formation, and between a violent and non-violent style of play, and can vary these choices continuously over the duration of the match. Section 5.3 summarises a data set containing minute-by-minute details of the timings of player dismissals and goals scored. Section 5.4 describes the specification of an empirical model for the incidence and timings of dismissals and goals. Section 5.5 reports and interprets the estimation results. Finally, Section 5.6 uses stochastic simulations to obtain in-play probabilities for match results conditional upon the state of the match (goals already scored and dismissals already having occurred) at any stage. 5.1  The penalty kick

Academic interest in the penalty kick in football, viewed primarily as a vehicle for empirical tests of the propositions of game theory, has grown rapidly since the publication of a seminal paper by Chiappori, Levitt and Groseclose (2002). This study examines the selection of strategies by kickers and goalkeepers during the execution of penalty kicks. In the theoretical model devised by Chiappori, Levitt and Groseclose, the kicker selects one of three strategies denoted L, C and R: kick left, kick centre or kick right. Similarly the goalkeeper selects one of three strategies also denoted L, C, R: dive to the kicker’s left (the goalkeeper’s right), remain in the centre, or dive to the kicker’s right (the goalkeeper’s left). The following assumptions are made:

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Game theory and football games

• Kicks taken with the kicker’s natural foot are more effective. Accordingly, kicks taken by right-footed kickers (the majority) are more likely to score when L is selected. • If the kicker selects C, a goal is never scored if the goalkeeper also selects C. • If the kicker selects L and the goalkeeper selects L, the probability that a goal is scored is positive but smaller than the probability when the goalkeeper selects R. • If the goalkeeper selects L, the probability that a goal is scored is smaller if the kicker selects C than it is if the kicker selects R. • Relations similar to those stated in the previous two bullets hold between the probabilities when either the kicker or the goalkeeper selects R. The structure of this game is such that there is no pure-strategy equilibrium. If a right-footed kicker always selects L so as to kick on his stronger side, for example, it would pay the goalkeeper to always select L. In that case, however, it would be better for the kicker to select R rather than L. The game does have a mixedstrategy equilibrium, in which both players make their selections randomly, but with specific probabilities that depend upon the probabilities that the penalty is converted for all of the possible permutations of strategies. In equilibrium, the kicker’s scoring probability is the same whether he kicks L, C or R, and the goalkeeper’s probability of averting a goal is the same whether he dives L, C or R. This indifference property is a standard feature of mixed-strategy equilibria. If the players were not indifferent, then it would pay them to adjust their probabilities towards more frequent selection of the strategy with the higher scoring probability (in the case of the kicker) or the strategy with the higher probability of averting a goal (in the case of the goalkeeper). The indifference property leads to several testable propositions: (i) The right-footed kicker selects L (his natural side) more often than R; (ii) The goalkeeper selects L more often than R; (iii)  The goalkeeper selects L more often than the right-footed kicker; (iv) The kicker selects C more often than the goalkeeper. It is straightforward to show that departures from these propositions lead to violations of the indifference property. In the case of (i) for example, if the rightfooted kicker selects L and R with equal probability, the goalkeeper would not be indifferent between L and R, because he would avert a goal more often by selecting R (diving to the kicker’s weaker side). Likewise in the case of (ii), if the goalkeeper selects L and R with equal probability, the right-footed kicker would not be indifferent between L and R, because he would score more often by selecting L (kicking on his stronger side). Selecting C is highly damaging for the kicker if the goalkeeper also selects C. For the kicker to be indifferent between C and either L or R, in accordance with (iv), the goalkeeper must only select C very rarely.

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109

Using data compiled from match videotapes from the top tiers of the French and Italian leagues containing 459 penalty kicks, Chiappori, Levitt and Groseclose subject these propositions to empirical scrutiny. The empirical analysis is subject to an aggregation problem. While the relationships identified above should hold for the game played between each individual kicker and goalkeeper, equivalent relationships might not hold at the aggregate level in data that are compiled over a heterogeneous collection of players. For example, if Kevin always selects L when taking a penalty against Gareth, and Kevin always selects R when taking a penalty against Graham (in contravention of the randomisation strategy that is predicted by the model), the aggregated data on Kevin’s kicks might appear random, but Kevin’s selections against either goalkeeper are in fact completely deterministic. Despite the difficulties created by this aggregation issue, several tabulations and statistical tests are presented that appear consistent with the main propositions of the model. Table 5.1 reports a summary tabulation of the proportions of occasions kickers and goalkeepers selected each strategy, and the outcomes (proportions of occasions the kicks were successful) in each case. In accordance with the indifference property, the proportions of successful kicks and goals averted are similar for each of the three strategies available to both kickers and goalkeepers. Propositions (i) to (iv) are all supported. Both kickers and goalkeepers select L more often than R; and goalkeepers select L more often than kickers. Kickers select C more often than goalkeepers; the latter do so only rarely. In accordance with the randomisation hypothesis, Chiappori, Levitt and Groseclose find that the strategy selected for the previous kick taken by the kicker or faced by the goalkeeper does not predict the strategy chosen for the next kick, after controlling for the overall proportions of selections by each player in the data set. While most footballers might very well be oblivious to the intricacies and technicalities of game theory, the results of this study suggest that they nevertheless succeed, through either good intuition or good coaching, in devising optimising strategies that correspond closely to those that are recommended by the theoreticians. Using the same data set as Chiappori, Levitt and Groseclose, Coloma (2007) tests for the validity of the mixed-strategy equilibrium by estimating a simultaneous equations regression model in which the dependent variables are linear probability model-type regressions, with the kicker’s and goalkeeper’s selections and the outcome (whether the penalty is converted or not) as the dependent variables, and covariates including a dummy variable for the kicker’s right- or ­left-footedness and various other indicators of the state of the match at the time the penalty is taken. The game-theoretic model imposes various restrictions on the coefficients of these equations, which are supported by hypothesis tests on the estimated model. Palacios-Huerta (2003) presents further empirical evidence to support the hypothesis that the behaviour of kickers and goalkeepers is consistent with a mixedstrategy equilibrium and random selection of strategies, based on a larger data set obtained from TV footage of 1,417 penalty kicks from several European countries

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Game theory and football games

Table 5.1 Observed proportions of penalty kicks, goalkeeper dives and goals Kicker Goalkeeper ↓

Left

Centre

Right

Percentages of all penalty kicks classified by kicker and goalkeeper strategies Left 25.5 10.5 20.7 Centre 0.9 0.7 0.9 Right 18.5 6.1 16.3 Total 44.9 17.2 37.9 Percentages of successful kicks for each pairing of kicker and goalkeeper strategies Left 63.2 81.2 89.5 Centre 100.0 0.0 100.0 Right 94.1 89.3 44.0 Total 76.7 81.0 70.1

Total 56.6 2.4 41.0 100.0 76.2 72.7 73.4 74.9

Source: Adapted from Chiappori, Levitt and Groseclose (2002)

that were screened on US TV. The larger data set permits more repeat observations on individual kickers and goalkeepers than were available in the Chiappori, Levitt and Groseclose study, and more powerful tests of the null hypothesis of no serial correlation or persistence in the selection of strategies by individual players over successive kicks. Palacios-Huerta reports runs tests (Mood, 1940) for the randomness of observed sequences of strategic choices by individual players. In some other cases where theory suggests that players should randomise their selections, empirical evidence of negative serial correlation has been reported. The observed choice of first serves by tennis players, for example, tends to switch too frequently (alternating selections on successive serves) for consistency with randomisation (Walker and Wooders, 2001). In the case of penalty kicks, by contrast, Palacios-Huerta is usually unable to reject a null hypothesis of no serial correlation. There is also evidence consistent with the indifference property of the mixed-strategy equilibrium: the success rates of both kickers and goalkeepers are similar for each strategic choice. In other empirical research on penalty-taking and goalkeeping, Bar-Eli et al. (2007) analyse data on 286 penalties drawn from TV footage of various European leagues, for 18 of which the goalkeeper selected C (remain in the centre), 6 of which in turn were saved. On the basis of this 33 per cent success rate, it is suggested that goalkeepers dive more frequently than is optimal, and should remain in the centre more often. This is attributed to an action bias on the part of goalkeepers: the desire to be seen to be taking positive action (diving) results in suboptimal behaviour in the form of a reluctance to select the neutral action of non-movement. Azar and Bar-Eli (2010) report further analysis of the same data set, in the form of tests for the validity of the mixed-strategy equilibrium model.

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Dohmen (2008b) uses data on all 3,619 penalties awarded in the top tier of the German Bundesliga from its inception until the 2004 season, in order to examine whether the proportions of penalties not converted due to the kicker shooting high or wide are sensitive to either the importance of the kick for the match result, or to home-team status. Kickers are found to shoot high or wide more frequently when playing at home than when playing away. Using a smaller German Bundesliga data set comprising 835 penalties, Kuss, Kluttig and Stoll (2007) investigate whether there are differences in conversion rates of penalties when the kicker was the victim of the foul that led to the award of the penalty, and penalties taken by kickers who were not the victims. No evidence is found of any significant difference in conversion rates. Jordet et al. (2007) report that the number of penalty misses increases with the importance of the kick, and Jordet, Hartman and Sigmundstad (2009) find that kickers who were delayed in taking a penalty, often by the goalkeeper, were more likely to miss. Bauman, Friehe and Wedow (2010) find that a kicker’s general ability is a reliable indicator of his success rate. McGarry and Franks (2000) examine the optimal selection of kickers in penalty shoot-outs, held to determine winners at the end of drawn matches in some tournaments (usually after 30 minutes’ extra time has been played in addition to the regulation 90 minutes). In a shoot-out, each team has a minimum of five penalties, each of which must be taken by a different kicker. If the scores are level after five kicks each, the shoot-out continues on a sudden-death basis until a winner emerges. In a probability analysis, the later kicks in the initial sequence of five bear greater weight in determining the match result than the earlier kicks. On this basis, a case can be made for the later kicks to be assigned to the team’s most proficient kickers. Carillo (2007) proposes that penalty shoot-outs should be staged at the end of 90 minutes’ play in matches that are level at that stage, before the match enters a 30-minute period of extra time. The result of the penalty shoot-out would only count if the match were still level at the end of extra time. It is suggested that this proposal would improve the attractiveness of play during extra time, by giving the team that loses the shoot-out an incentive to play offensively. 5.2  A game-theoretic model of in-play strategic choice for football teams

Section 5.2 describes a game-theoretic model of strategic choice for football teams, in which the teams (or their managers or coaches on their behalf) choose between an offensive (attacking) or a defensive formation, and between a violent and nonviolent style of play. These choices are permitted to vary continuously over the duration of each match. This model of optimising strategic behaviour has three important antecedents in the literature. First, Palomino, Rigotti and Rustichini (2000) develop a dynamic game-theoretic model, in which the two teams choose between defensive and attacking formations, and can alter these choices continuously. Working backwards from the end of the match, the teams’ optimal strategies

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conditional on the current state of the match are determined by solving a series of two-player non-cooperative subgames. In regressions estimated using data on 2,855 matches played in the top tiers of the English, Italian and Spanish leagues, covariates measuring team quality effects, the current score and home-field advantage are all significant determinants of the probability of scoring. Teams tend to play more defensively when they are leading than they play when they are either level or trailing. The analysis relies upon an unproven assumption that if one team adopts an attacking strategy and the other adopts a defensive strategy, the goal-scoring rate of the attacking team increases by more than that of the defending team. The attacking and defensive strengths of the two teams are assumed to be the same; and the payoff structure at the end of the match is assumed, for simplicity, to be zero-sum. However, the analysis does not account for what appears to be a strong empirical regularity, that after controlling for team quality and duration effects, the scoring rates of both teams when the scores are level tend to be lower than those of teams that are trailing, and not significantly different from those of teams that are leading. Second, Brocas and Carrillo (2004) develop a dynamic game-theoretic model to examine the effects of the introduction of three-points-for-a-win, and the ­so-called ‘golden goal’ rule,2 on the choice of attacking and defensive strategies by football teams. The model consists of three periods: the first and second halves of regular time, and (for matches that were level after 90 minutes’ play) extra time. As in the Palomino, Rigotti and Rustichini model, the teams’ optimal strategies conditional on the state of the match at the start of each period are established by working backwards from the end of the match. In the Brocas and Carrillo model, threepoints-for-a-win encourages attacking play during the later stages of matches that are level, but it may have a perverse effect of encouraging teams to play more defensively during the early stages. Third, Banerjee, Swinnen and Weersink (2007) examine the impact on team strategies in the NHL of a change in the league points scoring system affecting matches that were tied at the end of regular time.3 Both the theoretical model and the empirical analysis suggest that the rule change had the desired effect of encouraging attacking play during overtime. However, it also had a perverse effect of encouraging defensive play during regular time. Dobson and Goddard (2010) explore the properties of a theoretical model that allows football teams to choose between defensive and attacking formations, and between a non-violent and a violent style of play. This model is reviewed in the remainder of this section. It is assumed that each match consists of a number of discrete unit time intervals, such that durations within the match can be represented by t = 0, …, T where T is the complete match duration. It is both convenient and natural to think of each time interval as representing one minute, so that T = 90. The payoff for each team at the end of the match is dependent on the number of league points gained, and the cost of future player suspensions arising from

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any dismissals incurred during the current match. To allow for the possibility of risk-averse behaviour on the part of the teams, the payoffs from the league points gained are determined through a utility function, which may be either linear in points gained (risk-neutrality) or concave (risk-aversion). The available league points are 3 for a win, 1 for a draw (tie) and 0 for a loss. Without any loss of generality, the utility function may be specified as follows: U(0) = 0, U(1) = 1, U(3) = 1+2λ, where λ = 1 represents risk neutrality and 0 < λ < 1 represents risk aversion. For simplicity the utility cost of a dismissal (arising from future player suspensions) is a fixed utility deduction per player dismissed, denoted ω. Let s denote the difference in scores at any time during the match, and let dh and da denote the numbers of dismissals incurred by the home and away teams prior to that time, respectively. For notational simplicity, time-subscripts denoting the point in time within the match are suppressed from s, dh and da. Let the value functions h890(s,dh,da) and a890(s,dh,da) denote the final payoffs to the home and away teams at the end of the match. Using the notation introduced above, h890(s,dh,da) = 1+2λ–ωdh for s>0 and for any da; 1–ωdh for s = 0; and –ωdh for s < 0. Similarly, a98 0 (s,dh,da) = –ωda for s>0 (and for any dh); 1–ωda for s = 0; and 1+2λ–ωda for s < 0. For every minute within the match, it is assumed that each team manager or coach can select either a non-violent or a violent style of play, and either a defensive or an attacking team formation. The home team’s strategic choices are denoted by i, defined as follows: i = 1 denotes (non-violent, defend); i = 2 denotes (violent, defend); i = 3 denotes (non-violent, attack); and i = 4 denotes (violent, attack). The away team’s choices are denoted by j, defined in the same manner. Let p denote the probability that the home team scores a goal during any minute of the match, denoted t. It is assumed, and it is important to note, that p is conditional on x = dh–da, on i and j, and on t. x-, i-, j- and t-subscripts could be appended to p to represent the dependence of p on these values; but these ­subscripts are omitted in order to keep the notation as simple as possible. Similarly, let q denote the probability that the away team scores a goal during any minute of the match. Again, it is assumed that q is conditional on x, i, j and t. Let u denote the probability that the home team has a player dismissed during any minute of the match. It is assumed that u is dependent on i and on t (but not on x or on j). Finally, let v denote the probability that the away team has a player dismissed during any minute of the match. It is assumed that v is dependent on j and on t (but not on x or on i). For simplicity, it is assumed that only one goal may be scored and one player dismissed within each minute. Stylised numerical examples will illustrate how the teams’ strategic choices are determined. The home team’s expected payoff at the start of the 90th minute is dependent on the strategic choices, i and j, of both teams for the 90th minute. These strategic choices determine the values of p, q, u and v, the probabilities of a goal being scored or a player being dismissed during the 90th minute. From the i,j home team’s perspective, let h89 (s,dh,da) denote the expected payoff at the end of the 89th minute, conditional on the choices of i and j for the 90th minute and the

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Table 5.2 Hypothetical goal-scoring and player-dismissal probabilities for numerical examples Hypothetical goal-scoring probabilities Home team = p i=1 2 3 4

j=1 0.03 0.04 0.04 0.05

j=2 0.02 0.03 0.03 0.04

Away team = q j=3 0.05 0.06 0.06 0.07

j=4 0.04 0.05 0.05 0.06

j=1 0.02 0.01 0.04 0.03

j=2 0.03 0.02 0.05 0.04

j=3 0.03 0.02 0.05 0.04

j=4 0.04 0.03 0.06 0.05

j=3 0.015 0.015 0.015 0.015

j=4 0.020 0.020 0.020 0.020

Hypothetical player-dismissal probabilities Home team = u i=1 2 3 4

j=1 0.005 0.010 0.005 0.010

j=2 0.005 0.010 0.005 0.010

Away team = v j=3 0.005 0.010 0.005 0.010

j=4 0.005 0.010 0.005 0.010

j=1 0.015 0.015 0.015 0.015

j=2 0.020 0.020 0.020 0.020

values of s, dh and da at the end of the 89th minute. Suppose initially that the home team is leading by one goal after 89 minutes, and no players have been dismissed. i,j Accordingly, s = 1, dh = 0 and da = 0. h89 (s,dh,da) can be defined as a probabilityweighted average of the payoffs to the home team after 90 minutes contingent on the values taken by s, dh and da after 90 minutes, which in turn depend only upon whether a goal is scored or a player is dismissed during the 90th minute: i,j h89 (1, 0, 0 ) = q[vh90 ( 0, 0,1) + (1 − u − v ) h90 ( 0, 0,1) + uh90 ( 0,1, 0 )] + (1 − p − q )[vh90 (1, 0,1) + (1 − u − v )h90 (1, 0, 0 ) + uh90 (1,1, 0 )]  + p[vh900 ( 2, 0,1) + (1 − u − v )h90 ( 2, 0, 0 ) + uh90 ( 2,1, 0 )]

[5.1]

i,j (s,dh,da), the away team’s expected payA similar expression can be defined for a89 off at the end of the 89th minute, conditional on the choices of i and j for the 90th minute and the values of s, dh and da at the end of the 89th minute: i,j a89 (1, 0, 0 ) = q[v a90 ( 0, 0,1) + (1 − u − v )a90 ( 0, 0, 0 ) + u a90 ( 0,1, 0 )] + (1 − p − q )[v a90 (1, 0,1) + (1 − u − v ) a90 (1, 0, 0 ) + u a90 (1, 0, 0 )] + p[v a90 ( 2, 0,1) + (1 − u − v ) a90 ( 2, 0, 0 ) + u a90 ( 2,1, 0 )]

[5.2]  Table 5.2 specifies some hypothetical values for p, q, u and v in the 90th minute, i,j (1,0,0) conditional on i and j. These values of p, q, u and v are used to evaluate h89 i,j and a89(1,0,0) over all possible permutations of i and j. The values of h890(s,dh,da) and a890(s,dh,da) in [5.1] and [5.2] are calculated assuming λ = 0.5 and ω = 0.5. Table 5.3 identifies the two-person non-cooperative subgame solution for the two teams’ optimal choices of i and j for the 90th minute. For the home team,

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Table 5.3 Determination of the two teams’ optimal strategies for the 90th minute, home team leading by one goal after 89 minutes Expected pay-offs after 90 minutes at the start of the 90th minute i,j Home team = h89 (1,0,0)

i=1 2 3 4

i,j Away team = a89 (1,0,0)

j=1

j=2

j=3

j=4

j=1

j=2

j=3

j=4

1.9675 1.9750 1.9475 1.9550

1.9575 1.9650 1.9375 1.9450

1.9575 1.9650 1.9375 1.9450

1.9475 1.9550 1.9275 1.9350

0.0275 0.0175 0.0475 0.0375

0.0350 0.0250 0.0550 0.0450

0.0375 0.0275 0.0575 0.0475

0.0450 0.0350 0.0650 0.0550

Note: Payoffs for dominant strategies are highlighted in bold

i = 2 is a dominant strategy. Reading down the columns of the left-hand panel of Table 5.3, i = 2 always produces the highest payoff to the home team, no matter whether j = 1,2,3 or 4 is chosen by the away team. For the away team, j = 4 is a dominant strategy. Reading across the rows of the right-hand panel of Table 5.3, j = 4 always produces the highest payoff to the away team, no matter whether i = 1,2,3 or 4 is chosen by the home team. Therefore the noncooperative solution is {i = 2,j = 4}: the home team, which leads and wishes to avoid conceding a goal, plays defensively and aggressively; while the away team, which trails and needs to score a goal, plays offensively and aggressively. Since {i = 2,j = 4} are the teams’ chosen strategies for the 90th minute, the unconditional expectations of the final payoffs to the home and away teams at the end of the 89th minute are h889(1,0,0) = 1.9550 and a889(1,0,0) = 0.0350. The solution {i = 2,j = 4} is a Nash equilibrium, because neither team would wish to alter its choice in view of the choice that is being made by the other team. However, the solution {i = 2,j = 4} also has the characteristics of a prisoner’s dilemma. There exists an alternative cooperative solution, {i = 1,j = 3}, at which both teams would have a higher expected return than they have at the non-cooperative solution {i = 2,j = 4}. If both teams were to cooperate by playing non-aggressively, both would become better off, because both would avoid incurring the increased risk of a dismissal. However, the cooperative solution is unstable, because both teams would have an incentive to alter their choices in view of the choice that is being made by the other team. Starting from {i = 1,j = 3} for example, if the home team defects from i = 1 to i = 2 while the away team selects j = 3, the home team increases its expected payoff at the away team’s expense. This gives the away team an incentive also to defect to j = 4, restoring the stable, noncooperative solution {i = 2,j = 4}. Table 5.4 identifies the non-cooperative equilibrium solution in the case where the scores are level at the end of the 89th minute. The expected payoffs are calculated by adapting [5.1] and [5.2]:

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Table 5.4 Determination of the two teams’ optimal strategies for the 90th minute, scores level after 89 minutes Expected payoffs after 90 minutes at the start of the 90th minute i,j Home team = h89  (0,0,0)

i=1 2 3 4

i,j Away team = a89  (0,0,0)

j=1

j=2

j=3

j=4

j=1

j=2

j=3

j=4

1.0075 1.0250 0.9975 1.0150

0.9875 1.0050 0.9775 0.9950

1.0175 1.0350 1.0075 1.0250

0.9975 1.0150 0.9875 1.0050

0.9825 0.9625 0.9925 0.9725

1.0000 0.9800 1.0100 0.9900

0.9725 0.9525 0.9825 0.9625

0.9900 0.9700 1.0000 0.9800

Note: Payoffs for dominant strategies are highlighted in bold

i,j h89 ( 0, 0, 0 ) = q[vh90 ( −1, 0,1) + (1 − u − v )h90 ( −1, 0, 0 ) + uh90 ( −1,1, 0 )] + (1 − p − q )[vh90 ( 0, 0,1) + (1 − u − v )h90 ( 0, 0, 0 ) + uh90 ( 0,1, 0 )]  + p[vh90 (1, 0,1) + (1 − u − v )h90 (1, 0, 0 ) + uh90 (1,1, 0 )]

[5.3]

i,j a89 ( 0, 0, 0 ) = q[v a90 ( −1, 0,1) + (1 − u − v )a90 ( −1, 0, 0 ) + u a90 ( −1,1, 0 )] + (1 − p − q )[v a90 ( 0, 0,1) + (1 − u − v ) a90 ( 0, 0, 0 ) + u a90 ( 0,1, 0 )] + p[v a90 (1, 0,1) + (1 − u − v ) a90 (1, 0, 0 ) + u a90 (1,1, 0 )] 

[5.4]

In Table 5.4, {i = 2,j = 2} is the non-cooperative solution, in which both teams play defensively and aggressively. As before, the non-cooperative solution is a Nash equilibrium, because neither team would wish to alter its choice in view of the choice that is being made by the other team. However, the non-cooperative solution also has the characteristics of a prisoner’s dilemma. In this case there are two alternative cooperative solutions, {i = 1,j = 1} and {i = 3,j = 3}, at which both teams would have a higher expected return than they have at the non-­cooperative solution {i = 2,j = 2}. If both teams were to cooperate by playing non-aggressively, both would become better off. Once again, however, the cooperative solutions are unstable, because both teams would have an incentive to defect in view of the choice that is being made by the other team. Since {i = 2,j = 2} are the teams’ chosen strategies for the 90th minute, the unconditional expectations of the final payoffs to the home and away teams at the end of the 89th minute are h889(0,0,0) = 1.0050 and a88 9(0,0,0) = 0.9800. By following similar procedures, a complete set of values for h889(s,dh,da) and a889(s,dh,da) can be established, for all possible values of s, dh and da. Then, the two teams’ optimal choices of strategy for the 89th minute can be examined, by identifying the expected payoffs at the end of the 88th minute conditional on both team’s choices of i and j for the 89th minute. This procedure establishes

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a complete set of values for h888(s,dh,da) and a888(s,dh,da), for all possible values of s, dh and da. Then, the two teams’ optimal choices of strategy for the 88th minute can be examined, by identifying the expected payoffs at the end of the 87th minute conditional on both team’s choices of i and j for the 88th minute. By working backwards in a similar manner, the optimal choices of i and j at any stage of the match can be determined. The general expressions for the relations that are used to obtain these solutions (of which [5.1] to [5.4] are particular cases) are: hti,j (s, d h , da ) = q[vht +1 (s − 1, d h , da + 1) + (1 − u − v )ht+1 (s − 1, d h , da ) + uht +1 (s − 1, d h + 1, da )] + (1 − p − q )[vht +1 (s,d h ,da + 1) + (1 − u − v )ht+1 (s,d h ,da ) + uht+1 (s,d h + 1, da )] + p[vht+1 (s + 1,d h ,da + 1)  + (1 − u − v )ht+1 (s + 1, d h ,da ) + uht+1 (s + 1, d h + 1, da )]

[5.5]

a ti,j (s, d h , da ) = q[v at +1 (s − 1, d h , da + 1) + (1 − u − v ) at+1 (s − 1, d h , da ) + u at +1 (s − 1, d h + 1, da )] + (1 − p − q )[v at +1 (s,d h ,da + 1) + (1 − u − v ) at+1 (s,d h ,da ) + u at+1 (s,d h + 1, da )] + p[v at+1 (s + 1,d h ,da + 1) + (1 − u − v )at+1 (s + 1, d h ,da ) + u at+1 (s + 1, d h + 1, da )] 

[5.6]

The two previous examples illustrating the determination of the non-cooperative solution for the teams’ strategic choices in the 90th minute result in both teams choosing a violent style of play. Is the resort to violence a pervasive feature of this model, or are there circumstances in which the teams would be able to adhere to a cooperative solution involving non-violence? Dobson and Goddard (2010) show that the Nash equilibrium is more likely to coincide with the cooperative solution in the earlier stages of matches, because the overall cost to the team of having a player dismissed is higher if the dismissal occurs near the start of the match than it is if the dismissal occurs near the end. For example, if a player is dismissed in the first minute, the team plays virtually the entire match at a numerical disadvantage, and is significantly less likely to take league points from the match. The team also loses the right to field the dismissed player in one or more future matches through suspension. If a player is dismissed in the 90th minute, the cost in terms of future suspension is the same, but the team suffers virtually no disadvantage in the current match. Table 5.5 provides the data for a further stylised example, in the form of a set of (hypothetical) match result probabilities applicable at the end of the first minute

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Table 5.5 Hypothetical match result probabilities at the end of the first minute, conditional on score and player dismissals, for numerical examples

Score after 1 minute 0–1 0–0 1–0

Home-team player dismissed

No player dismissed

Away-team player dismissed

Home win 0.12 0.22 0.32

Home win 0.30 0.40 0.50

Home win 0.48 0.58 0.68

Draw 0.30 0.30 0.30

Away win 0.58 0.48 0.38

Draw 0.30 0.30 0.30

Away win 0.40 0.30 0.20

Draw 0.30 0.30 0.30

Away win 0.22 0.12 0.02

Table 5.6 Determination of the two teams’ optimal strategies for the first minute Expected payoffs after one minute at the start of the match Home team = hi,j0 (0,0,0)

i=1 2 3 4

Away team = ai,j0 (0,0,0)

j=1

j=2

j=3

j=4

j=1

j=2

j=3

j=4

0.8975 0.8972 0.8955 0.8952

0.8953 0.8950 0.8933 0.8930

0.8995 0.8992 0.8975 0.8972

0.8973 0.8970 0.8953 0.8950

0.4975 0.4953 0.4995 0.4973

0.4972 0.4950 0.4992 0.4970

0.4955 0.4933 0.4975 0.4953

0.4952 0.4930 0.4972 0.4950

Note: Payoffs for dominant strategies are highlighted in bold

of a match, conditional upon whether a goal is scored or a player is dismissed during the first minute.4 For the purposes of the example, the goal-scoring and player-dismissal probabilities specified in Table 5.2 are assumed to apply to the first minute. It is assumed that if no players were dismissed during the first minute, the expectations at the end of the first minute of the numbers of players dismissed by the end of the match are 0.4 for the home team, and 0.8 for the away team; as before, the probabilities for goals and dismissals have been exaggerated for the purposes of constructing a stylised example. On the basis of these assumptions, Table 5.6 reports the payoffs that determine the two teams’ optimal choices of i and j for the first minute. In Table 5.6, {i = 1,j = 1} is the cooperative solution, in which both teams play defensively and non-violently. In this case the cooperative solution is a Nash equilibrium, because neither team would wish to alter its choice in view of the choice that is being made by the other team. Data on the incidence of goal scoring and disciplinary sanction within matches, reported in Section 5.3 below, indicate that the award of red cards increases sharply during the latter stages of play. This empirical pattern is consistent with the central prediction of the theoretical model described in this section, which suggests a tendency for a shift from a cooperative and non-violent pattern

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Table 5.7 Rates of player dismissal and goal scoring conditional on current duration, English League, T1–T4, 2002–2009 seasons Players dismissed per minute

Goals scored per minute

Home team

Away team

Home team

Away team

0 < t ≤ 10 10 < t ≤ 20 20 < t ≤ 30 30 < t ≤ 40 40 < t ≤ 44 44 < t ≤ 45

.00009 .00034 .00041 .00052 .00043 .00356

.00029 .00045 .00056 .00086 .00103 .00387

.0119 .0137 .0142 .0142 .0148 .0539

.0090 .0101 .0104 .0109 .0104 .0378

45 < t ≤ 55 55 < t ≤ 65 65 < t ≤ 75 75 < t ≤ 85 85 < t ≤ 89 89 < t ≤ 90

.00060 .00099 .00107 .00128 .00118 .00952

.00090 .00142 .00184 .00205 .00232 .01375

.0156 .0161 .0164 .0169 .0174 .0861

.0122 .0127 .0125 .0128 .0128 .0662

Match duration, t (minutes)

Source: Sky Sports Football Yearbook

of play in the early stages of matches, to a non-cooperative and violent pattern in the latter stages. This is attributed to a shift in the structure of rewards and penalties over the course of the match, and in particular, a decline over the course of the match in the cost borne by a team that has a player dismissed, measured in terms of expected league points foregone. Dobson and Goddard (2010) report the results of numerical simulations of the model, in which the strategic choices at all points during the match are determined more rigorously than was the case in the previous stylised example, by solving the model backwards from the end of the match to the start. Speaking generally, it is found that teams that are trailing tend to attack, and teams that are trailing tend to play violently for as long as there is a realistic chance of salvaging the match. Teams that are trailing by three goals or more tend not to play violently. The stage at which a team that is trailing by two goals or more ceases to play violently, implicitly conceding that the match is beyond salvation, depends upon relative team quality and upon home-field advantage. Stronger teams when trailing play violently for longer than weaker teams, and home teams when trailing play violently for longer than away teams. The propensity for teams that are either trailing or level to play violently and/or to attack is increasing in λ, the risk-aversion parameter. 5.3  The timings of player dismissals and goals

The data sample for the empirical analysis that is reported in this section comprises all 16,288 matches played in the four tiers of the English Premier League and Football League during the eight seasons from 2002 to 2009 (inclusive).5 Tables 5.7, 5.8 and 5.9 report descriptive statistics, which highlight several of the

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Table 5.8 Rates of player dismissal and goal scoring conditional on current difference in scores, English League, T1–T4, 2002–2009 seasons Difference in scores, s (home goals – away goals)

Players dismissed per minute Goals scored per minute Home team

Away team

Home team

Away team

.00123 .00202 .00130 .00057 .00079 .00086 .00056

.00069 .00145 .00126 .00090 .00187 .00206 .00201

.0182 .0183 .0170 .0150 .0167 .0182 .0213

.0169 .0140 .0124 .0113 .0134 .0134 .0132

s ≤ –3 s = –2 s = –1 s=0 s=1 s=2 s≥3 Source: Sky Sports Football Yearbook

Table 5.9 Rates of player dismissal and goal scoring conditional on numerical disparity in players, English League, T1–T4, 2002–2009 seasons Numerical disparity in players, x (home players dismissed – away players dismissed)

Players dismissed per minute Goals scored per minute Home team

Away team

Home team

Away team

.00182 .00075 .00173

.00238 .00121 .00306

.0287 .0159 .0123

.0093 .0122 .0228

x ≤ –1 x=0 x≥1 Source: Sky Sports Football Yearbook

key strategic issues that are outlined above. Table 5.7 reports the average numbers of dismissals per minute and the average rates at which goals were scored by the home and away teams per minute, at various durations within matches. Table 5.8 reports the average dismissal rates and scoring rates conditional on the current difference between the scores of the two teams; and Table 5.9 reports the rates conditional on the current numerical imbalance between the two teams (if any) due to any players having already been dismissed. In Table 5.7 the data for the 45th and the 90th minutes are displayed separately from those for other durations. These cells include all player dismissals and goals scored during the 45th and 90th minutes, and during stoppage time (played immediately after the 45th and 90th minutes have elapsed). The data source does not record the amount of stoppage time played, which is variable but typically of between two and five minutes’ duration at the end of each 45-minute period. Accordingly the rates of player dismissal and goal scoring recorded in these cells are several times the magnitudes of those in adjacent cells.

The timings of player dismissals and goals

121

According to Table 5.7, there is a pronounced upward trend in the numbers of dismissals over the duration of matches. The rates for 85 < t ≤ 89 (durations between 85 and 89 minutes) are around 18 times and 9 times those for 0 < t ≤ 10 for home teams and away teams, respectively. There is also a clear, but less heavily pronounced, upward trend in the numbers of goals scored. The goal-scoring rates for 85 < t ≤ 89 are around 1.5 times those for 0 < t ≤ 10 for both home teams and away teams. Except in the case where either team is leading by more than two goals (for which the data are relatively sparse), the probability of having a player dismissed is lowest when the scores are level; is of intermediate value for teams leading by one or two goals (s = 1,2 for the home team, s = –1,–2 for the away team); and is highest for teams trailing by one or two goals (s =  –1,–2 for the home team, s = 1,2 for the away team). The probability of either team scoring is lowest when the scores are level, and is somewhat increased when the scores are unequal. In the latter case, and provided the current scores difference is not more than two goals, the scoring probabilities of both teams increase in similar proportions (no matter which team is leading and which is trailing). However, a team that is leading by three goals or more appears to experience a large increase in its probability of scoring further goals. The tendency for scoring rates to increase over the duration of the match (see Table 5.7) is well known to commentators, pundits and spectators, and is commonly attributed to a tendency for players to become fatigued and commit defensive errors, which lead to goals being scored. Errors due to fatigue could also produce more fouls in last-ditch attempts to prevent goals, which could in turn account for the upwardly trended rates of player dismissal. Since goals in football are relatively infrequent events (in comparison with scores in other team sports such as rugby or basketball), observations in Table 5.8 for level scores tend to be weighted towards the earlier match durations, while observations for a non-zero difference in scores tend to be weighted towards later durations. Therefore player fatigue could also account for some of the variation shown in Table 5.8. However, the data in Table 5.8 could also reflect a form of team quality selection effect. Observations of scoring rates when the away team is already leading (for example) are drawn predominantly from matches in which the away team is of higher quality than the home team. This means the probability that the away team scores further goals should be higher than the average. This team quality selection effect might explain why teams score more frequently when leading than when scores are level, but it does not explain why teams that are trailing also tend to score more frequently. Distinct from the player fatigue and team quality selection effects, an alternative explanation for the variations in scoring rates shown in Tables 5.7 and 5.8 is suggested by the analysis in Section 5.2. A team that switches from a defensive to an attacking formation increases both its own and its opponent’s probabilities of scoring. By leaving itself open to a counter-attack and the possibility of having

122

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to commit a last-ditch foul in order to prevent an opponent from scoring, it also increases its own probability of having a player dismissed. A team that switches from a non-violent to a violent style of play disrupts the pattern of play, in a manner that may increase both teams’ scoring probabilities. As noted in Section 5.2, the dismissal of a player imposes two separate costs upon his own team. First, the team must complete the match at a numerical disadvantage in players (unless an opposing player is also dismissed). Table 5.9 indicates that there is a large reduction in the scoring probability for a team that is playing at a numerical disadvantage, and a still larger increase in the probability of conceding a goal. This portion of the cost of a player dismissal is highest for dismissals that occur at the early stages of matches, because the team that loses a player is exposed to these adverse probabilities for longer. Second, a dismissal results in the player’s suspension from one or more future matches. This portion of the cost is independent of the stage of the (current) match at which the dismissal occurs. Therefore the overall cost of a dismissal in the current match, expressed in terms of expected league points foregone, is higher for dismissals during the early stages of matches. A tendency for dismissal rates to increase over the duration of matches (see Table 5.7) seems consistent with rational strategic behaviour in the light of this cost structure. 5.4  An empirical model for the in-play arrival rates of player dismissals and goals

In this section we develop an empirical model for the in-play arrival rates of player dismissals and goals. Following a modelling approach similar to that of Dixon and Robinson (1998), it is assumed that the arrival rates can be represented as Poisson processes, such that the probability that a new arrival occurs is independent of the time that has elapsed since the previous arrival. It is also assumed, for simplicity, that arrivals of player dismissals and goals are independent of each other.6 Let μk denote the arrival rate for event k, where k = 1 denotes a home-team player dismissal, k = 2 denotes an away-team player dismissal, k = 3 denotes a goal scored by the home team, and k = 4 denotes a goal scored by the away team. Let mk denote the number of minutes that elapse before the next occurrence of event k. If player dismissals and goals are Poisson processes, mk follows an exponential distribution, with distribution function Fk(t) = prob(mk ≤ t) = 1–exp(–μkt) and density function fk(t) = Fk′(t) = μkexp(–μkt). Section 5.4 reports estimation results for a competing risks model, comprising hazard functions for the four events (k = 1, … ,4), in which μk are assumed to be linear in a set of covariates that are time-varying over the duration of the current match. Spells of continuous play that end in the occurrence of event k are treated as right-censored in the likelihood functions for the events other than k. The covariates include team quality covariates obtained from the goals-based match results forecasting model that is described in Chapter 4, Section 4.2. In order to generate the team quality covariates for all of the matches played in a particular

Empirical model for arrival rates: dismissals, goals

123

season, the match results forecasting model is estimated using data from the ten seasons immediately preceding the season in question. Probabilities in win-­drawlose format for the result of each match within the season are obtained using the procedure described in Chapter 4, Section 4.3, by substituting into the fitted model covariate values that relate to the match, all of which are calculated using data that are available prior to the start of the match. HWINPR and DRAWPR are probabilities for the current match to end in a home win and a draw. EXPHG and EXPAG are the expected numbers of goals scored by the home and away teams in the current match, defined as the fitted values of λ1,i,j and λ2,i,j in equation [4.1]. The full list of covariate definitions for the conditional hazard functions for home- and away-team player dismissals (μ1 and μ2) are as follows: RELQUAL = HWINPR+ 0.5×DRAWPR (see above). UNCERT = RELQUAL×(1–RELQUAL). DUR = duration (number of minutes elapsed prior to the start of the current minute) within the current match, measured from 0 to 89. SECOND = 0 during the first halves of matches, 1 during the second halves. M45, M90 = 0–1 dummy variables that allow for step changes in the arrival rates recorded for the 45th and 90th minutes of the match, due to stoppage time. HOFF, AOFF = 0–1 dummy variables indicating whether either team is currently experiencing a numerical disadvantage due to one or more players having previously been dismissed during the current match. HOFF = 1 if the home team is currently at a disadvantage in player numbers, and 0 otherwise. AOFF is defined similarly for the away team. DIFFs = 0–1 dummy variables indicating the goal difference between the home and away teams at the start of the current minute: DIFF–3 = 1 if the away team is leading by three goals or more at the start of the current minute, and 0 otherwise. DIFF–2 = 1 and DIFF–1 = 1 if the away team is leading by two goals or one goal, respectively. DIFF+1, DIFF+2 and DIFF+3 indicate the home team leading by one goal, by two goals, or by three goals or more, respectively. The additional covariate definitions for the conditional hazard functions for goals scored by the home and away teams (μ3 and μ4) are as follows: EXPHG and EXPAG = expected numbers of goals scored by the home and away teams in the current match (see above). These covariates are invariant across all of the observations pertaining to the current match. KICKOFF = 1 for the 1st and 46th minutes, and for any minute when a goal has been scored by either team in the preceding minute, and 0 otherwise. In the hazard functions for home- and away-team player dismissals, the covariate RELQUAL measures home-team quality relative to away-team quality, also taking account of home-field advantage. RELQUAL appears in the player dismissal hazard functions because previous empirical evidence suggests that players from lower-quality teams and players from away teams are at greater risk of disciplinary

124

Game theory and football games

sanction (Dawson et al., 2007; see also Chapter 10). UNCERT = RELQUAL×(1– RELQUAL), a standard measure of uncertainty of match outcome, also appears in the player dismissal hazard functions. In accordance with the theoretical model and simulation results, and with empirical evidence reported by Dawson et al. (2007), violent play is more likely when the two teams are closely balanced (in terms of underlying quality) than when they are unbalanced. Therefore positive coefficients on UNCERT are expected in both the home-team and away-team hazard functions. RELQUAL and UNCERT are non-varying with duration across all of the observations pertaining to the current match. In hazard functions for goals scored by the home and away teams (μ3 and μ4), EXPHG and EXPAG, the expected numbers of goals scored by the home and away teams in the current match (see above), control for the relationship between relative team quality and the scoring rates of the home and away teams. These covariates are also non-varying with duration across all observations pertaining to the current match. The covariates RELQUAL and UNCERT do not appear in the hazard functions for goals scored, because any relative team quality effects on goal-scoring rates are captured directly by the EXPHG and EXPAG covariates. The dummy variables M45 and M90 control for the fact that any dismissal that takes place during stoppage time at the end of each 45-minute period, and any goal scored during stoppage time, is recorded as having occurred in either the 45th or the 90th minute. As noted above, the amount of stoppage time added on at the end of each half is commonly between two and five minutes; although shorter or longer amounts are possible. The recording system for dismissals or goals scored during stoppage time ensures that the hazards of these events being recorded as having occurred in either the 45th or the 90th minute are several times the size of the hazards for the 44th and 89th minutes (for example), and for other periods of one minute’s duration. Accordingly, positive coefficients on M45 and M90 are expected in all estimations. It is expected that goal-scoring rates should be relatively low in the first minute (the start of the match), the 46th minute (the resumption of the match following the half-time interval), and in the minute immediately after a goal is scored by either team. In each case, play starts or resumes from a kick-off at the halfway line, and the teams regroup into balanced defensive formations when play kicks off. Goals are unlikely to be scored during the first few seconds following kick-off, and the scoring rates for those minutes are reduced accordingly. The dummy variable KICKOFF takes a value of one for the first and 46th minutes, and for any minute when a goal has been scored by either team in the preceding minute, and zero otherwise. 5.5  Estimation results and interpretation Empirical arrival rates for player dismissals

Table 5.10 reports the estimated equations for the arrival rates of home-team player dismissals, as equations [5.7], [5.8] and [5.9], and away-team player dismissals as

Estimation results and interpretation

125

Table 5.10 Estimation results: player-dismissal hazard functions Home-team player dismissal hazard [5.7]

[5.8]

[5.9]

−1.576 −3.82 7.875 3.44 .023 16.1 —

−1.123 −2.69 7.623 3.33 .022 14.9 —

—

—

DIFF–3

1.844 13.5 1.766 18.4 .435 3.09 .386 3.29 —

DIFF–2

—

DIFF–1

—

DIFF+1

—

DIFF+2

—

DIFF+3

—

DIFF–1×SECOND

—

1.828 13.4 1.785 18.5 .360 2.55 .465 3.95 −.072 −0.30 .589 5.33 .410 5.26 −.018 −0.22 −.127 −1.04 −.722 −3.18 —

DIFF–1×DUR×SECOND

—

—

DIFF+1×SECOND

—

—

DIFF+1× DUR×SECOND

—

—

−9.451 −13.3

−9.708 −13.6

−1.120 −2.69 7.620 3.33 .031 5.72 .592 1.85 −.014 −2.06 1.668 9.69 1.847 17.4 .364 2.57 .474 4.02 −.075 −0.31 .577 5.17 .393 2.64 .031 −0.20 −.140 −1.14 −.723 −3.18 −.592 −1.22 .008 1.31 .243 0.48 −.005 −0.70 −9.963 −13.7

RELQUAL UNCERT DUR SECOND DUR×SECOND M45 M90 HOFF AOFF

Constant

Away-team player dismissal hazard [5.10]

[5.11]

[5.12]

1.366 3.25 4.711 2.55 .023 20.5 —

1.004 2.37 4.539 2.45 .022 19.0 —

—

—

1.444 11.2 1.628 20.7 .950 10.3 .267 2.70 —

—

1.429 11.0 1.644 20.9 1.008 10.9 .223 2.25 −1.092 −3.41 −.167 −1.38 −.054 −0.75 .352 5.97 .253 3.07 .052 0.42 —

—

—

—

—

—

—

−9.951 −15.39

−9.753 −15.0

1.000 2.36 4.519 2.44 .034 8.15 .521 2.05 −.016 −3.19 1.185 7.80 1.650 19.3 1.016 11.0 .222 2.24 −1.047 −3.26 −.140 −1.15 .055 −0.42 .071 0.60 .277 3.31 .099 0.79 −.539 −1.16 .005 0.91 −.493 −1.35 .011 2.50 −9.994 −15.2

— — — — —

Note: z-statistics for the significance of the estimated coefficients are reported in italics.

126

Game theory and football games

[5.10], [5.11] and [5.12]. In all of the estimations, the dependent variable is ln(μk) for k = 1 and 2, the natural logarithm of the arrival rate for home-team dismissals and away-team dismissals, respectively.7 Three alternative specifications are reported. Equations [5.7] and [5.10] exclude any effects related to the current difference in scores. Equations [5.8] and [5.11] include dummy variables for the current difference in scores. Finally, [5.9] and [5.12] also include several interaction terms, which permit some of the coefficients to vary between the first and second halves of matches. The additional terms included in [5.9] and [5.12] are jointly significant, and improve the model’s explanatory power. Accordingly, [5.9] and [5.12] are used in the evaluation of in-play home win, draw and away win probabilities at various stages of the match, conditional on the state of the match at that stage, that are reported in Section 5.6. Since the coefficients of [5.7], [5.8], [5.10] and [5.11] are easier to interpret, however, the following commentary focuses mainly on these specifications. In all of the player dismissal arrival rate estimations, the coefficients on DUR, the linear trend in duration, are positive and significant, reflecting the tendency for the likelihood of a dismissal occurring to increase over the duration of the match. The coefficients on M45 and M90 are positively signed and significant, as expected. The coefficients on RELQUAL are negative and significant in the home-team player dismissal equation, and positive and significant in the away-team equation. These coefficients indicate that weaker teams are more likely to be penalised than stronger teams. The coefficients on UNCERT are positively signed and significant, indicating that players are more likely to be dismissed in matches that are equally balanced, and less likely in matches where there is a large difference in quality between the home and away teams. The coefficients on HOFF and AOFF are positively signed and significant. The coefficients on HOFF are particularly large in the away-team player dismissal equation. This might perhaps reflect a tendency for referees who have already dismissed a home-team player in the current match to succumb to pressures from the home crowd to ‘even things up’ by dismissing an away-team player. When the dummy variables DIFFs (for s =  –3,–2,–1,1,2,3) are added to the specification (comparing [5.8] with [5.7], and [5.11] with [5.10]), the coefficients and z-statistics on DUR are reduced, but only fractionally. Accordingly, strategic choices on the part of the two teams dependent on the current difference in scores do not explain the tendency for the rates of player dismissal to increase over the duration of the match. Nevertheless, the dummy variables DIFFs do make a significant contribution to the explanatory power of [5.8] and [5.11], suggesting that strategic effects are important. The coefficients on DIFF–2 and DIFF–1 are positive and significant in the home-team player dismissal equation, [5.8]. The coefficient on DIFF+3 is negative and significant. The pattern for the away-team player dismissal equation [5.11] is the mirror image of the home-team equation. The coefficients on DIFF+1 and DIFF+2 in [5.11] are positive and significant,

Estimation results and interpretation

127

but smaller in absolute magnitude than the coefficients on DIFF–2 and DIFF–1 in [5.8]. The coefficient on DIFF–3 in [5.11] is negative and significant. These findings are consistent with the properties of the theoretical model that is developed in Section 5.2. The probability of incurring a player dismissal tends to be higher for a team that is trailing than for the same team either when it is leading or when the scores are level. Teams when leading tend to play cautiously (non-violent, defence) in order to minimise both the probability of conceding a goal and the probability of losing a player through dismissal. The probability of incurring a dismissal is particularly low when either team is leading by three goals or more, suggesting that when the match result is beyond reasonable doubt, violent play tends to fall to a particularly low level. Teams when trailing tend to take risks (violent, attack), because it is worthwhile bearing an increased probability of a dismissal in order to increase the probability of scoring. This willingness to bear additional risk is conditional on the prospects of salvaging the match, however. Teams trailing by either one or two goals are more inclined to take risks than teams trailing by larger margins; and the tendency for home teams when trailing to take risks is stronger than the same tendency for away teams. Empirical arrival rates for goals scored

Table 5.11 reports the estimated arrival rates for home-team goals ([5.13] to [5.15]) and away-team goals ([5.16] to [5.18]). The dependent variable is ln(μk) for k = 3 and 4, the natural logarithm of the arrival rate for home-team goals and awayteam goals, respectively. As before, three alternative specifications are reported. Equations [5.13] and [5.16] exclude any effects related to the current difference in scores. Equations [5.14] and [5.17] include dummy variables for the current difference in scores. Finally, [5.15] and [5.18] also include several interaction terms, which permit some of the coefficients to vary between the first and second halves of matches and with variation in the team quality control variables. The additional terms included in [5.15] and [5.18] are jointly significant, and these specifications are used in the evaluation of in-play home win, draw and away win probabilities reported in Section 5.6. The coefficients on KICKOFF, M45, M90, EXPHG, EXPAG and DUR in the goals equations are all signed as expected and significant, and require no further comment. The coefficients on HOFF and AOFF are signed in accordance with the ‘common sense’ view that when a team is playing at a numerical disadvantage because a player has been dismissed, the likelihood of scoring a goal is reduced and the likelihood of conceding is increased. The popular theory that a team playing at a numerical disadvantage are more likely to score is firmly rejected by the empirical evidence. There is little change in the magnitudes of the coefficients on DUR when the dummy variables DIFFs (for s =  –3,–2,–1,1,2,3) are added to the specification (comparing [5.14] with [5.13], and [5.17] with [5.16]). Accordingly and as

DIFF–3

AOFF

HOFF

KICKOFF

M90

M45

DUR×SECOND

SECOND

1.277 37.1 1.566 52.6 −.618 −14.85 −.324 −5.96 .486 17.0 —

—

.003 12.7 —

—

EXPAG^2

DUR

—

.599 25.2 —

EXPAG

EXPHG^2

EXPHG

[5.13]

1.276 37.0 1.568 52.6 −.623 −15.0 −.339 −6.20 .494 17.2 .112 1.78

—

.003 10.8 —

—

—

.615 25.5 —

[5.14]

Home-team goal hazard

.841 4.25 −.097 −1.61 −.453 −1.90 .088 0.84 .004 4.53 .174 2.55 −.003 −2.12 1.269 32.3 1.613 49.5 −.632 −15.1 −.336 −6.16 .498 17.4 .126 1.99

[5.15]

Table 5.11 Estimation results: goal-scoring hazard functions

1.202 29.3 1.570 46.2 −.332 −7.90 .506 12.6 −.412 −8.28 —

—

.004 13.7 —

.851 24.2 —

—

—

[5.16]

1.199 29.2 1.574 46.3 −.338 −8.05 .521 12.9 −.428 −8.59 .037 0.56

—

.004 11.6 —

.883 24.7 —

—

—

[5.17]

Away-team goal hazard

−.252 −1.21 .008 0.11 1.186 4.07 −.184 −1.53 .004 4.16 .307 3.96 −.004 −3.09 1.213 26.0 1.635 43.9 −.354 −8.35 .520 12.9 −.425 −8.53 .042 0.64

[5.18]

— — — — — — — — — — —

DIFF+1

DIFF+2

DIFF+3

DIFF–1×SECOND

DIFF–1×DUR×SECOND

DIFF+1×SECOND

DIFF+1× DUR×SECOND

DIFF–1×EXPHG

DIFF+1×EXPHG

DIFF–1×EXPAG

DIFF+1×EXPAG −5.316 −129.7

—

—

—

—

—

—

—

.131 3.88 .066 3.43 −.016 −0.90 −.017 −0.65 .040 1.08 —

−5.058 −28.7

—

.135 3.95 −.168 −1.48 .251 2.45 −.033 −1.21 .026 0.68 −.098 −0.78 .002 1.08 .145 1.27 −.003 −1.91 .139 1.97 −.146 −2.38 —

−5.642 −127.0

—

—

—

—

—

—

—

—

—

—

—

—

—

Note: z-statistics for the significance of the estimated coefficients are reported in italics.

−5.289 −131.0

—

DIFF–1

Constant

—

DIFF–2

−5.686 −126.1

—

—

—

—

—

—

—

−.041 −1.05 −.048 −2.14 .107 5.35 .098 3.22 .074 1.59 —

.023 0.23 −.061 −0.67 −5.428 −27.7

—

−.045 −1.14 −.077 −0.61 .139 1.27 .111 3.58 .108 2.26 −.068 −0.47 .001 0.45 −.145 −1.14 .003 1.73 —

130

Game theory and football games

commented previously, strategic choices on the part of the two teams dependent on the current difference in scores do not explain the tendency for the goal-scoring rates to increase over the duration of the match. As before, however, the dummy variables DIFFs do make a significant contribution to the explanatory power of [5.14] and [5.17], suggesting that strategic effects are important. The coefficients on DIFF–2 and DIFF–1 are positive and significant in [5.14]; and the coefficients on DIFF+1 and DIFF+2 are positive and significant in [5.17]. The coefficient on DIFF–1 in [5.17] is negative and significant. The positive and significant coefficients on DIFF–1 and DIFF–2 in [5.14], and on DIFF+1 and DIFF+2 in [5.17], are consistent with a tendency for teams that are trailing to play offensively, and consequently for the likelihood of scoring to be increased. The negative and significant coefficient on DIFF–1 in [5.17] suggests a tendency for away teams when protecting a narrow lead to play defensively, reducing the probability that the lead will be extended. For home teams, in contrast, although the coefficient on DIFF+1 in [5.14] is also negative, this coefficient is small in absolute magnitude, and not significant. Looking at the raw data summarised in Table 5.8, the scoring rates of teams that are leading are higher than those of teams that are level. The scoring rates reported in Table 5.8 are unconditional on team quality. An implication of Table 5.11 is that after controlling for team quality, the scoring rates of teams that are leading by one or two goals are slightly lower than those of teams that are level (although in most cases the coefficients are not significant). Accordingly, the patterns in Table 5.8 should be attributed to a team quality selection effect (see also Section 5.3). After including controls for team quality in [5.13] to [5.18], the differences that are apparent in the raw data, between the scoring rates of teams that are leading and of teams that are level, are eliminated. 5.6  Stochastic simulations for in-play match result probabilities conditional on the current state of the match

This section presents a practical application of equations [5.9], [5.12], [5.15] and [5.18], for the use of team managers, in-play bettors and others who may wish to obtain in-play probabilities for the final outcome of a match conditional upon the current state of the match at any stage. For the purposes of evaluating the in-play match result probabilities, the current state of the match comprises two components: (i) the RELQUAL measure of the relative underlying quality of the two teams, which is based on previous match results and other data that are observable prior to the start of the match in question; and (ii) the difference in scores defined by s (using the same notation as before), and any numerical disparity in players defined by x = dh–da (where dh and da are the numbers of home-team and away-team players dismissed) at the stage in the match at which the in-play probabilities are required.

Simulations for in-play match result probabilities

131

Given any set of values for RELQUAL, s and x and starting from any match duration denoted t, the in-play home win, draw and away win probabilities can be calculated from stochastic simulations of player dismissals and goals over the remaining duration of the match (t+1, …,T). The home win, draw and away win probabilities at the start of the match are computed by running the simulations from t = 0, over the full 90-minute match duration. In accordance with the underlying probability model, occurrences of each of the relevant events (k = 1,2 for player dismissals, k = 3,4 for goals scored) are simulated by means of random drawings from an exponential distribution with conditional mean μk, which varies over the remaining duration of the simulated match in accordance with [5.9], [5.12], [5.15] and [5.18]. The in-play probabilities are the proportions of simulated home wins, draws and away wins obtained from 10,000 replications of this procedure. Tables 5.12–5.14 report selected in-play probabilities, calculated for five different values of RELQUAL at five different durations within the match, for three possible values of x and five possible values of s. Table 5.12 reports in-play home win probabilities; Table 5.13 reports draw probabilities; and Table 5.14 reports away win probabilities. The values of RELQUAL are the averages within each of the five quintile ranges formed by ranking the 16,288 matches used in the estimations reported in Tables 5.10 and 5.11 in ascending order of RELQUAL. The assumed values of UNCERT are calculated by substituting the five RELQUAL values into the formula UNCERT = RELQUAL×(1–RELQUAL). The assumed values of EXPHG and EXPAG are the average values within each of the five RELQUAL quintile ranges. This procedure produces five sets of values for the relative team quality variables and the home win, draw and away win probabilities at the start of the match taking home-field advantage into account:  (i) large difference in team quality favouring the away team (home win/draw/away win probabilities = 0.2974/0.2752/ 0.4274); (ii) small difference favouring away team (0.3940/0.2840/0.3220); (iii) equally balanced teams (0.4488/0.2845/0.2667); (iv) small difference favouring home team (0.4878/0.2810/0.2312); and (v) large difference favouring home team (0.5948/0.2452/0.1600). The five match durations for which probabilities are computed are t = 15,30,45,60 and 75 minutes; the three values for the numerical disparity in players are x = 1,0,–1; and the five values for the difference in scores are s = –2,–1,0,1,2.8 For example, referring to the central panels of Tables 5.12, 5.13 and 5.14 (the case of equally balanced teams), an opening goal scored by the home team in the first 15 minutes (with a one-goal lead sustained until the 15th minute) tilts the in-play home win/draw/away win probabilities for the 15th minute in the home team’s favour, from 0.4199/0.3070/0.2731 to 0.6995/0.1934/0.1071. For an opening goal scored by the away team in the same period (with the lead also sustained until at least the 15th minute), the probabilities at the 15th minute tilt in the away team’s favour, to 0.2010/0.2648/0.5342.

.0220 .0165 .0093 .0051 .0010

.0330 .0233 .0125 .0062 .0008

.0547 .0389 .0223 .0120 .0015

15 30 45 60 75

15 30 45 60 75

15 30 45 60 75

.3940/.2840/.3220

.4488/.2845/.2667

.4878/.2810/.2312

.5948/.2452/.1600

.1549 .1342 .0966 .0621 .0269

.1017 .0850 .0676 .0456 .0187

.0805 .0680 .0508 .0337 .0153

.0583 .0530 .0427 .0312 .0125

.0345 .0327 .0264 .0195 .0087

–1

.3416 .3336 .2939 .2575 .1903

.2579 .2499 .2292 .2115 .1505

.2166 .2114 .2043 .1827 .1411

.1839 .1775 .1786 .1584 .1262

.1248 .1292 .1280 .1238 .1020

0

+1

.6006 .6105 .6383 .6852 .7605

.5047 .5319 .5642 .6225 .7159

.4544 .4827 .5282 .5823 .7002

.4116 .4355 .4919 .5537 .6784

.3124 .3437 .3926 .4831 .6126

1

.8208 .8490 .8792 .9226 .9671

.7432 .7787 .8312 .8952 .9521

.6960 .7417 .8037 .8726 .9481

.6530 .7044 .7644 .8472 .9260

.5495 .6053 .6941 .7929 .9090

2

.1443 .1104 .0646 .0303 .0077

.1001 .0667 .0369 .0171 .0031

.0737 .0538 .0338 .0149 .0027

.0586 .0435 .0240 .0096 .0023

.0312 .0254 .0128 .0088 .0017

–2

.3206 .2743 .2008 .1282 .0523

.2358 .1950 .1459 .0941 .0357

.2010 .1656 .1245 .0796 .0317

.1620 .1372 .1002 .0636 .0249

.1090 .0899 .0701 .0437 .0205

–1

0

.5621 .5296 .4786 .3958 .2737

.4657 .4483 .3870 .3425 .2347

.4199 .4009 .3562 .3078 .2152

.3693 .3553 .3110 .2775 .2028

.2879 .2771 .2565 .2278 .1654

0

.8070 .8034 .8076 .8214 .8589

.7436 .7452 .7538 .7719 .8368

.6995 .7024 .7224 .7496 .8132

.6568 .6611 .6885 .7251 .7947

.5707 .5826 .6208 .6675 .7572

1

.9375 .9421 .9565 .9692 .9876

.9009 .9135 .9399 .9575 .9812

.8798 .8986 .9188 .9480 .9783

.8524 .8749 .9007 .9390 .9752

.7894 .8216 .8650 .9114 .9623

2

.4050 .3101 .1952 .1045 .0268

.2902 .2212 .1365 .0656 .0155

.2441 .1883 .1082 .0503 .0108

.1980 .1476 .0904 .0421 .0097

.1256 .0974 .0589 .0271 .0060

–2

.6220 .5351 .4116 .2906 .1320

.5105 .4207 .3241 .2148 .0922

.4438 .3746 .2806 .1894 .0782

.3860 .3304 .2492 .1621 .0723

.2956 .2471 .1729 .1114 .0472

–1

.8083 .7644 .6931 .6036 .4244

.7371 .6823 .6144 .5328 .3751

.6813 .6416 .5669 .4857 .3414

.6390 .5963 .5318 .4452 .3219

.5485 .5090 .4579 .3857 .2721

0

–1

.9404 .9344 .9154 .9143 .9223

.9059 .8909 .8838 .8850 .8980

.8812 .8752 .8577 .8752 .8914

.8551 .8459 .8421 .8457 .8745

.7935 .7911 .7945 .8145 .8449

1

.9859 .9871 .9865 .9913 .9934

.9742 .9727 .9784 .9866 .9919

.9634 .9682 .9762 .9810 .9899

.9554 .9621 .9634 .9776 .9882

.9323 .9347 .9461 .9673 .9868

2

Notes: Table 5.12 reports home win probabilities enumerated at various values of t, s, x, conditional on relative team quality represented by the home win, draw and away win probabilities at the start of the match, shown in the first column. t is the number of minutes’ play completed. x = dh–da is the number of home-team players dismissed minus the number of away-team players dismissed prior to the t’th minute. s is the difference between the home-team score and away-team score prior to the t’th minute.

.0156 .0125 .0070 .0035 .0009

15 30 45 60 75

.2974/.2752/.4274

–2

.0065 .0057 .0036 .0022 .0004

t↓s→

x→

15 30 45 60 75

Home/draw/away probabilities, t = 0 ↓

Table 5.12 Home-win probabilities, conditional on relative team strengths and the state of the match at various durations

.0703 .0696 .0510 .0384 .0163

.0896 .0788 .0671 .0445 .0198

.1323 .1166 .0899 .0672 .0306

15 30 45 60 75

15 30 45 60 75

15 30 45 60 75

.3940/.2840/.3220

.4488/.2845/.2667

.4878/.2810/.2312

.5948/.2452/.1600

.2356 .2459 .2449 .2353 .1945

.1999 .1913 .2016 .2007 .1594

.1742 .1855 .1787 .1707 .1416

.1498 .1523 .1530 .1549 .1298

.1050 .1122 .1171 .1165 .1016

–1

.3146 .3327 .3908 .4701 .6121

.2998 .3248 .3786 .4552 .6109

.2773 .3077 .3610 .4519 .6011

.2561 .2909 .3564 .4349 .5898

.2288 .2501 .3103 .3943 .5604

0

+1

.2484 .2543 .2554 .2459 .2068

.2754 .2732 .2829 .2770 .2380

.2735 .2895 .3019 .2992 .2495

.2746 .2946 .3042 .3143 .2619

.2673 .2972 .3303 .3274 .3063

1

.1286 .1079 .0941 .0662 .0303

.1641 .1533 .1267 .0861 .0428

.1835 .1667 .1381 .1024 .0459

.2005 .1829 .1668 .1191 .0641

.2275 .2254 .1992 .1550 .0776

2

.2216 .1953 .1691 .1174 .0561

.1763 .1597 .1294 .0894 .0384

.1534 .1378 .1133 .0746 .0339

.1326 .1234 .0911 .0657 .0294

.0881 .0838 .0656 .0426 .0207

–2

.2980 .3125 .3173 .3140 .2725

.2777 .2922 .2924 .2836 .2239

.2648 .2654 .2713 .2562 .2134

.2506 .2549 .2525 .2400 .1948

.2089 .2014 .2015 .1948 .1557

–1

0

.2783 .3101 .3615 .4592 .6118

.3013 .3225 .3968 .4688 .6272

.3070 .3360 .3964 .4854 .6273

.3169 .3438 .4082 .4822 .6236

.3044 .3306 .3972 .4734 .6203

0

.1415 .1535 .1588 .1537 .1310

.1804 .1817 .1931 .1899 .1483

.1934 .2079 .2105 .2060 .1664

.2170 .2309 .2322 .2199 .1818

.2509 .2572 .2597 .2569 .2106

1

.0511 .0497 .0383 .0280 .0114

.0731 .0698 .0501 .0378 .0179

.0905 .0799 .0663 .0467 .0207

.1088 .0931 .0785 .0531 .0225

.1413 .1275 .1082 .0751 .0346

2

.2593 .2693 .2566 .2132 .1160

.2524 .2504 .2264 .1772 .0942

.2444 .2366 .2072 .1547 .0744

.2254 .2170 .1865 .1430 .0677

.1970 .1757 .1552 .1105 .0523

–2

.2335 .2732 .3272 .3699 .3545

.2550 .2987 .3316 .3495 .3197

.2802 .3077 .3326 .3387 .3006

.2837 .3015 .3184 .3312 .2773

.2771 .2841 .3054 .2887 .2444

–1

.1434 .1835 .2474 .3320 .5138

.1830 .2293 .2911 .3823 .5450

.2104 .2511 .3161 .4074 .5764

.2303 .2699 .3372 .4224 .5771

.2591 .3055 .3566 .4504 .6045

0

–1

.0499 .0556 .0745 .0767 .0729

.0770 .0915 .0978 .1029 .0962

.0919 .0974 .1172 .1080 .1012

.1102 .1179 .1278 .1363 .1144

.1446 .1529 .1619 .1553 .1418

1

.0129 .0114 .0124 .0084 .0064

.0224 .0242 .0191 .0125 .0078

.0301 .0271 .0215 .0174 .0098

.0362 .0326 .0321 .0207 .0115

.0516 .0522 .0460 .0297 .0123

2

Notes: Table 5.13 reports draw probabilities enumerated at various values of t, s, x, conditional on relative team quality represented by the home win, draw and away win probabilities at the start of the match, shown in the first column. t is the number of minutes’ play completed. x = dh–da is the number of home-team players dismissed minus the number of away-team players dismissed prior to the t’th minute. s is the difference between the home-team score and away-team score prior to the t’th minute.

.0623 .0548 .0432 .0323 .0154

15 30 45 60 75

.2974/.2752/.4274

–2

.0392 .0300 .0264 .0219 .0080

t↓s→

x→

15 30 45 60 75

Home/draw/away probabilities, t = 0 ↓

Table 5.13 Draw probabilities, conditional on relative team strengths and the state of the match at various durations

.9077 .9139 .9397 .9565 .9827

.8774 .8979 .9204 .9493 .9794

.8130 .8445 .8878 .9208 .9679

15 30 45 60 75

15 30 45 60 75

15 30 45 60 75

.3940/.2840/.3220

.4488/.2845/.2667

.4878/.2810/.2312

.5948/.2452/.1600

.6095 .6199 .6585 .7026 .7786

.6984 .7237 .7308 .7537 .8219

.7453 .7465 .7705 .7956 .8431

.7919 .7947 .8043 .8139 .8577

.8605 .8551 .8565 .8640 .8897

–1

.3438 .3337 .3153 .2724 .1976

.4423 .4253 .3922 .3333 .2386

.5061 .4809 .4347 .3654 .2578

.5600 .5316 .4650 .4067 .2840

.6464 .6207 .5617 .4819 .3376

0

+1

.1510 .1352 .1063 .0689 .0327

.2199 .1949 .1529 .1005 .0461

.2721 .2278 .1699 .1185 .0503

.3138 .2699 .2039 .1320 .0597

.4203 .3591 .2771 .1895 .0811

1

.0506 .0431 .0267 .0112 .0026

.0927 .0680 .0421 .0187 .0051

.1205 .0916 .0582 .0250 .0060

.1465 .1127 .0688 .0337 .0099

.2230 .1693 .1067 .0521 .0134

2

.6341 .6943 .7663 .8523 .9362

.7236 .7736 .8337 .8935 .9585

.7729 .8084 .8529 .9105 .9634

.8088 .8331 .8849 .9247 .9683

.8807 .8908 .9216 .9486 .9776

–2

.3814 .4132 .4819 .5578 .6752

.4865 .5128 .5617 .6223 .7404

.5342 .5690 .6042 .6642 .7549

.5874 .6079 .6473 .6964 .7803

.6821 .7087 .7284 .7615 .8238

–1

0

.1596 .1603 .1599 .1450 .1145

.2330 .2292 .2162 .1887 .1381

.2731 .2631 .2474 .2068 .1575

.3138 .3009 .2808 .2403 .1736

.4077 .3923 .3463 .2988 .2143

0

.0515 .0431 .0336 .0249 .0101

.0760 .0731 .0531 .0382 .0149

.1071 .0897 .0671 .0444 .0204

.1262 .1080 .0793 .0550 .0235

.1784 .1602 .1195 .0756 .0322

1

.0114 .0082 .0052 .0028 .0010

.0260 .0167 .0100 .0047 .0009

.0297 .0215 .0149 .0053 .0010

.0388 .0320 .0208 .0079 .0023

.0693 .0509 .0268 .0135 .0031

2

.3357 .4206 .5482 .6823 .8572

.4574 .5284 .6371 .7572 .8903

.5115 .5751 .6846 .7950 .9148

.5766 .6354 .7231 .8149 .9226

.6774 .7269 .7859 .8624 .9417

–2

.1445 .1917 .2612 .3395 .5135

.2345 .2806 .3443 .4357 .5881

.2760 .3177 .3868 .4719 .6212

.3303 .3681 .4324 .5067 .6504

.4273 .4688 .5217 .5999 .7084

–1

.0483 .0521 .0595 .0644 .0618

.0799 .0884 .0945 .0849 .0799

.1083 .1073 .1170 .1069 .0822

.1307 .1338 .1310 .1324 .1010

.1924 .1855 .1855 .1639 .1234

0

–1

.0097 .0100 .0101 .0090 .0048

.0171 .0176 .0184 .0121 .0058

.0269 .0274 .0251 .0168 .0074

.0347 .0362 .0301 .0180 .0111

.0619 .0560 .0436 .0302 .0133

1

.0012 .0015 .0011 .0003 .0002

.0034 .0031 .0025 .0009 .0003

.0065 .0047 .0023 .0016 .0003

.0084 .0053 .0045 .0017 .0003

.0161 .0131 .0079 .0030 .0009

2

Notes: Table 5.14 reports away win probabilities enumerated at various values of t, s, x, conditional on relative team quality represented by the home win, draw and away win probabilities at the start of the match, shown in the first column. t is the number of minutes’ play completed. x = dh–da is the number of home-team players dismissed minus the number of away-team players dismissed prior to the t’th minute. s is the difference between the home-team score and away-team score prior to the t’th minute.

.9221 .9327 .9498 .9642 .9837

15 30 45 60 75

.2974/.2752/.4274

–2

.9543 .9643 .9700 .9759 .9916

t↓s→

x→

15 30 45 60 75

Home/draw/away probabilities, t = 0 ↓

Table 5.14 Away-win probabilities, conditional on relative team strengths and the state of the match at various durations

Simulations for in-play match result probabilities

135

Naturally, the later in the match the opening goal (or any goal that establishes a lead) is scored, the greater is the impact on the match outcome and the greater is the value of the goal to the scoring team. A goal scored between the 60th and 75th minutes which gives the home team a one-goal lead (sustained until at least the 75th minute) tilts the in-play probabilities at the 75th minute rather dramatically in the home team’s favour, from 0.2152/0.6273/0.1575 to 0.8132/0.1664/0.0204. The away team’s prospects for recovering from a one-goal deficit after 75 minutes to win the match are considered close to negligible. For a goal scored at the same stage that gives the away team a one-goal lead (with the lead again sustained until the 75th minute), the in-play probabilities at the 75th minute tilt in the away team’s favour, to 0.0317/0.2134/0.7549. The home team’s chances of recovering from a one-goal deficit after 75 minutes to win the match are somewhat higher than those for the away team, but still slender. Similarly, Tables 5.12, 5.13 and 5.14 can be used to determine the cost to either team (in terms of the outcome of the current match) of incurring a player dismissal. Using the same example, if the away team loses a player after 15 minutes, the in-play probabilities tilt in the home team’s favour, from 0.4199/0.3070/0.2713 to 0.6813/0.2104/0.1083. If the home team loses a player after 15 minutes, the in-play probabilities tilt in the away team’s favour, to 0.2166/0.2773/0.5061. Accordingly, the impact of a player dismissal after 15 minutes on the match result probabilities is only marginally smaller than the impact of an opening goal being scored at the same stage. Naturally, the later in the match a player dismissal creating a numerical disparity between the teams takes place, the smaller is the impact on the in-play match result probabilities, because the shorter is the remaining match duration over which one team plays at a numerical disadvantage. The dismissal of an away-team player in the 75th minute when the scores are level tilts the probabilities in the home team’s favour much less dramatically than a goal giving the home team the lead at that stage, from 0.2152/0.6273/0.1575 to 0.3414/0.5764/ 0.0822. Likewise the dismissal of a home-team player at the same stage tilts the probabilities by a smaller amount than a goal giving the away team the lead, to 0.1411/0.6011/0.2578. As a further illustration, Table 5.15 tracks the model’s in-play probabilities for two of the 2009 season fixtures included in Table 4.6 (used to illustrate the match results forecasting models reported in Chapter 4, Sections 4.3 and 4.5), Fulham vs West Bromwich Albion and Newcastle United vs Everton. Prior to the Fulham vs West Bromwich match, the goals-based forecasting model (Sections 4.2 and 4.3) assessed the home win/draw/away probabilities as 0.5521/0.2521/0.1958. The match remained scoreless until the 61st minute when Fulham took a 1–0 lead. Fulham scored again in the 72nd minute to make the final score 2–0. Immediately before Fulham’s first goal, with just over two-thirds of the match having been completed, the probabilities had shifted to 0.3639/0.4637/0.1724. The first goal immediately tilted the probabilities in Fulham’s favour to 0.7999/0.1703/0.0298. Immediately prior to the second

136

Game theory and football games

Table 5.15 In-play home-win/draw/away-win probabilities: illustration

Minute  5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

Fulham vs West Bromwich Albion

Newcastle United vs Everton

Goals or dismissals

Goals or dismissals

Fulham score, 61st min. Fulham score, 72nd min.

Home win

Draw

Away win

.5357 .5319 .5170 .5138 .4980 .4911 .4830 .4644 .4404 .4160 .4064 .3690 .8016 .8221 .9823 .9904 .9961 .9984

.2727 .2759 .2884 .2911 .3040 .3199 .3301 .3484 .3701 .4043 .4202 .4639 .1720 .1586 .0166 .0094 .0037 .0015

.1916 .1922 .1946 .1951 .1980 .1890 .1869 .1872 .1895 .1797 .1734 .1671 .0264 .0193 .0011 .0002 .0002 .0001

Newcastle player sent off, 44th min.

Home win

Draw

Away win

.3027 .3040 .2980 .2968 .2923 .2814 .2879 .2733 .1301 .1315 .1297 .1335 .1260 .1224 .1071 .0902 .0691 .0399

.2933 .3036 .3093 .3186 .3258 .3433 .3487 .3696 .3214 .3437 .3685 .4097 .4438 .4917 .5551 .6367 .7269 .8509

.4040 .3924 .3927 .3846 .3819 .3753 .3634 .3571 .5485 .5248 .5018 .4568 .4302 .3859 .3378 .2731 .2040 .1092

Source: Sky Sports Football Yearbook

Fulham goal, as the match moved into the final 20 minutes, the probabilities had drifted further to 0.8225/0.1583/0.0192. The second Fulham goal eliminated most of the remaining uncertainty over the match outcome, with the probabilities tilting even further to 0.9807/0.0184/0.0009 immediately afterwards. For the Newcastle vs Everton fixture, the forecasting model’s prior probabilities were 0.3073/0.2936/0.3991. The match finished 0–0, with the most noteworthy event being the dismissal of Newcastle’s Kevin Nolan in the 44th minute. Immediately before this incident, with nearly half of the allotted time having been played and the match still scoreless, the probabilities had drifted to 0.2621/0.3852/ 0.3527. Immediately after Newcastle were reduced to ten men the probabilities tilted in Everton’s favour, to 0.1301/0.3214/0.5485. As the second half progressed with the score remaining goalless, the draw probability steadily increased. By the 80th minute, for example, the probabilities had shifted to 0.0902/0.6367/0.2731. Conclusion

Chapter 5 has examined the extent to which the strategic behaviour of individual players or football teams during the course of the matches they play can be

Simulations for in-play match result probabilities

137

rationalised in accordance with game-theoretic principles of optimising strategic behaviour by independent agents when payoffs are interdependent. Whenever a penalty kick is awarded and executed, a two-person non-­cooperative zero-sum game is played out, in the space of a few seconds, between the kicker and the opposing goalkeeper. Theoretical and empirical research on the strategic choices of penalty kickers and goalkeepers suggests that, perhaps unknowingly, the behaviour of the players conforms closely to the predictions of game theory. Kickers and goalkeepers appear to randomise their choices between kicking and diving in either direction, and the proportions of penalties converted and penalties where a goal is averted are insensitive to the decisions of the kicker and the goalkeeper, as the theory suggests. Viewed more generally, the football match in its entirety has many of the characteristics of a dynamic ‘game’ in the economist’s sense. At any stage of the match, teams choose between defensive and attacking formations and between a non-violent and a violent style of play, so as to maximise their expected payoffs at the end of the match. Their strategic choices determine the probabilities of scoring and conceding goals at the current stage of the match, and the probabilities of having a player dismissed. In the dynamic game-theoretic model that is presented in this chapter, optimal strategic behaviour at any stage of the match is dependent on the current difference in scores, and on the amount of playing time that has elapsed. Teams that are trailing tend to attack, and teams that are trailing tend to play aggressively for as long as there is a realistic chance of salvaging the match. Stronger teams when trailing play aggressively for longer than weaker teams, and home teams when trailing play aggressively for longer than away teams. Towards the end of matches in which scores are level, the subgames have a prisoner’s dilemma structure, and there is a tendency for the teams to defect from nonviolence to violence. This feature of the model is consistent with an observed tendency for the number of dismissals to increase markedly during the closing stages of matches. The model is subjected to empirical scrutiny, using data on the timings of goals and player dismissals from more than 16,000 English professional league matches. Several features of the empirical hazard functions for the conditional arrival rates of player dismissals and goals are found to be consistent with the theoretical model. In particular, teams that are currently trailing by one goal or by two goals are willing to bear an increased probability of losing a player through dismissal, in order to increase the probability of scoring a goal quickly. Similarly, the goal-scoring rates of teams that are trailing by one goal or by two goals are significantly higher than they are for teams that are leading or level in scores. Stochastic simulations are used to obtain in-play match result probabilities, conditional upon the current state of the match at any stage, defined by an underlying relative team quality measure, the difference in scores and any numerical disparity in players.

138

Game theory and football games

Notes 1 The 90-minute duration is notional, because there are frequent discontinuities in play for various reasons: play is interrupted when the ball travels outside the confines of the pitch, when a foul is committed or a player is penalised under the offside law, when a goal is scored and when a player requires treatment on the pitch for injury. Although a few minutes of stoppage time are added on at the end of each 45-minute period of play, the time added is invariably less than the time lost through routine stoppages. 2 The ‘golden goal’ rule was used in several elimination tournaments during the 2000s, in matches that were drawn after 90 minutes’ play and were continued into an additional period of extra time. Extra time normally lasts for 30 minutes, and extra time continues regardless of whether any goals are scored. In tournaments where the golden goal rule was applied, a goal scored during extra time would finish the match immediately, with the scoring team victorious. 3 Prior to the 2000 season when the new rule was introduced, a team that won a match during a five-minute sudden-death overtime period (played when the scores were tied at the end of regular time) was awarded two league points, while its losing opponent received zero points. The new rule awarded two points to a team that won during overtime, and one point to the losing team. 4 The solutions for the two teams’ optimal strategies for the first minute should be determined by solving the model iteratively ‘backwards’, all the way from the 90th minute to the first minute. In order to construct this example, however, a set of match result probabilities applicable at the end of the first minute has been specified arbitrarily. These probabilities determine the two teams’ payoffs at the end of the first minute conditional on their strategies for the first minute. 5 The data source is soccernet.esp.go.com. Match information posted on this website records the match durations (in minutes) at which player dismissals occurred and goals were scored. The data set was compiled by transcribing these details for each match individually. 6 This is a simplification because a player who commits a foul in his own team’s penalty area, and by so doing denies the opposing team a goal-scoring opportunity, is liable to be dismissed, while the opposing team has an opportunity to score from the resulting penalty kick. The proportions of all player dismissals and goals that arrive simultaneously in this manner are relatively low, however. Ignoring this element of simultaneity greatly simplifies the specification and estimation of the empirical model. 7 Applying the log transformation to the arrival rates ensures that the fitted arrival rates generated by the estimated model are always positive. 8 Approximations for in-play match result probabilities at other durations, or for matches where the value of RELQUAL differs from those reported in Tables 5.12–5.14, may be obtained by means of interpolation or extrapolation based on the reported probabilities. The accuracy of results obtained by linear interpolation will depend upon how linear or non-linear are the relationships between RELQUAL or match duration and the reported probabilities in the nearest vicinity of the interpolated probabilities.

6

English professional football: historical development and commercial structure

Introduction

Professional football as a sport has always been inextricably linked to its attributes as a business, but never more so than during the modern era. Complaints are aired regularly in the media and elsewhere that players are overpaid; that the transfer market is out of control; that the whims of wealthy owners are driving many clubs to penury; that exorbitant ticket prices are driving spectators away from football; and that the priorities of television are dictating both the strategic and the operational decisions of football clubs and the sport’s organising bodies. Chapter 6 presents an overview of the historical development of English club football as a business, and analyses its current economic, financial and commercial structure. Section 6.1 describes the competitive structure of the major league and cup tournaments in which English teams participate, and identifies historical trends and patterns in the performance of groups of teams distinguished by characteristics such as geographical location, city size and date of entry into the league. Section 6.2 describes trends in match attendances, and the explanations for changing patterns of attendance that have been proposed by historians, sociologists and economists. Section 6.3 provides an overview of the profitability or loss-making propensities of English football clubs. The following three sections describe historical and current trends in the main revenue and cost items that appear in a football club’s profit and loss account:  namely gate revenues, examined in Section 6.4; broadcast revenues, examined in Section 6.5; and expenditure on players’ wages and salaries, and transfer expenditure, examined in Section 6.6. Finally, Section 6.7 describes historical and current trends in the ownership, governance and financing of English football clubs. 6.1  English professional football: competitive structure and team performance Origins and competitive structure

The origins of English football can be traced back to the late Middle Ages. Originally football was a rough and violent game, involving unspecified numbers 139

140

English professional football

of young men pursuing a ball through urban or rural locations, often resulting in serious damage to property, personal injury and even death. Despite repeated attempts by both church and state to ban the sport, street or village football remained popular until the arrival of industrialisation, when newly emerging patterns of urban residence and employment imposed new constraints and disciplines. In the first half of the nineteenth century football survived mainly within the upper-class public schools and universities, where the codes that define the modern sports of association football and rugby football were developed. By imposing rules and conventions on school sports that previously were perhaps no less disorderly than their street and village antecedents, reform-minded schoolmasters such as Sir Thomas Arnold of Rugby sought to inculcate qualities of discipline, courage and leadership among pupils. Slowly, as successive generations of pupils graduated from education into adult life, the popularity of sports such as football and rugby spread beyond the schools and universities. At a landmark meeting of representatives of a number of London and suburban clubs in October 1863, English football’s present-day governing body, the Football Association (FA), was established (Walvin, 1994; Szymanski and Zimbalist, 2006). English football’s two most durable and important club competitions both emerged soon afterwards. Fifteen clubs first contested the FA Cup during the winter of 1871–2. The Wanderers, a team comprising players who had attended the leading public schools and Oxford or Cambridge Universities, defeated the Royal Engineers in the first final, watched by 2,000 spectators. During the 1880s, football’s geographic centre of power shifted away from the predominantly southern ex-public school and ex-university clubs, towards teams based in manufacturing towns and cities in the Midlands and the North West. Enlightened factory owners and employers, many of whom were themselves public school graduates, began to see the benefits of regular Saturday afternoon holidays for workplace morale and productivity, and created new opportunities for the development of organised working-class leisure activities. New football clubs were formed, often at the instigation of local church leaders, throughout England during the late 1870s and 1880s. A northern team, Blackburn Olympic, won the FA Cup for the first time in 1883, followed by Blackburn Rovers, three-time winners between 1884 and 1886. The principle of professionalism was accepted by the FA in July 1885. Its recognition was a key development in the processes leading to the eventual formation of the Football League in 1888. Twelve teams were members of the league during its first three seasons, with Preston North End the inaugural champions in the 1889 and 1890 seasons, followed by Everton in 1891. During the next three decades, membership of the Football League expanded progressively. In the 1893 season, a second tier of twelve teams was created, while membership of the top tier was expanded to sixteen. Several of the leading names of the modern era made their debut appearances in the 1890s, including Manchester United (then Newton Heath) in the 1893 season and Liverpool in the 1894 season. Woolwich Arsenal was the first southern club admitted, also in the 1894 season. Total membership

Competitive structure and team performance

141

was increased to thirty-two teams in the 1895 season, then thirty-six in the 1899 season, then forty in the 1906 season. The league finally achieved a membership of magnitude comparable to the combined strength of the present Premier League and Football League (ninety-two teams) shortly after the First World War. In the 1921 season, twenty-two teams from the Southern League were added to the existing two-tier structure (which had by then expanded to forty-four teams) to form the new Division 3 (South). In the 1922 season a new Division 3 (North) was created, initially comprising twenty teams, but with membership increased to twenty-two two seasons later. The most important structural changes to the league’s format since the 1920s were as follows: • A further increase in league membership from eighty-eight to ninety-two teams in the 1951 season; • The reorganisation of the lower two tiers into Divisions 3 and 4 from the 1959 season, with membership determined on merit (by promotion and relegation) rather than by geographical location; • An increase in mobility within the league with three (rather than two) teams promoted and relegated between T1 and T2, and between T2 and T3, each season from the 1974 season onwards, and a play-off system introduced in the 1987 season to determine one of the promotion places for each of T2, T3 and T4; • Several adjustments to the size of the tiers during the late 1980s and early 1990s, with automatic promotion and relegation between T4 and the highest tier below the Football League also implemented in a number of seasons during this period and routinely during the 2000s; and • The withdrawal from the Football League of the T1 clubs to form a breakaway Premier League, starting in the 1993 season. This development has not affected professional football’s basic competitive structure, but it has had profound organisational and financial implications. In addition, there were several changes to the names of the four tiers during the 1990s and 2000s. As was noted in Chapter 3, the official nomenclature at the time of writing (during the 2010 season) is Premiership, Championship, League One and League Two. In the rest of this chapter, as throughout this volume, the four divisions are known as T1, T2, T3 and T4 (tiers one to four). Since the Second World War, the number of tournaments has proliferated. Although the FA Cup has continued in a sudden-death format essentially unchanged since its inception in the 1870s, many more clubs (both amateur and professional) now enter, with the major clubs competing only in the final stages. By the 2009 season, the total entry had expanded to 762 teams, with the qualifying stages starting in August, and the showpiece final played at the end of the domestic season in May. The most important domestic competition of post-war vintage is the League Cup. Entry to this sudden-death knockout tournament is open to league clubs

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only. The League Cup made an uncertain start with a number of leading clubs either refusing to enter, or to take the competition seriously, for several years following its introduction in the 1961 season. Aston Villa of T1 defeated Rotherham of T3 over two legs in the first final, and several other lower-tier teams reached the final during the 1960s. By the start of the 1970s, the League Cup was established as a prestigious competition which all clubs considered worth taking seriously. The prestige of both major domestic cup competitions has suffered in recent seasons, however, with the leading clubs (in particular) often choosing to field reserve teams in order to keep their star players fresh for league and European fixtures that they consider to be more important. Regular competitive football at European level was first introduced in 1955. Birmingham City and a combined London team both competed in the first Fairs Cup tournament (the predecessor of the UEFA Cup) staged between 1955 and 1958. Meanwhile, Manchester United was the first English club to enter the European Cup in the 1957 season. By the 1961 season, both the Fairs Cup and a new European Cup Winners’ Cup were also operating on an annual basis. From then until 1985, when English clubs were excluded from European tournaments following the hooligan-related Heysel stadium disaster at the European Cup Final in Brussels, the three European competitions attracted a combined quota of up to eight leading English clubs per season. England’s ban was rescinded in the 1991 season. Since then, European competition has acquired an increasingly prominent position in the fixture lists of the top clubs. The importance of regular European participation has been enhanced by rapid growth in the financial rewards available from increasingly lucrative television contracts. During the 1990s, a league format was introduced for the early stages of the European Cup, which was renamed the Champions League. This removed the threat of early elimination, and guaranteed all entrants a minimum number of fixtures. In the 2009 season, thirty-two clubs, including up to four from each of the leading European domestic leagues (rather than just the domestic champions) gained entry to the Champions League. Some clubs (the champions and runners-up from the major football powers) enter the league direct, while others (third- and fourth-placed clubs from the major powers, and champions from lesser powers) participate in a qualifying tournament, which eliminates many of the weaker aspirants before the main competition gets underway. The 1999 season also saw the consolidation of the UEFA and Cup Winners’ Cups into a single UEFA Cup tournament. Following several further changes of format, the UEFA Cup was retitled as the Europa League at the start of the 2010 season. Team performance

Although the main focus of this chapter is the financial performance, rather than the sporting performance, of English football clubs, it is obvious that there are direct linkages between the two. At the micro level, a club’s capacity to generate

Competitive structure and team performance

143

revenue depends on its team’s success on the field of play. On the other hand, a club’s capacity to strengthen its team by purchasing better players in the transfer market and by offering remuneration at a level that will attract and retain the best players depends on the strength of its finances. At the macro level, economists have argued that the attractiveness to spectators, and therefore the revenue-­generating potential of any sports league, depends on the maintenance of a reasonable level of competitive balance (see Chapters 1, 2 and 3). Before considering the various economic and financial aspects of English football’s historical development as a business, however, it is useful first to identify a few key facts concerning team performance and championship dominance. Table 6.1 summarises data on the best-performing teams in the league championship and the cup (domestic and European) competitions. The first panel shows the number of championship victories per team in each decade since the end of the First World War. As an alternative and slightly broader measure of championship dominance, the second panel shows the top-performing teams in each decade, scored by awarding three, two and one points respectively to the teams finishing first, second and third in T1 in each season. The third and fourth panels show, for each decade, all teams that won the FA Cup and League Cup. The fifth panel shows the winners in European competition in each decade. On both sets of measures of championship dominance, Arsenal in the 1930s, Liverpool in the late 1970s and 1980s and Manchester United in the 1990s and 2000s all achieved a level of dominance that was not matched by any team in any of the other decades. Many commentators attribute Arsenal’s success in the 1930s to superior training methods and mastery of tactics, initially under the management of Herbert Chapman until his death in 1934. Continuity of an effective managerial style, maintained through a series of internal appointments (with Bill Shankly followed by Bob Paisley, Joe Fagan and Kenny Dalglish) is seen as a key factor in Liverpool’s success during the 1970s and 1980s. While Alex Ferguson’s managerial contribution during the 1990s and 2000s is widely acknowledged, detractors tend to see a degree of inevitability in Manchester United’s success given the club’s overwhelming financial strength. Table 6.1 indicates that the 1920s and 1960s were the decades in which the destination of the championship from season to season was most unpredictable. Although Huddersfield Town was by some distance the most successful team of the 1920s, this decade was unusual in respect of the total number of teams that managed to achieve a top three position on at least one occasion. Two teams shared top honours almost evenly during the 1950s: Wolverhampton Wanderers and Manchester United. The 1960s and the first half of the 1970s can be seen as a continuum, with ten different teams winning the championship during sixteen seasons, and no team winning in consecutive seasons. By winning three of the last four championships in the 1970s, another six during the 1980s, and one more in 1990, Liverpool established a degree of dominance unprecedented at the time, but subsequently matched, and perhaps even surpassed, by Manchester United. The

1930–1939 Man Utd 3 Wolves 3 Portsmouth 2 Arsenal 2 Chelsea 1 Liverpool 1 Tottenham 1

1947–1959

League championship – points for a top three finish Huddersf’ld 14 Arsenal 18 Man Utd 19 Liverpool 6 Sheff Wed 7 Wolves 16 Burnley 6 Everton 6 Arsenal 8 Sunderland 5 Sunderland 5 Tottenham 8 WBA 5 Aston Villa 4 Portsmouth 7 Everton 3 Derby 4 Preston 5 Leicester 3 Man City 4 Blackpool 3 Newcastle 3 Wolves 4 Chelsea 3 Sheff Wed 3 Charlton 3 Liverpool 3 Arsenal 2 Huddersf’ld 3 WBA 2 Bolton 2 Preston 1 Burnley 1 Cardiff 2 Tottenham 1 Derby 1 Man City 2 Huddersf’ld 1 Tottenham 2 Sunderland 1 Aston Villa 1 Chelsea 1

League championships Huddersf’ld 3 Arsenal 5 Liverpool 2 Everton 2 Burnley 1 Man City 1 Everton 1 Sheff Wed 1 Newcastle 1 Sunderland 1 Sheff Wed 1 WBA 1

1920–1929

Man Utd 10 Liverpool 9 Tottenham 8 Burnley 7 Leeds 7 Everton 5 Ipswich 3 Man City 3 Wolves 3 Nottm Forest 2 Sheff Wed 2 Chelsea 1

Liverpool 2 Man Utd 2 Burnley 1 Everton 1 Ipswich 1 Leeds 1 Man City 1 Tottenham 1

1960–1969

Liverpool 19 Leeds 10 Derby 7 Arsenal 5 Nottm Forest 5 Everton 4 Ipswich 2 Man City 2 QPR 2 Chelsea 1 Man Utd 1 Tottenham 1 WBA 1

Liverpool 4 Derby 2 Arsenal 1 Everton 1 Leeds 1 Nottm Forest 1

1970–1979

Table 6.1 Historical performance of top English teams in league and cup competition

Liverpool 24 Everton 8 Man Utd 6 Ipswich 5 Arsenal 4 Aston Villa 3 Nottm Forest 3 Southampton 2 Tottenham 2 Watford 2 West Ham 1

Liverpool 6 Everton 2 Arsenal 1 Aston Villa 1

1980–1989

Man Utd 21 Arsenal 9 Liverpool 7 Blackburn 5 Newcastle 5 Aston Villa 4 Leeds 3 Chelsea 1 Crystal Pal 1 Norwich 1 Nottm Forest1 Sheff Wed 1 Tottenham 1

Man Utd 5 Arsenal 2 Blackburn 1 Leeds 1 Liverpool 1

1990–1999

Man Utd 23 Arsenal 15 Chelsea 13 Liverpool 7 Leeds 1 Newcastle 1

Man Utd 6 Arsenal 2 Chelsea 2

2000–2009

Arsenal 2 Everton 1 Man City 1 Newcastle 1 Portsmouth 1 Preston 1 Sheff Wed 1 Sunderland 1 WBA 1

Newcastle 3 Arsenal 1 Aston Villa 1 Blackpool 1 Bolton 1 Charlton1 Derby 1 Man City 1 Man Utd 1 Nottm Forest 1 WBA 1 Wolves 1

Arsenal 2 Chelsea 1 Ipswich 1 Leeds 1 Liverpool 1 Man Utd 1 Southampton 1 Sunderland 1 West Ham 1

European competition wins (from 1956) Leeds 1 Liverpool 4 Man Utd 1 Chelsea 1 Newcastle 1 Leeds 1 Tottenham 1 Man City 1 West Ham 1 Nottm Forest 1 Tottenham 1

League Cup wins (from 1961) Aston Villa 1 Aston Villa 2 Birmingham 1 Man City 2 Chelsea 1 Nottm Forest 2 Leeds 1 Tottenham 2 Leicester 1 Stoke 1 Norwich 1 Wolves 1 QPR 1 Swindon 1 WBA 1

Tottenham 3 Everton 1 Liverpool 1 Man City 1 Man Utd 1 WBA 1 West Ham 1 Wolves 1

Source: Butler (1987), Smailes (1992), Rothmans/Sky Sports Football Yearbook

FA Cup wins Bolton 3 Aston Villa 1 Blackburn 1 Cardiff 1 Huddersf’ld 1 Newcastle 1 Sheff Utd 1 Tottenham 1

Liverpool 2 Aston Villa 1 Everton 1 Ipswich 1 Nottm Forest 1 Tottenham 1

Liverpool 4 Arsenal 1 Luton 1 Norwich 1 Nottm Forest 1 Oxford 1 Wolves 1

Liverpool 2 Man Utd 2 Tottenham 2 Coventry 1 Everton 1 West Ham 1 Wimbledon 1

Man Utd 2 Arsenal 1 Chelsea 1

Aston Villa 2 Arsenal 1 Chelsea 1 Leicester 1 Liverpool 1 Man Utd 1 Nottm Forest 1 Sheff Wed 1 Tottenham 1

Man Utd 4 Arsenal 2 Chelsea 1 Everton 1 Liverpool 1 Tottenham 1

Liverpool 2 Man Utd 1

Chelsea 2 Liverpool 2 Man Utd 2 Blackburn 1 Leicester 1 Middlesbro 1 Tottenham 1

Arsenal 3 Chelsea 3 Liverpool 2 Man Utd 1 Portsmouth 1

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latter’s championship victory in 1993 ended a barren run stretching back to 1967 and was the first of eleven triumphs in seventeen seasons. By winning the championship in 1989 and 1991, Arsenal were instrumental in ending Liverpool’s long spell of dominance; and further victories in 1998, 2002 and 2004 consolidated Arsenal’s status as Manchester United’s closest challengers. Chelsea’s emergence as a major force, with championship victories in 2005 and 2006, saw Manchester United deprived of the title for three consecutive seasons, before a run of consecutive victories (2007–9) reaffirmed their dominance. Also notable in Table 6.1 is a shift in demographic base of the most successful clubs. In all decades since the 1930s, clubs from the six largest English cities (London, Birmingham, Liverpool, Manchester, Sheffield and Leeds) have claimed the majority of championship wins (at least six out of every ten). As late as the early 1960s, however, Burnley and Ipswich Town repeated the earlier championship successes of other smaller-market clubs like Huddersfield Town and Portsmouth. In the 1970s, Derby County and Nottingham Forest also interrupted the dominance of the largest-market clubs. Since the 1980s, however, only Blackburn Rovers have achieved the same feat, in the 1995 season. In any event, as arguably the wealthiest club in the league at the time thanks to the extraordinary largesse of their benefactor Jack Walker, Blackburn have some cause to be seen as an exceptional case. Table 6.1 indicates that success at the top of T1 has never previously been as highly concentrated as it was during the 2000s, when only three different teams won the league championship and only six achieved a top three finish (two of which, Leeds United and Newcastle United, did so only once, finishing in third position in the 2000 and 2003 seasons, respectively). Likewise only five different teams won the FA Cup. Portsmouth (2008) were the only team to do so from outside the small clique of four (Arsenal, Chelsea, Liverpool and Manchester United) that also dominated the league championship. Perhaps more surprisingly, the 2000s were the least successful decade for English teams in terms of European trophy success since the 1950s. Despite regularly dominating the latter stages of the Champions League, particularly towards the end of the decade, only Liverpool (2005) and Manchester United (2008) won the coveted title; and Liverpool (2001) were the only successful English team in the UEFA Cup.1 As noted in Chapter 3, Section 3.1, FA Cup match results data suggest there was an increase in competitive inequality during the 1920s and 1930s, and a further increase that began during the mid-1970s and was still in progress by the end of the 1990s (Dobson and Goddard, 2004). Table 6.2 reports data on the incidence of ‘giant-killings’ in FA Cup ties between the 1974 and 2009 seasons, in the form of the proportions of ties contested by teams from different tiers that were won by the lower-ranked team. These data are reported in four-season bands, collectively for all ties contested by teams from different tiers, and separately for each permutation of rankings (for example, T1 versus T2, T1 versus T3, T2 versus T3, and so on). Ties contested by a league team and a non-league team are included, with all non-league teams treated as a single category. The final column of Table 6.2

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Table 6.2 Incidence of giant-killings in FA Cup ties, 1974–2009 T1 vs T2

T1 vs T3

T1 vs T4

T1 vs NL

T2 vs T2 vs T2 vs T3 T4 NL

Proportion of ties won by lower-ranked team 1974–1977 .279 .222 .125 .125 .481 1978–1981 .306 .214 .091 .000 .458 1982–1985 .299 .267 .000 .000 .435 1986–1989 .197 .200 .125 .333 .478 1990–1993 .279 .208 .154 .000 .444 1994–1997 .263 .250 .000 .000 .455 1998–2001 .172 .250 .091 .222 .364 2002–2005 .299 .231 .100 .000 .263 2006–2009 .200 .300 .100 .000 .300 Number of ties 1974–1977 61 1978–1981 62 1982–1985 67 1986–1989 61 1990–1993 68 1994–1997 80 1998–2001 64 2002–2005 67 2006–2009 70

27 28 30 20 24 24 28 13 20

8 11 5 16 13 10 11 20 10

8 5 4 6 4 7 9 5 7

27 18 20 20 34 28 22 18 18

T3 vs T3 vs T4 NL

T4 vs NL All

.200 .600 .250 .400 .250 .182 .111 .471 .200

.000 .250 .000 .000 .167 .250 .167 .200 .111

.333 .292 .368 .421 .283 .339 .293 .474 .391

.189 .161 .164 .125 .127 .185 .203 .234 .217

.463 .286 .340 .298 .309 .276 .292 .224 .298

.292 .265 .272 .272 .256 .256 .236 .284 .255

10 10 16 15 8 11 9 17 15

3 8 5 5 6 8 6 5 9

60 48 57 57 53 56 58 57 64

74 62 67 48 55 54 59 64 46

41 42 53 57 55 58 65 58 47

319 294 324 305 320 336 331 324 306

Note: NL denotes non-league. NL is treated as a single category. The column headed ‘All’ refers to all FA Cup ties contested by league teams from different tiers, and ties contested by a league team and a non-league team. Source: Rothmans/Sky Sports Football Yearbook

reports the overall proportion of ties won by the lower-ranked team, and reflects a declining incidence of giant-killings during the 1970s, 1980s and 1990s. During the 2000s, however, the downward trend in the incidence of giant-killings has not continued. This could reflect a cessation of the trend towards rising competitive inequality; or it could reflect the increasing popularity among the leading teams (and even among some of the lesser teams) of a policy of resting star players and selecting reserve-team players for FA Cup ties. Below we seek to identify some broader patterns in the performance of teams throughout the entire league. For this purpose, Table 6.3 identifies five groups of clubs with broadly similar characteristics (Groups 1 to 5, henceforth known as G1 to G5), using three simple criteria to define the clubs that make up each group: • The club’s home-town population recorded in the 1961 Census of Population; • The date of the club’s initial entry into the league; • The club’s geographical location (for which there are two broad categories: South and Midlands/North).

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Table 6.3 Group definitions Group 1:

Clubs from towns with populations larger than 500,000, which entered the league before its expansion in the early 1920s. Arsenal, Aston Villa, Birmingham City, Chelsea, Everton, Leeds United, Liverpool, Manchester City, Manchester United, Sheffield United, Sheffield Wednesday, Tottenham Hotspur, West Bromwich Albion, West Ham United (14 clubs).

Group 2:

Clubs from towns with populations in the range 250–500,000 in the Midlands and North (all English regions from the East and West Midlands northwards). Bradford City, Bradford Park Avenue, Coventry City, Derby County, Hull City, Leicester City, Newcastle United, Notts County, Nottingham Forest, Port Vale, Stoke City, Sunderland, Wolverhampton Wanderers (13 clubs).

Group 3:

Other clubs from towns in the south (the South East, South West and East Anglia regions, plus South Wales) with populations below 500,000, as well as the smaller London clubs not included in Group 1. Most of these clubs (except Bristol City, Luton Town, Fulham and Leyton Orient) joined the League during or after its early 1920s expansion. Aberdare, Aldershot, Barnet, Bournemouth, Brentford, Brighton and Hove Albion, Bristol City, Bristol Rovers,Cambridge United, Cardiff City, Charlton Athletic, Cheltenham Town, Colchester United, Crystal Palace, Dagenham and Redbridge, Exeter City, Fulham, Gillingham, Ipswich Town, Leyton Orient, Luton Town, Maidstone United, Merthyr Town, Millwall, Newport County, Norwich City, Oxford United, Peterborough United, Plymouth Argyle, Portsmouth, Queens Park Rangers, Reading, Southampton, Southend United, Swansea City, Swindon Town, Thames, Torquay United, Watford, Wimbledon/Milton Keynes Dons, Wycombe Wanderers, Yeovil Town (42 clubs).

Group 4:

All clubs from smaller towns in the Midlands/North which entered the League before 1920. Barnsley, Blackburn Rovers, Blackpool, Bolton Wanderers, Burnley, Bury, Chesterfield, Crewe Alexandra, Doncaster Rovers, Gateshead, Grimsby Town, Huddersfield Town, Lincoln City, Middlesbrough, Oldham Athletic, Preston North End, Rotherham United, Stockport County, Walsall (19 clubs).

Group 5:

Clubs from the Midlands/North which entered the League during or after the early 1920s expansion. Accrington Stanley, Ashington, Barrow, Boston United, Carlisle United, Chester City, Darlington, Durham City, Halifax Town, Hartlepool United, Hereford United, Kidderminster Harriers, Macclesfield Town, Mansfield Town, Morecambe, Nelson, New Brighton, Northampton Town, Rochdale, Rushden and Diamonds, Scarborough, Scunthorpe United, Shrewsbury Town, Southport, Stalybridge Celtic, Tranmere Rovers, Wigan Athletic, Workington Town, Wrexham, York City (30 clubs).

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149

Figure 6.1 shows the percentage share of the clubs in each of the five groups in an aggregate performance score, calculated by awarding 92 points to the club which finished first in T1, 91 points to the club which finished second, and so on, in each season. Minor adjustments to the points system are made for seasons when the number of teams in the league was greater or less than 92. Teams finishing in equal positions in the old Divisions 3 (South) and (North) are awarded equal points: first position in either division gains 48 points, second gains 46 points, and so on. The relative constancy of G1’s performance score emphasises the fact that the dominance of the clubs from the largest cities has been a consistent feature throughout the league’s history, and is by no means a uniquely recent phenomenon. In contrast, the G2 clubs from the next city size-band, which include three championship winners from the 1920s, 1930s and 1950s (Newcastle United, Sunderland and Wolverhampton Wanderers), experienced a significant decline in their performance as a group between the late 1930s and late 1950s, and again during the 2000s. G3 clubs registered a steady and sustained improvement in average performance between the 1920s and the end of the 1980s. Their progressive advance represents the most important long-term shift in the geographical balance of football power. Since the Second World War, a small majority of the clubs that gained admission to the league are located in the south.2 More important, however, has been a progressive rise in the status of many of southern clubs that entered the league during its early 1920s expansion or later, and were engaged in a catching-up process for several decades subsequently. Charlton Athletic, Crystal Palace, Ipswich Town, Norwich City, Portsmouth, Queens Park Rangers, Southampton and Swindon Town all rose from modest starting positions in Division 3 (South) eventually to feature prominently in T1 and T2. Collectively, however, the G3 clubs were not the main beneficiaries of English football’s popular revival during the 1990s. According to Figure 6.1, G3’s performance peaked in the late 1980s and early 1990s. A sharp decline during the mid to late 1990s preceded a partial recovery during the 2000s. G4 consists mainly of northern clubs from smaller towns, all of which were already established in the two upper tiers at the time of the league’s early 1920s expansion. These clubs were the main victims of the southern clubs’ upward progress between the 1920s and 1980s. Many clubs located in traditional industrial or manufacturing towns especially hard-hit by three major recessions during the 1970s, 1980s and 1990s, have not been able to keep pace with their more upwardly mobile southern counterparts. Nevertheless, several G4 members (Blackburn Rovers, Bolton Wanderers, Middlesbrough) have responded adroitly to the opportunities presented by the recovery in football’s popular appeal. Accordingly, G4’s performance score improved significantly during the 1990s and this improvement has been sustained subsequently.

English professional football

150 40

35

Group 3

30

Group 1 Per cent

25

Group 4

20

15

Group 2

10

Group 5

5

0

1922 1925 1928 1931 1934 1937 1947 1950 1953 1956 1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007

Season

Figure 6.1  Percentage shares in aggregate performance of clubs in Groups 1 to 5

The long-term performance of the G5 clubs, many of which were the founder members of Division 3 (North) in the early 1920s, is in marked contrast to that of their southern counterparts in G3. From the start, there was an imbalance between the respective strengths of the southern and northern Division 3 clubs. In the 1920 season, the last before the formation of Division 3 (South), the league comprised thirty-seven clubs from the North and Midlands, and only seven from the South. At this point a strong pool of aspiring southern clubs were clamouring for entry; while most of the larger northern and midland towns were already represented. This meant that Division 3 (North) was formed from a weaker pool of clubs than Division 3 (South). Since the 1920s, several G5 clubs lost their league status, and few of the survivors have enjoyed anything more than the briefest spells in the top two tiers. During the second half of the 2000s, Wigan Athletic became a notable exception by achieving and retaining T1 status. 6.2  Match attendances Trends in attendances

This subsection describes broad trends in English league match attendances at an aggregate level. A statistical analysis of the long-term determinants of attendance for individual clubs during the post-Second World War period is included in Chapter 11. Table 6.4 reports data on aggregate English league attendances between 1922 and 2009. During the inter-war period, the trend in attendances mirrored the

Match attendances

151

Table 6.4 English league attendances, aggregate and by tier Aggregates (millions)

Percentage shares

Season

Total

T1

T2

T3

T4

T1

T2

T3

T4

1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973

25.6 23.6 23.3 23.1 23.1 23.4 23.5 23.9 22.9 21.0 21.8 21.4 22.5 23.1 24.7 26.4 27.9 27.0 35.4 40.2 41.0 40.6 39.5 39.0 37.1 36.4 34.1 33.2 32.7 33.5 33.7 32.5 28.6 28.0 28.8 28.5 27.6 27.2 28.9 30.1 29.2 29.5 28.2 28.7 25.4

12.5 10.7 10.5 10.0 10.4 10.6 10.6 10.5 10.5 9.5 9.9 9.5 10.4 10.8 11.4 11.4 11.6 11.5 14.9 16.7 17.9 17.4 16.7 16.1 16.1 16.1 15.1 14.2 13.8 14.4 14.7 14.4 12.9 12.1 12.4 12.5 12.7 12.5 14.2 15.3 14.5 14.8 14.0 14.5 14.0

6.1 6.2 5.8 6.7 6.1 6.5 6.9 6.7 6.3 6.1 5.6 6.1 5.8 6.1 6.9 8.0 8.6 8.6 11.0 12.3 11.1 11.7 10.8 11.1 9.7 9.7 9.0 9.1 8.7 8.6 8.6 8.4 7.0 7.5 7.4 7.6 7.0 6.9 7.3 7.4 7.4 7.6 7.1 6.8   5.6

4.4 4.3 4.0 3.9 3.9 3.8 3.6 4.0 3.9 3.2 3.9 3.5 3.8 3.8 4.0 4.4 4.6 4.0 5.6 6.7 7.0 7.1 7.3 6.9 6.7 6.3 6.0 5.7 5.6 6.1 6.1 5.7 4.8 5.2 5.7 5.4 4.4 4.8 4.4 4.0 4.3 4.2 4.4 4.7 3.7

2.5 2.3 3.0 2.6 2.6 2.5 2.5 2.7 2.3 2.3 2.2 2.3 2.5 2.4 2.4 2.6 3.1 2.9 3.9 4.6 5.0 4.4 4.8 4.9 4.7 4.2 4.0 4.3 4.6 4.3 4.2 4.0 3.9 3.3 3.2 3.0 3.5 3.0 3.0 3.4 3.0 2.9 2.8 2.7 2.1

48.8 45.5 44.9 43.2 45.3 45.2 44.9 43.9 45.6 45.0 45.7 44.6 46.5 46.8 46.1 43.0 41.7 42.4 42.1 41.5 43.7 42.8 42.2 41.3 43.2 44.4 44.2 42.7 42.2 43.1 43.6 44.4 45.3 43.1 43.3 43.8 46.0 45.8 49.2 50.8 49.8 50.2 49.6 50.5 55.0

23.9 26.4 25.1 28.8 26.6 27.9 29.3 28.0 27.5 28.9 25.9 28.4 25.8 26.4 28.0 30.3 30.9 31.9 31.1 30.5 27.1 28.8 27.3 28.4 26.0 26.7 26.4 27.3 26.6 25.8 25.6 25.8 24.5 26.6 25.8 26.6 25.3 25.4 25.1 24.7 25.2 25.7 25.1 23.6 22.1

17.4 18.2 17.3 16.7 16.8 16.1 15.2 16.6 17.1 15.3 18.0 16.3 16.8 16.4 16.1 16.8 16.5 14.8 15.9 16.5 17.0 17.5 18.5 17.8 18.0 17.4 17.6 17.1 17.1 18.2 18.2 17.6 16.7 18.6 19.7 19.0 16.0 17.6 15.3 13.4 14.8 14.2 15.5 16.4 14.7

9.9 9.9 12.7 11.2 11.4 10.8 10.6 11.5 9.8 10.8 10.3 10.7 11.0 10.5 9.8 9.9 11.0 10.8 10.9 11.4 12.2 10.9 12.0 12.5 12.7 11.5 11.9 12.9 14.0 12.9 12.6 12.3 13.5 11.7 11.3 10.6 12.7 11.1 10.3 11.1 10.2 9.9 9.8 9.5 8.3

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Table 6.4 (cont.) Aggregates (millions)

Percentage shares

Season

Total

T1

T2

T3

T4

T1

T2

T3

T4

1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

25.0 25.6 24.9 26.0 25.4 24.5 24.6 21.9 20.0 18.8 18.3 17.8 16.5 17.4 18.0 18.5 19.5 19.5 20.4 20.6 21.7 21.8 21.9 22.8 24.7 25.4 25.4 26.1 27.8 28.5 29.2 29.2 29.1 29.5 29.9 29.9

13.1 12.6 13.1 13.6 13.3 12.7 12.2 11.4 10.4 9.3 8.7 9.7 9.0 9.1 8.1 7.8 7.9 8.6 10.0 9.7 10.7 11.2 10.5 10.8 11.1 11.6 11.7 12.5 13.0 12.8 13.3 12.9 12.9 13.1 13.7 13.5

6.3 7.0 5.8 6.2 6.5 6.1 6.1 5.2 4.8 5.0 5.4 4.0 3.6 4.2 5.3 5.8 6.9 6.3 5.8 5.9 6.5 6.0 6.6 6.9 8.3 7.5 7.8 7.9 8.4 9.3 8.8 9.6 9.7 10.1 9.4 9.9

3.4 4.1 3.9 4.1 3.3 3.4 4.0 3.6 2.8 2.9 2.7 2.7 2.5 2.4 2.8 3.0 2.8 2.8 3.0 3.5 3.0 3.0 2.9 3.2 3.5 4.1 3.7 3.5 4.0 3.9 4.1 4.2 4.2 4.1 4.4 4.2

2.2 1.9 2.1 2.1 2.3 2.3 2.4 1.7 2.0 1.6 1.6 1.4 1.4 1.7 1.8 1.8 1.9 1.8 1.6 1.5 1.6 1.6 2.0 1.9 1.8 2.1 2.2 2.2 2.4 2.5 3.0 2.6 2.3 2.3 2.4 2.3

52.3 49.2 52.6 52.2 52.2 51.7 49.4 52.0 52.1 49.6 47.4 54.7 54.8 52.6 45.1 42.3 40.5 44.2 49.0 47.2 49.1 51.4 47.7 47.4 44.9 45.8 46.0 47.9 47.0 44.9 45.6 44.0 44.2 44.2 45.8 45.3

25.3 27.2 23.3 23.9 25.5 25.1 24.8 23.6 23.8 26.5 29.2 22.6 21.5 24.0 29.7 31.6 35.4 32.2 28.5 28.5 29.9 27.5 30.0 30.5 33.7 29.6 30.9 30.4 30.1 32.8 30.0 32.9 33.4 34.0 31.4 33.1

13.7 16.0 15.8 15.8 13.1 13.8 16.2 16.6 14.1 15.7 14.9 15.0 15.1 13.5 15.3 16.4 14.4 14.6 14.7 16.9 13.7 13.9 13.3 14.0 14.2 16.3 14.6 13.4 14.3 13.7 14.2 14.3 14.4 14.0 14.7 14.0

8.7 7.5 8.3 8.1 9.2 9.4 9.5 7.7 10.0 8.3 8.5 7.7 8.5 9.9 9.9 9.7 9.7 9.0 7.8 7.5 7.3 7.1 9.0 8.1 7.2 8.3 8.5 8.4 8.6 8.6 10.2 8.8 8.0 7.8 8.0 7.7

Note: Until the 1958 season, T3 is Division 3 (South) and T4 is Division 3 (North). Source: Tabner (1992), Rothmans/Sky Sports Football Yearbook

fortunes of the national economy closely, with a short post-war boom followed by a period of decline from the 1922 season onwards, and then a gradual recovery starting in the 1932 season. Following the Second World War, attendances surged, achieving an all-time high of 41 million in the 1949 season. Again, the post-war

Match attendances

153

boom was relatively short-lived, and was followed by sustained decline in attendances that continued, almost uninterrupted, until the 1986 season. The downward trend was punctuated only by a few brief interludes, most notably following England’s World Cup victory in 1966. The decline in aggregate attendance accelerated briefly in the early 1980s, but then levelled out. The 1987 season witnessed an unexpected improvement, which has continued ever since; although the rate of growth has slowed towards the end of the 2000s. Nevertheless the total attendance for the 2008 season was the highest recorded for forty years, and the 2009 total was only fractionally smaller. The growth in aggregate attendance would have been faster had it not been for capacity constraints that are effective at the refurbished allseated stadia of many of the larger-market clubs (see Chapter 11, Section 11.1). Table 6.4 also shows attendances by tier, and the percentage share of each tier in the aggregate attendance. The percentage shares by tier were roughly constant through the 1920s and most of the 1930s. During the last three seasons before the Second World War, however, the attendances of T1 were 5.5 per cent higher than during the previous three seasons; those of the clubs outside T1 were 24.1 per cent higher. Consequently, T1’s percentage share fell by around 5 per cent just before the Second World War. The story was similar during the post-war boom, but as aggregate attendances started to decline, the lower-tier clubs shed spectators at a faster rate than their T1 counterparts. Between the 1949 season when the aggregate attendance peaked, and the 1986 season when the nadir was finally reached, T1’s aggregate attendance fell by 49.7 per cent, while the combined attendance of the lower three tiers fell by 67.5 per cent. Consequently, T1’s attendance share increased by about 10 per cent. Most of the improvement in T1’s relative position took place between the late 1950s and the mid-1970s. Between the mid-1970s and the mid-1980s, as aggregate attendances continued to fall, T1’s share hovered at just over 50 per cent. Since the mid-1980s, T2 has enjoyed the fastest growth in attendance. T1 attendances did not start to increase until the 1990 season, fully three seasons after the aggregate figure first started to rise. While stadium capacity constraints are responsible for restricting the attendance share of T1 to below 50 per cent in all but one season during the 1990s and 2000s, the creation of new capacity through either redevelopment (Manchester United, Newcastle United) or relocation to new stadia (Arsenal, Manchester City, Sunderland) has permitted continued growth in T1 attendances. The percentage shares in aggregate attendance of the clubs in each of the five groups (defined in Table 6.3) are shown in Figure 6.2. The graphs confirm the narrowing of differentials between clubs in terms of attendance share immediately before and after the Second World War, and the widening that has taken place since, especially between the late 1950s and the mid-1970s. It is noticeable that the trends in the fortunes of the G1 and G3 clubs, measured in terms of performance on the one hand and attendance on the other, differ strikingly between Figures 6.1 and 6.2. While the average performance of the G1 clubs hardly changed between the 1920s and 2000s, their attendance share has fluctuated

English professional football

154 45 40

Group 1

35

Per cent

30

Group 3

25

Group 2

20 15

Group 4 10 5

Group 5

0 1922 1925 1928 1931 1934 1937 1947 1950 1953 1956 1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007

Season

Figure 6.2  Percentage shares in aggregate attendance of clubs in Groups 1 to 5

markedly, between about 27 per cent (in the early 1950s) and 39 per cent (in the mid-1980s). G3 clubs in contrast enjoyed significant improvements in performance until the 1980s, but struggled to achieve a corresponding increase in attendance share. The attendance share of the twenty-seven G3 clubs in the league in the 1922 season (one of which was in T1, and four in T2) was 22.1 per cent. By the 1988 season, the number of G3 clubs had increased to 33 (nine of which were in T1 and six in T2); but G3’s attendance share had only increased rather modestly, to 29.1 per cent. Explanations for changes in attendances

Economists, sociologists and social historians have all made strenuous efforts to explain the trends in attendances that are summarised above. Social and demographic change, increasing material affluence, the growth of televised football, football hooliganism, the state of football’s physical infrastructure and the quality of the entertainment on the field of play, are among the many factors considered to have contributed to the long post-war decline in football attendances (Walvin, 1994; Russell, 1997). More recently, several of the same factors have begun to operate in directions that are more favourable from football’s perspective. This subsection provides a brief survey of the debate in respect of English club football attendances, starting in the inter-war period. The geographical bond between English football clubs and their spectators was undoubtedly stronger in the first half of the twentieth century than it became later.

Match attendances

155

Specific evidence on the geographical composition of football crowds is rather sparse, but it seems certain that the proportion of home supporters drawn from each club’s immediate vicinity was high. For example, twenty-one of the thirtythree spectators who died in the 1947 Bolton Wanderers stadium disaster were recorded as living within ten miles of the stadium (Fishwick, 1989). Although both financial and time constraints militated against regular travel to away matches in the 1930s and 1940s, Dunning, Murphy and Williams (1988) show that occasional big games (especially FA Cup ties) were capable of attracting several thousand travelling spectators. Fishwick (1989) also cites anecdotal evidence that some Wiltshire spectators preferred to travel regularly to watch Reading, West Bromwich Albion or Aston Villa rather than see the local team Swindon Town struggling in the lower reaches of Division 3 (South) during the early 1930s. In a historical survey focused primarily on the hooliganism phenomenon, Dunning, Murphy and Williams (1988) characterise the typical football crowd of the inter-war period as slightly more respectable than its pre-First World War counterpart. While inter-war crowds remained predominantly working class and male, there were significant and probably increasing middle-class and female minorities. Russell (1999) suggests that local rivalries were sometimes less intense than wider regional hostilities:  while spectators often took pleasure in the success of any team in their own region, football provided a convenient outlet for resentments arising from the contrasting economic fortunes of northern and southern England. Although football hooliganism was never eliminated completely, it seems to have been less pervasive during the inter-war period than before the First World War. Subsequently it seems to have declined further during the 1940s and early 1950s, before returning with a vengeance in the mid-1950s. Demobilisation and the relaxation of many wartime restrictions after the Second World War released a widespread and unprecedented pent-up demand for recreation and entertainment, which manifested itself not only in booming football attendances, but also in record-breaking cinema audience figures, and packed beaches at British seaside holiday resorts during summer. In explaining the subsequent sustained decline in football’s popularity as a spectator sport, social historians have emphasised the impact of broader socioeconomic changes. The growth of the affluent society saw the emergence of more home-oriented and privatised patterns of leisure activity, with the range of options extended in particular by television and the car. Many women became less willing to acquiesce in a homebased or child-minding function while men’s leisure was centred on the pub, club or football terrace. The spread of home-ownership led to an increase in the popularity of alternative weekend activities such as DIY and gardening (Dunning, Murphy and Williams 1988; Walvin, 1994; Russell, 1997). The increase in incidents of crowd misconduct both inside and outside football stadia, of which the train-wrecking exploits of Everton and Liverpool supporters

156

English professional football

in the late 1950s were an early manifestation, can also be attributed at least in part to broader social changes. Dunning, Murphy and Williams (1988) interpret football hooliganism as one unfortunate consequence of a general upsurge in working-class assertiveness and decline in social deference, stimulated by a new self-confidence boosted by high and stable levels of employment and increasing affluence, which also manifested itself positively through the novels, films, plays and popular music of the period. Whatever the causes, there is no doubt that over time, hooliganism and the counter-measures taken by clubs and the police prompted many spectators to switch from the terraces to the living room and TV set. Football grounds became increasingly the preserve of the more fanatical supporters, as the less committed drew the conclusion that the entertainment on offer was inadequate to compensate for the inconvenience, discomforts and occasional physical dangers caused by the hooligan phenomenon. Rising affluence combined with improvements in both public and private transport, including the spread of car ownership and the construction of the motorway network, led to important changes in the geographical composition of demand. With long-distance travel now practical both financially and logistically, the top clubs began to drain support from their smaller counterparts. In the late 1960s there emerged a distinctive and vociferous London contingent among the hooligan fringe of Manchester United’s support. This was symptomatic not only of the growing hooligan problem, but also of the increasing tendency of the leading clubs to draw support at a national rather than purely local or regional level. Increased personal mobility increased the propensity for regular travel to away fixtures. Demographic changes also eroded the bonds between communities and their local clubs. Suburbanisation led to population movements away from city centre districts where most football stadia were located, to be replaced by incomers who did not necessarily have any affinity or interest in the local club, or football in general. But paradoxically, spectators who remained loyal to their local clubs appeared to become increasingly hostile towards the supporters of neighbouring clubs, adding further fuel to the flames of hooliganism. During the 1970s, a growing atmosphere of financial desperation enveloped many football clubs. Neither the clubs nor the police seemed able to curb the hooligan-related incidents, which had become a regular Saturday afternoon occurrence, both inside football stadia and outside in town centres and railway stations. There was a widespread perception of declining standards of conduct on the field of play. Much of this seemed to reflect unerringly a malaise afflicting English society on a broader scale, as politicians grappled with problems such as inflation, unemployment, industrial unrest and social breakdown. With the economy in deep recession by the start of the 1980s, it is unsurprising that the downward trend in attendances accelerated. Margaret Thatcher’s Conservative government came increasingly to favour direct intervention to confront football’s problems head-on, including punitive legislation to tackle hooliganism, and proposals (never implemented) for compulsory identity cards for all spectators.

Match attendances

157

English football hooliganism reached its apotheosis with the deaths of thirtyeight mainly Italian supporters at the Heysel Stadium in Brussels at the Liverpool– Juventus European Cup Final in May 1985. Heysel’s poor physical condition, which was similar to that of many major stadia in Britain, was a contributory factor in this tragedy, as was misbehaviour among the Liverpool section of the crowd. The declining state of domestic football’s physical infrastructure had already been demonstrated catastrophically a few days earlier, as fifty-five spectators died when a wooden stand caught fire during a T3 match between Bradford City and Lincoln City on the final day of the 1985 league season. But it was only after ninety-six Liverpool supporters were crushed to death against a collapsed section of perimeter fencing at the start of the Liverpool–Nottingham Forest FA Cup semi-final played at Hillsborough (the home of Sheffield Wednesday) in April 1989, that the momentum for fundamental change finally became irresistible. One of the main recommendations of the ensuing report by Lord Justice Taylor (1990), that the stadia of all clubs in the top two tiers should be converted to all-seated accommodation by the start of the 1995 season, was accepted and implemented with scarcely a murmur of dissent. During the 1990s, the demand for conversion to all-seated accommodation provided both the opportunity and the impetus for more general refurbishment, and in some cases the wholesale reconstruction of England’s major football stadia. The removal of terracing, improvements to stadium facilities, advances in crowd surveillance technologies, together with a new public mood of revulsion following the worst excesses of the 1980s, all contributed to the marginalisation of the hooliganism phenomenon. Russell (1997) is surely correct to draw the obvious connection between the improvement in standards of crowd behaviour (at club level at least) and the reversal in the downward trend in attendances. The level of investment in stadium relocation and redevelopment increased markedly towards the end of the 1990s. According to data compiled by Deloitte (2009), an average total investment of just under £200 million per annum has been sustained throughout the 2000s. Between the 1993 and 2008 seasons, £2.571 billion in total was invested in stadia and facilities by all Premier League and Football League clubs. Clubs that relocated to new stadia during this period include Arsenal, Bolton Wanderers, Coventry City, Derby County, Doncaster Rovers, Hull City, Leicester City, Manchester City, Middlesbrough, MK Dons, Millwall, Reading, Southampton, Stoke City, Sunderland, Swansea City and Wigan Athletic. Most of these relocations involved the abandonment of stadia situated in congested inner-city or residential locations, which in many cases had been occupied since the late nineteenth century, in favour of new sites offering better access to road links and space for car-parking. Football’s rehabilitation as the most popular and fashionable national sport has also been aided by skilful exploitation by the industry of selective aspects of its own ‘heritage’. Whether viewing in person or on television, spectator and (especially) media interest is now focused to a greater extent than ever before on

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English professional football

a handful of large-market clubs. It is still the case, however, that the majority of spectators who attend English professional football in person do not watch Arsenal, Chelsea, Liverpool and Manchester United. As Table 6.4 shows, more than 54 per cent of the total attendance in the 2009 season went to matches outside T1. English football largely succeeded in ‘rebranding’ itself as a middle-class spectator sport during the 1990s and 2000s. Viewed in a positive light, the 1990s witnessed the re-emergence of the Victorian tradition of the modern English football stadium as an important source of civic pride, in terms of its up-to-date amenities and facilities … (and) the popular ‘rediscovery’ of the much cherished and at least part-mythical traditions of the English sports crowd for its mutual tolerance and sociability.

Viewed negatively the same period witnessed the effective end of the local and ‘organic’, the self-administering and creative, English football crowd … (and) the emergence of the regulated, individuated, surveilled and high spending seated bourgeoisie football audience. (Williams, 1997, p243, 244)

It is perhaps surprising to find that empirical evidence on the composition of football crowds is in limited supply. On the basis of a review of eleven different surveys conducted at various times over a fourteen-year period between 1983 and 1997 in England and Scotland, Malcolm, Jones and Waddington (2000) question the common perception that the demographic composition of a typical 1990s football crowd was markedly different to that of its predecessors in earlier decades.3 There is no convincing evidence that the age composition of the typical crowd has changed very much overall. The proportion of female spectators remained fairly constant, at between 10 and 13 per cent in most of the surveys. There is some evidence, however, that female spectators tend to be younger on average than males, and less likely to be married or living with a partner. Attempts to trace changes in the social composition of crowds are hampered by definitional problems and inconsistencies. However, there is little sign of a change over time in the proportions of unemployed or retired spectators. The proportion of students appears to have declined, perhaps due to the deteriorating state of student finances. In general Malcolm, Jones and Waddington suggest that the composition of the typical British football crowd may have changed less than many commentators assume. By contrast, Tapp and Clowes (2002) and Tapp (2004) suggest that the representation in the modern-day football crowd of the fanatical hard-core supporter, who identifies solely with a particular club, may be in a state of long-term decline. Casual spectators, often with loose allegiances to several clubs, and interested in the quality of the entertainment on offer as well as practical details such as ease of access to the stadium and the nature of the arrangements for purchasing tickets, constitute a growing but perhaps unrecognised element. ‘The commonly held view of football supporters moving more towards a

Financial structure of English football

159

­ eterogeneous mix of social classes with an increasing number of female supporth ers was broadly supported’ (Tapp and Clowes, 2002, p1267). 6.3  Financial structure of English football: overview of profit and loss accounts

Section 6.3 provides an overview of the profit and loss accounts of English football clubs, and the next three sections describe historical and recent trends in the main revenue and cost items that appear in a football club’s profit and loss account: namely gate revenues (Section 6.4), broadcast revenues (Section 6.5), and expenditure on players’ salaries and transfer expenditure (Section 6.6). Table 6.5 summarises the trends in total revenues, wages and salaries expenditure, and operating profits, of all English league football clubs between the mid-1990s and the late 2000s. The clubs are subdivided into T1, T2, and T3 and T4 combined, and the figures are averages per season calculated over three-season periods. The data clearly highlight the divergence in financial strength between T1 (the Premier League) and the other three tiers (the Football League) since the formation of the Premier League at the start of the 1993 season. For seasons 1994 to 1996, T1 accounted for 66.4 per cent of total Premier League and Football League revenues. For seasons 2006 to 2008, the figure was 76.3 per cent. Even within the Football League the story has been similar, with the revenues of T2 consistently having grown at a faster rate than those of T3 and T4 combined. For seasons 1994 to 1996, T2 accounted for 60.1 per cent of the revenues of T2, T3 and T4 combined. For seasons 2006 to 2008, the figure was 65.5 per cent. The financial strength of T1 is also reflected in the relativities between expenditures on wages and salaries, and total revenues. During the 1990s the expenditures of T1 clubs on players’ salaries grew at a faster rate than the clubs’ revenues. Salary expenditure expressed as a percentage of total revenue increased from below 50 per cent in the mid-1990s to more than 60 per cent by the start of the 2000s. Due to the Bosman ruling (see Section 6.6, below), the mid-1990s witnessed a major shift in the balance of power in salary negotiations between the players and the clubs, favouring the former at the expense of the latter. By the start of the 2000s, however, the post-Bosman adjustment to players’ salary levels appears to have been completed. During the 2000s the growth in the T1 clubs’ salary expenditure proceeded at a similar rate to the growth in revenue. The ratio of the Football League clubs’ salary expenditure to their revenues was much higher than the corresponding ratio for the Premier League clubs throughout the period covered by Table 6.5. The finances of the T2 clubs in particular seem precarious, with this ratio having risen from just over 70 per cent for seasons 1994 to 1996 to a peak of more than 86 per cent for seasons 2000 to 2002. The collapse in 2002 of ITV Digital, a broadcaster that held the Football League broadcast rights at the time (see Section 6.5, below), and the consequent unanticipated loss of broadcast revenue, placed many Football League clubs under severe

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English professional football

Table 6.5 Average revenue, wages and salaries and operating profit per season, three-season periods, English League, 1994–2008 seasons Revenue T1

Wages and salaries T2

Operating profit

T3/ T4

T1

T2

T3/ T4

T1

T2

T3/ T4

61 99 138 155 173

142 305 582 786 1006

66 118 198 218 259

42 80 113 113 122

47 84 73 145 139

−18 −22 −63 −52 −77

−9 −29 −35 −32 −26

Percentage growth in revenue and wages and salaries over previous three-season period 1997–1999 88.6 72.6 61.4 115.1 78.5 89.6 — — 2000–2002 65.6 43.9 39.7 91.0 67.0 42.3 — — 2003–2005 37.5 23.3 11.7 35.0 10.3 −0.6 — — 2006–2008 23.9 15.9 11.7 28.1 19.0 8.0 — —

— — — —

Average values per season, £m 1994–1996 303 92 1997–1999 572 159 2000–2002 947 229 2003–2005 1302 283 2006–2008 1614 328

Wages and salaries and operating profit as percentage of revenue 1994–1996 — — — 46.7 71.8 68.5 1997–1999 — — — 53.3 74.3 80.5 2000–2002 — — — 61.5 86.2 81.9 2003–2005 — — — 60.3 77.1 72.9 2006–2008 — — — 62.4 79.1 70.5

15.6 14.6 7.7 11.1 8.6

−19.5 −13.6 −27.6 −18.3 −23.4

−14.1 −29.6 −25.3 −20.5 −15.3

Source: Deloitte

financial duress. Subsequently the ratio for the T2 clubs has dropped and stabilised to a level just below 80 per cent: a figure that most analysts would still consider dangerously high. For many T2 clubs, there is a temptation to gamble on the possibility of achieving promotion to T1, and the financial resources that would flow as a consequence. The gamble involves ratcheting up expenditures on players’ salaries, to levels that would be covered easily if promotion is achieved, but which are unsustainable otherwise. The contrast between the Premier League and the Football League is also reflected, starkly, in the data for operating profits. The Premier League clubs combined turned in positive operating profits in each of the three-season periods covered by Table 6.5; while the Football League clubs turned in operating losses. The operating profits data do not include expenditures on player transfers (see Section 6.6, below). The Premier League clubs are heavy net spenders on transfers, while transfer fees received continued to make an important contribution to the solvency of many Football League clubs during the 2000s, as was the case in earlier decades. The revenue and salary data aggregated by tier highlight the divergence in financial strength between the Premier League and the Football League, but they also mask divergences within the top two tiers that carry significant implications for

Financial structure of English football

161

Table 6.6 Financial data, leading English clubs and averages by tier, 2008 season, £m

Total revenue

Salary expenditure

Operating profit before player transfers

257.1 213.6 209.3 164.2 66.2

121.1 172.1 101.3 90.4 43.4

71.8 −30.9 48.5 28.4 3.7

−44.8 −84.5 36.7 −40.9 −7.8

27.4 11.1

22.1 10.2

−4.3 −4.4

−1.5 −3.8

T3 24 clubs (average)

5.2

3.7

−1.0

−0.8

T4 24 clubs (average)

2.7

1.9

−0.3

−0.3

T1 Manchester United Chelsea Arsenal Liverpool 16 other T1 clubs (average) T2 4 ‘parachute’ clubs (average) 20 other T2 clubs (average)

Pre-tax profit

Source: Deloitte

competitive inequality. Based on data compiled by Deloitte (2009), Table 6.6 provides some further analysis of football clubs’ profit and loss accounts for the 2008 season. For T1, these data are tabulated separately for the four clubs with the largest total revenues: Arsenal, Chelsea, Liverpool and Manchester United; and for the other sixteen clubs in the form of cross-sectional averages. The so-called ‘big four’ are reported separately because the revenue arising from Champions League participation renders their profit and loss accounts atypical of T1 as a whole. For T2, separate averages are reported for four clubs that benefited under the ‘parachute’ system, and the other twenty clubs. The parachute system allocates a share of the Premier League’s broadcast revenues to clubs recently relegated from T1, during the first two seasons following relegation. Charlton Athletic, Sheffield United, Watford and West Bromwich Albion were the four T2 recipients of parachute payments during the 2008 season, and their profit and loss accounts were atypical of T2 as a whole. Table 6.7 provides some further detail on the contributions of UEFA (Champions League) and Premier League TV income to the total revenues of T1 and T2 clubs. The data reported in Tables 6.6 and 6.7 emphasise the inequality in financial structure that exists within the Premier League between the ‘big four’ and the other sixteen clubs, and between the Premier League as a whole and the other three Football League tiers. Participation in the Champions League is rewarded by a share of UEFA’s TV income, worth £34 million to Manchester United, the tournament

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English professional football

Table 6.7 TV and other revenue, leading English clubs and averages by tier, 2008 season, £m UEFA TV

Premier League TV

Other revenue

Total revenue

T1 Manchester United Chelsea Arsenal Liverpool 16 other T1 clubs (average)

34 29 18 21 —

50 46 47 45 34

173 139 144 98 32

257 214 209 164 66

T2 4 ‘parachute’ clubs (average) 20 other T2 clubs (average)

— —

12 —

15 11

27 11

Source: Deloitte

winners in 2008, and just over half that amount to Arsenal, the least successful of the four English participants in 2008 (eliminated at the quarter-final stage). Champions League participation also yields additional matchday income, and enhances the value of sponsorship and advertising deals for the clubs involved. Consequently, the average revenues of the ‘big four’ were in excess of £200 million, while the average for the other sixteen Premier League clubs was around £66 million. For the average Premier League club, relegation to the Football League would be expected to eliminate around one-third of this revenue immediately. The parachute system (yielding a payment of around £12 million per eligible club) helps cushion what would otherwise be an even larger drop in revenue, of perhaps 50–60 per cent. Relegated clubs that fail to achieve a rapid return to the Premier League must downsize to this extent in full over a two-year period. Parachute payments create a degree of inequality within T2 that is similar to the situation in T1 due to the Champions League involvement of the elite clubs. A key difference, however, is that the year-on-year turnover in the T2 clubs eligible to receive parachute payments is high, and any correspondence that might exist between the additional revenue and success on the field of play is variable and uncertain. In contrast, the same four T1 clubs participated in the Champions League in every season between 2004 and 2009,4 a period during which these four clubs also exerted a near-stranglehold upon success in ­domestic football. 6.4  Gate revenues and admission prices

Until the 1990s, gate revenues from league matches represented the largest source of revenue for all football clubs. It was not until the start of the 1990s that clubs’

Gate revenues and admission prices

163

revenue sources became sufficiently diversified that the share of league gate revenues in aggregate revenue fell below 50 per cent for the league as a whole. Over the longer term, however, gate revenues data provide an accurate representation of trends in football’s overall revenue-raising capability and performance. An attraction of a gate revenues data set for researchers is that it can be combined with match attendance data to calculate an average admission price per club per season, by dividing total gate revenue by total attendance. Tables 6.8 and 6.9 draw on a data set comprising annual gate revenues from league matches for all English league clubs, obtained from Football League archives and (for the later seasons) from Football Trust, and reported previously by Dobson and Goddard (1998b, 2001). The 1926 season is the first and the 1999 season the last for which these records were available. Table 6.8 reports the average admission price per spectator in nominal and real terms, and average nominal admission prices by tier, for each season between 1926 and 1999. For the period up to the mid-1970s, admission prices for spectators paying at the gate were subject to a statutory minimum determined by the Football League, also shown in Table 6.8. At certain times, however, concessions were available to groups such as juniors, pensioners and the unemployed. Clubs were also permitted to charge more than the minimum. Many did so for seated accommodation (especially) and, increasingly as time went by, for standing accommodation as well. The original objective of the League’s minimum admission price was to prevent clubs from attempting to poach spectators from other clubs in the same geographical catchment area by cutting prices. Table 6.9 reports aggregate gate revenue data in nominal and real terms, together with gate revenue shares by tier. Figure 6.3 shows the percentage shares of the G1 to G5 clubs (see Table 6.3) in aggregate gate revenue. Table 6.8 suggests that there was little difference between clubs in admission prices during the inter-war period, with most clubs charging the league minimum of one shilling (£0.05) to all but a relatively small minority of more affluent, seated spectators. The gentle increase in the real admission price series up to the mid-1930s and its subsequent reversal reflects the constancy of admission prices in nominal terms, against a background of retail prices that were falling in the late 1920s and early 1930s and rising thereafter. When football resumed after the Second World War, the increase in admission prices was just sufficient to compensate for wartime price inflation. The post-war attendance boom generated revenues more than 50 per cent higher than before the war in real terms. The relative homogeneity of football’s pricing structure was preserved throughout the 1950s. In the 1960 season, T1 clubs were charging only 25 per cent more on average than their T4 counterparts, a ratio not much greater than that which had prevailed during the inter-war period. From the 1960s onwards, however, the story is one of steadily increasing divergence between the prices of clubs in different tiers. By the 1970 season, T1 clubs were charging 48 per cent more per spectator on average than T4 clubs. This gap increased to 64 per cent in 1980, 70 per cent in

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English professional football

Table 6.8 English league average admission prices Average admission price Season 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976

Average nominal admission price (£)

Nominal (£)

Real (1926 = 100)

T1

T2

T3

T4

0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.08 0.09 0.09 0.09 0.10 0.11 0.12 0.12 0.12 0.13 0.13 0.13 0.14 0.14 0.16 0.18 0.18 0.19 0.21 0.23 0.24 0.26 0.29 0.30 0.35 0.38 0.46 0.53 0.59 0.76

100 103 106 107 112 118 119 124 123 122 118 114 113 110 120 118 120 120 112 112 126 124 120 122 118 115 117 120 135 141 141 141 151 160 162 164 176 172 186 185 209 204 185 202

0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.09 0.09 0.10 0.10 0.10 0.11 0.13 0.13 0.13 0.14 0.14 0.14 0.15 0.15 0.18 0.20 0.20 0.21 0.24 0.26 0.27 0.29 0.33 0.34 0.41 0.43 0.52 0.59 0.66 0.83

0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.08 0.09 0.10 0.10 0.10 0.11 0.12 0.12 0.12 0.13 0.13 0.13 0.14 0.14 0.17 0.18 0.19 0.19 0.21 0.22 0.23 0.24 0.26 0.28 0.32 0.35 0.43 0.49 0.60 0.75

0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.08 0.08 0.09 0.09 0.09 0.10 0.11 0.12 0.12 0.12 0.12 0.12 0.12 0.13 0.14 0.16 0.16 0.16 0.18 0.20 0.21 0.22 0.24 0.24 0.29 0.31 0.38 0.43 0.46 0.61

0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.07 0.08 0.08 0.08 0.08 0.09 0.10 0.10 0.10 0.11 0.11 0.11 0.11 0.12 0.13 0.13 0.14 0.15 0.16 0.18 0.18 0.20 0.22 0.23 0.27 0.28 0.36 0.39 0.41 0.59

Minimum admission price (£) 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.0625 0.0625 0.0625 0.0625 0.0625 0.075 0.075 0.075 0.075 0.10 0.10 0.10 0.10 0.10 0.125 0.125 0.125 0.125 0.125 0.20 0.20 0.20 0.25 0.25 0.30 0.30 0.40 0.40 0.40 0.65

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Table 6.8 (cont.) Average admission price Season 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999

Average nominal admission price (£)

Nominal (£)

Real (1926 = 100)

T1

T2

T3

T4

Minimum admission price (£)

0.85 1.05 1.18 1.50 1.84 2.03 2.24 2.44 2.77 2.97 3.21 3.56 3.95 4.48 5.32 6.25 7.09 7.55 8.75 9.64 10.74 11.37 12.30

197 224 222 239 261 265 281 291 312 323 336 354 365 378 424 481 537 557 625 672 722 749 799

0.96 1.19 1.29 1.67 2.05 2.32 2.55 2.76 3.21 3.42 3.70 4.26 4.73 5.39 6.46 7.55 8.77 9.17 11.58 12.74 14.59 14.99 16.27

0.83 0.99 1.16 1.53 1.85 1.93 2.17 2.42 2.46 2.63 2.92 3.22 3.71 4.21 4.82 5.47 6.21 6.64 6.46 7.62 7.96 9.30 9.81

0.68 0.82 0.99 1.21 1.43 1.59 1.83 1.91 2.11 2.33 2.48 2.83 3.13 3.42 3.94 4.45 5.11 5.32 5.46 5.97 6.66 7.51 8.64

0.58 0.75 0.91 1.02 1.20 1.35 1.45 1.63 1.79 2.05 2.35 2.51 2.69 3.17 3.70 4.28 4.31 4.49 5.60 5.37 5.72 5.85 6.45

n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a

Note: Until the 1958 season, T3 is Division 3 (South) and T4 is Division 3 (North). 1999 season data are based on estimates for some clubs. Source: Football Trust, Bird (1982), Football League, Premier League.

1990 and 152 per cent in 1999. Together with the eight or nine percentage point increase in T1’s attendance share between the late 1950s and mid-1970s (see Table 6.4), these relative price increases explain an increase of about 18 per cent in T1’s gate revenue share over the same period. Similarly, the growth of the revenue share of the G1 clubs between the late 1950s and mid-1970s (Figure 6.3) was an even faster rate than the growth in their attendance share (Figure 6.2). The increases in nominal admission prices in all tiers kept pace with inflation during the 1950s, but started to outstrip inflation in the 1960s, especially in the higher tiers. Cost pressures emanating from the removal of the maximum wage and changes affecting the terms of players’ contracts (see Section 6.6, below) were partly responsible for the imposition of real increases in admission prices during the 1960s. When retail price inflation began to soar and attendances continued

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English professional football

Table 6.9 English league gate revenues Aggregate league gate revenues Season 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976

Nominal (£m) 1.352 1.373 1.410 1.419 1.372 1.246 1.263 1.261 1.321 1.373 1.456 1.575 1.661 1.594 2.933 3.578 3.780 3.801 3.786 4.135 4.541 4.431 4.215 4.355 4.311 4.448 4.557 4.549 4.677 4.981 5.242 5.341 5.829 6.308 6.931 7.682 8.388 8.828 9.960 10.814 11.823 13.174 15.180 18.822

Real (1926 = 100) 100 105 109 111 111 108 112 115 120 123 127 131 136 129 185 205 214 211 192 189 202 196 177 176 167 167 171 168 168 171 176 174 181 189 203 214 222 220 227 229 230 221 205 218

Percentage share by tier in aggregate league gate revenues T1

T2

T3

T4

46.9 47.0 47.2 45.7 47.8 47.4 48.1 46.9 48.9 49.9 48.5 45.2 44.5 45.8 45.0 43.8 45.5 44.3 44.2 44.1 46.4 46.9 47.4 45.4 45.3 46.9 47.2 48.1 49.6 47.6 47.2 48.0 52.4 52.0 55.0 56.7 57.1 56.9 56.9 57.8 61.4 58.8 52.6 57.7

26.8 28.2 28.9 28.3 27.5 28.5 25.8 28.8 26.2 26.3 28.2 30.3 30.5 31.1 30.9 30.4 28.2 29.9 28.4 28.5 26.2 27.2 26.5 27.6 26.8 25.6 25.7 26.0 24.8 27.2 26.3 27.1 24.7 24.0 23.8 23.1 22.9 23.9 22.7 21.7 20.4 23.7 29.8 23.0

16.3 15.5 14.7 16.1 16.5 15.0 17.6 15.4 16.0 15.3 15.3 16.1 15.6 13.9 14.7 15.7 15.9 16.5 17.3 16.7 16.8 16.4 16.5 16.0 16.1 16.8 16.4 15.8 14.7 16.5 17.7 16.5 13.5 15.2 13.3 11.6 12.2 11.5 12.8 13.4 11.9 11.0 12.4 12.8

10.0 9.3 9.2 9.9 8.2 9.1 8.5 9.0 8.9 8.5 7.9 8.4 9.4 9.2 9.4 10.2 10.5 9.3 10.1 10.7 10.6 9.5 9.6 11.0 11.9 10.6 10.7 10.1 10.9 8.8 8.9 8.4 9.5 8.7 7.9 8.5 7.8 7.7 7.6 7.1 6.3 6.4 5.2 6.4

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Table 6.9 (cont.)

Aggregate league gate revenues

Percentage share by tier in aggregate league gate revenues

Season

Nominal (£m)

Real (1926 = 100)

T1

T2

T3

T4

1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999

22.220 26.651 28.960 36.911 40.239 40.523 42.096 44.760 49.276 48.901 55.844 63.906 72.885 87.219 103.691 127.329 146.238 163.655 191.610 211.500 244.838 283.313 312.056

222 246 236 255 248 230 229 232 240 231 253 276 292 319 359 425 480 524 593 639 714 804 879

58.6 59.3 56.6 55.0 58.2 59.6 56.3 53.7 63.5 63.2 60.6 54.0 50.7 48.8 53.7 59.2 58.3 59.7 64.4 63.0 64.4 59.4 60.6

23.3 23.9 24.6 25.4 23.8 22.6 25.6 29.0 20.1 19.1 21.8 26.9 29.7 33.3 29.2 25.0 24.9 26.3 22.3 23.7 22.6 27.5 23.6

12.6 10.3 11.6 13.1 12.9 11.1 12.8 11.6 11.4 11.9 10.4 12.2 13.0 11.0 10.8 10.5 12.2 9.7 9.3 8.3 8.7 9.4 11.5

5.5 6.5 7.3 6.5 5.0 6.6 5.3 5.7 5.0 5.9 7.2 7.0 6.6 6.9 6.3 5.3 4.5 4.3 4.0 5.0 4.3 3.7 4.3

Note: Until the 1958 season, T3 is Division 3 (South) and T4 is Division 3 (North). 1999 season data are based on estimates for some clubs. Source: Football Trust, Football League, Premier League.

to fall, for a few years clubs became more circumspect about raising prices by more than the rate of inflation. As inflation started to fall in the late 1970s and early 1980s and attendances continued to plummet, the clubs attempted to protect their dwindling real revenue base by imposing further price increases. But with attendances falling even faster than admission prices were rising (in real terms), football’s capacity to insulate itself from the effects of its declining spectator base appeared to have reached its limit. As the recovery in football’s popularity gathered pace during the late 1980s and 1990s, there were further large real increases in admission prices. The clubs argued that higher prices were justified by improvements in the quality of the product, with highly talented but expensive foreign players (in T1 at least) viewed from comfortable seats in glistening new stands, built on top of the ruins of the crumbling rain-soaked terraces of yesteryear. Simple economics predicts that prices

English professional football

168 50 45

Group 1

40 35

Per cent

30 Group 3

25 20

Group 2

15 10

Group 4

5 0

Group 5 1926 1929 1932 1935 1938 1948 1951 1954 1957 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996 1999

Season

Figure 6.3  Percentage shares in aggregate gate revenue of clubs in Groups 1 to 5

should rise sharply once capacity constraints are reached, and this is precisely what happened. Pricing behaviour of this kind explains why the G1 clubs’ revenue share increased sharply during the 1990s (Figure 6.3), while their attendance share barely changed (Figure 6.2). The gate revenues series was not published during the 2000s. For T1, however, Deloitte publish an estimated decomposition of total revenue into its matchday, broadcast and commercial components. Matchday revenue includes gate revenue from all matches, and other associated income (from matchday activities such as catering and programme sales). For the 1999 season, Deloitte’s matchday revenue figure for T1 is £248 million. Table 6.9 indicates that gate revenues from league matches contributed £189 million towards the matchday total. Deloitte’s total revenue estimate for the 1999 season is £670 million; therefore league gate revenue accounted for 28.2 per cent of total revenue, and all matchday revenue accounted for 38.0 per cent. For T2, T3 and T4 as a whole, the estimated total revenue for the 1999 season is £281 million, and the percentage contributions to this total of league gate revenue and total matchday revenue are 43.7 per cent and 48.4 per cent, respectively. Since the 1999 season, the percentage contribution of matchday revenue to total revenue for T1 has declined further. Deloitte’s estimates for the 2008 season are matchday revenue of £554 million (123 per cent growth since 1999), and total revenue of £1,932 million (188 per cent growth since 1999). The share of matchday

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revenue in total revenue is 28.7 per cent. Corresponding 2008 estimates are not available for T2, T3 and T4; but with the lower three tiers having experienced far slower growth in broadcast revenue than the top tier, it seems likely that the percentage contributions of matchday revenue in total revenue remained close to the 1999 figure throughout the 2000s. In a survey carried out during the 1999 season, Clowes and Clements (2003) find English T1 clubs using a broad range of ticket pricing strategies designed to maximise the value extracted from spectators with differing degrees of willingness to pay, enabling the clubs to generate more revenue than would be possible with a broad-brush uniform price structure. Several of these strategies are described by the economic theory of price discrimination. In this context, second-degree price discrimination involves charging each spectator a price that depends upon the number of matches attended; and third-degree price discrimination involves charging different prices to different groups of spectators.5 Revenue maximisation from the sale of tickets for seats in a stadium of fixed capacity over a finite number of matches of varying attractiveness requires a pricing structure that is sophisticated and finely-tuned to local conditions of spectator demand. Specific examples of second-degree price discrimination include season tickets offering a discount on the price the spectator would pay to purchase tickets for each match individually; and membership schemes requiring the payment of a fixed membership fee, and allowing the member to purchase individual match tickets at a discounted price (known in the literature as a two-part tariff). In the US, some major league teams charge a fee that guarantees the right to purchase a season ticket for a particular seat over the long term (twenty or thirty years). Personal seat licences typically lapse if the holder dies or fails to renew the season ticket. Several attempts to introduce similar schemes by English football clubs in the early 1990s were unpopular with spectators, and the idea failed to take off. Third-degree price discrimination is widely practised, by offering price concessions to specific groups, such as juniors, pensioners, students, the unemployed, people with disabilities, or families. Other common pricing or ticketing policies include bundling, whereby tickets for two or more matches can be or must be bought simultaneously; or proof of purchase of a ticket for one match is required to purchase a ticket for another match. Typically, a sell-out match is bundled together with one that is unlikely to sell out. Naturally most clubs charge different prices for seats located in different parts of the stadium; and some clubs operate a price banding system, with different prices applicable for different fixtures, dependent on the attractiveness of the opposition. Deloitte (2009) note that spectator demand is sensitive to economic conditions, and at the height of the recession of the late 2000s many T1 clubs announced ticket price freezes or reductions in an effort to sustain attendances in the face of adverse economic conditions.

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English professional football

Both cause and consequence of the widening financial gulf separating the leading clubs from the rest has been the erosion of arrangements for revenue sharing within the league. Until the early 1980s, 20 per cent of the notional receipts from every league match were paid to the visiting club. Notional receipts were based on minimum admission charges, with certain deductions permitted (e.g. for costs of policing and stewarding). Since the 1984 season, however, clubs have retained all of the proceeds from their home fixtures (Dobson and Goddard, 1998b). Under another revenue-sharing arrangement, 4 per cent of all notional receipts were paid into a pool, the proceeds from which were distributed evenly among all ninety-two league member clubs. The 4 per cent levy was reduced to 3 per cent from the 1987 season onwards, prior to the complete withdrawal from this scheme of the Premier League clubs at the start of the 1993 season. The 3 per cent levy and arrangements for equal distribution of the proceeds are still effective within the Football League. The reduction in the reliance of clubs at all levels on revenues from league matches is also attributable partly to an increase in the number of cup and other tournaments. For the top clubs, the revenue contribution of participation in European competition has grown significantly over time, and especially in recent seasons. For the rest, the introduction in the 1987 season of the end-of-season play-offs to determine one promotion place from each tier of the Football League, culminating (from the 1990 season onwards) in a series of three showpiece finals, played at the national stadia located at Wembley (London) or Cardiff, has added a dramatic and lucrative postscript to the domestic season. Elimination cup competitions provide an implicit cross-subsidy from the richer clubs to the poorer in several ways: • A lower-tier club may be able to attract an abnormally large attendance by being drawn to play a top club; • The rules for pooling gate receipts allow for a greater element of redistribution than is the case for league fixtures; • All clubs share in the proceeds of sponsorship agreements. As with the explicit arrangements for sharing league gate revenues, however, the willingness of the leading clubs to provide these implicit cross-subsidies by participating wholeheartedly in the two main cup tournaments, the FA Cup and the League Cup, has been strained during the modern era. The extension of the European calendar in particular has brought genuine problems of fixture congestion, which have been tackled in a number of ways: by delaying the entry of teams involved in Europe to the League Cup; by substituting penalty shoot-outs for replays as a means of settling drawn cup ties; by the clubs themselves choosing to field teams comprising reserve team players for cup matches; and on one occasion, by the withdrawal of Manchester United from participation in the 2000 season’s FA Cup competition. In the eyes of traditionalists, these developments have devalued the two domestic cup competitions, to the detriment of the league’s smaller member clubs and, in the case of the FA Cup, the non-league clubs as well.

Broadcast revenues

171

6.5  Broadcast revenues The early history of football on television

For the leading clubs in particular, paying spectators arriving through the turnstiles on match days represent only one part of the target audience. Pay-TV audiences form an increasingly important component of present-day football’s customer base. Section 6.5 describes the evolution of English football’s long-standing and intricate relationship with the broadcasting media. The British Broadcasting Company was first established in 1922. According to its first general manager John Reith, its mission was to bring into every home ‘all that was best in every department of human knowledge, endeavour and achievement’ (Taylor, 1965). The company was replaced by the state-owned British Broadcasting Corporation (BBC) in 1926, funded by means of a flat-rate licence fee payable by all owners of wireless sets. The BBC’s first television transmissions took place in the late 1930s, though it was not until the 1950s that sufficient households owned sets for television to begin to play a significant part in national life. The Independent Television (ITV) network of regional broadcasting companies was created in 1955. Funding was by means of advertising revenues. A second BBC channel was launched in 1964, to be followed by the introduction of colour transmissions in the late 1960s. Further free-to-air terrestrial channels were added in 1982 (Channel 4) and 1996 (Channel 5), both of which are funded by means of advertising. The two competing satellite broadcasters British Satellite Broadcasting (BSB) and Sky introduced Britain’s first pay-TV services in the late 1980s. Sky acquired BSB in 1991 to form British Sky Broadcasting (BSkyB) under the ownership of Rupert Murdoch’s media conglomerate News Corporation. The BBC transmitted English football’s first radio commentary of a match between Arsenal and Sheffield United in January 1927. Concern on the part of the Football League, however, about the potentially damaging effects on match attendances, led to a broadcasting ban being imposed in 1931. Regular radio coverage of league fixtures did not resume until after the Second World War, although cup matches and internationals were transmitted regularly during the 1930s. Televised transmission of football began on 9 April 1938 with the broadcast of an England–Scotland international match. Three weeks later the FA Cup final between Sunderland and Preston North End was also televised. Highlights of league matches were transmitted sporadically from 1955 onwards, but regular coverage did not start until the launch of the BBC’s recorded highlights programme Match of the Day in 1964. This was followed by the launch of regional highlights programmes on the ITV network in 1968. From then until the late 1970s, as buyers of broadcasting rights the BBC and ITV appear to have operated an informal cartel, which limited the fees paid to football by the TV companies. The proceeds were distributed evenly among all league clubs, each receiving a meagre £1,300 from the fee of £120,000 paid during the 1968 season. By the 1979 season

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English professional football

the total payment had increased modestly to £5,800 per club, or £534,000 in total (Goldberg and Wragg, 1991). The first attempted breach in the BBC–ITV stranglehold occurred in 1978, when London Weekend Television broke ranks with the other ITV companies, and attempted to negotiate exclusive rights to cover and distribute televised football to the rest of the ITV network. An Office of Fair Trading ruling prevented the deal from going ahead, but in the subsequently renegotiated contract, the amount received by each club rose to £23,900 from an aggregate annual fee of £2.2 million from the 1980 season onwards. Regular live coverage of league matches, shared between BBC and ITV, took place for the first time in the 1984 season, in a two-year deal which provided for coverage of ten matches per season at a cost of £2.6 million per season. Live coverage was suspended temporarily during the 1986 season, following the breakdown of negotiations for a new contract. Football’s parlous financial condition at the time, combined with increasing tensions between the larger and smaller clubs over the distribution of the proceeds, probably allowed the TV companies to retain the upper hand in the negotiations. A contract was eventually settled at the start of 1986, reinstating live coverage during the remainder of the 1986 season and for the following two seasons. The annual price was £3.1 million for fourteen matches, a smaller amount per match than under the previous contract. The 1986 contract was also the first to breach the principle of equal distribution of revenues between all ninety-two league member clubs; instead, the T1 clubs received 50 per cent of the proceeds, T2 25 per cent and T3 and T4 12.5 per cent each. The arrival of the two satellite broadcasters BSB and Sky in the late 1980s signalled a significant shift in the relative bargaining power of the football industry as the seller of broadcasting rights and the television companies as buyers. The BBC–ITV duopsony was gone for good, and the competition between the TV companies as purchasers of the rights intensified. In the 1988 round of negotiations, ITV secured exclusive rights to show eighteen matches per season over the next four seasons, from 1989 to 1992 inclusive. The annual fee was £11 million. The balance of bargaining power within football was also changing rapidly. Threats from the leading clubs to withdraw from the Football League and enter into separate negotiations secured a settlement in which roughly three-quarters of the ITV fee went to the T1 clubs. Of this, more than 40 per cent was shared between the so-called ‘big five’, which were to become the subject of the majority of ITV’s coverage:  Arsenal, Everton, Liverpool, Manchester United and Tottenham Hotspur. Televised football during the era of pay-TV

As the ITV contract’s 1992 expiry date started to approach, it was clear that the next round of negotiations would be shaped both by the ambitions of the newly merged satellite operator BSkyB to secure a significantly greater share of the

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173

coverage, and by the manoeuvrings of the leading clubs anxious to maximise their own share of the proceeds. Strategically, BSkyB identified the acquisition of regular live coverage of league football as the key step that would generate sufficient take-up of satellite services to enable the company to extend subscription charges beyond films, to sports and other channels. Meanwhile in early 1991, the Football Association’s Blueprint for the Future of Football announced that at the end of the 1992 season, the twenty-two T1 clubs would withdraw completely from the Football League to create a new Premier League, with its own governing body under the auspices of the Football Association. The Premier League would sell its own broadcasting rights, separately from any arrangements made by the Football League on behalf of its seventy remaining members. BSkyB succeeded narrowly in outbidding ITV for the contract providing exclusive live broadcast rights during the Premier League’s first five seasons, from 1993 to 1997 inclusive. The partnership with the BBC inherited by BSkyB following the BSB–Sky merger was to continue, with the BBC screening regular Saturday evening highlights of league matches played earlier the same day. The headline cost of the combined BSkyB–BBC Premier League coverage was £304 million for the five-year contract; although a smaller sum of around £190 million was eventually paid by BSkyB. Subsequently BSkyB was the dominant bidder in each of five further auctions of Premier League broadcast rights. The second auction, covering the next four seasons from 1998 to 2001, yielded proceeds of £670 million. The third, for which the duration was reduced to three seasons from 2002 to 2004 in an attempt to allay concerns expressed by the EU competition authorities, yielded £1.1 billion. In the fourth auction covering seasons 2005 to 2007, the phase of rapid growth in the value of the broadcast rights was temporarily halted, with BSkyB paying £1.024 billion for the renewal. For the fifth auction covering seasons 2008 to 2010, the Premier League and the European Commission agreed a new set of rules requiring the sale of the rights to be broken down into six packages of twenty-three matches each, with no broadcaster permitted to purchase all six packages. The packages were of differing levels of attractiveness to broadcasters, based on the timings of the slots (Sunday afternoon matches attract higher TV audiences than Saturday and Monday evenings), and the priority assigned to each broadcaster in selecting which match(es) to transmit from each weekend’s schedule. The Irish pay-TV broadcaster Setanta picked up two of the six packages for £392 million, with BSkyB collecting the other four (including the prime-time Sunday afternoon slots) for £1.31 billion. Two years into the three-year contract, however, with the uptake of subscriptions having lagged persistently behind projections, Setanta defaulted on its payment to the Premier League, and entered into administration in the UK in June 2009. The rights to broadcast the forty-six remaining matches for the 2010 season were acquired by ESPN, the American cable broadcaster owned by Disney, for around £90 million. With Setanta reportedly having already made an advance payment of £40 million on its final instalment of £130 million, the Premier League appears

174

English professional football

Table 6.10 Revenue from sale of broadcast rights, English Premier League, average per season, 1993–2010 seasons, £m

Live Highlights International Other domestic Total Number of live matches Fee per match

1993–1997

1998–2001

2002–2004

2005–2007

2008–2010

38 5 9 — 52 60 0.6

155 18 25 — 198 60 2.8

367 60 60 80 567 106 3.5

341 35 97 45 518 106 3.2

569 57 225 56 907 138 4.1

Source: Deloitte

not to have been embarrassed financially by Setanta’s collapse. Earlier in 2009, the sixth auction covering seasons 2011 to 2013 resulted in the acquisition of five of the six packages by BSkyB for £1.623 billion. ESPN assumed Setanta’s commitment for the sixth package for an amount that was close to Setanta’s original winning bid of £159 million. Table 6.10 shows estimates of the total value of the Premier League broadcast rights on a per-season basis over the period from the formation of the Premier League (start of the 1993 season) to the expiry of the fifth contract (end of the 2010 season). The broadcast rights for live transmission of matches to the UK accounted for more than 60 per cent of the total proceeds from each of the five auctions. Other proceeds are from the sale of a highlights package in the UK; sales of live or highlights packages overseas6; and (in the recent auctions) sales of content to be transmitted over broadband internet and 3G mobile phone networks, as well as delayed transmissions by BSkyB of entire matches played earlier the same day. The highlights package has been held by the BBC throughout the Premier League era (to the end of the 2010 season) except for seasons 2002 to 2004, when it switched to ITV. The latter’s £183 million winning bid was more than most analysts believed to be the true value of the rights at the time, and higher than the BBC’s subsequent winning bid of £105 million for seasons 2005 to 2007. The BBC eventually paid a higher price, £172 million, to renew the highlights package for seasons 2008 to 2010. The highlights package is prized by BBC because of the importance of Match of the Day in the corporation’s history, and (perhaps) its national cultural significance. Amidst the Premier League broadcast rights frenzy, however, the position of the free-to-air broadcasters BBC and ITV as weak competitors in a cut-throat market has been cruelly exposed. Since the Premier League breakaway, the chequered history of the Football League broadcast rights, both live and highlights, follows a similar trajectory. Between the 1993 and 1996 seasons, ITV screened selected Football League matches live on a regional basis. Between 1997 and 2000 these rights were

Broadcast revenues

175

switched to BSkyB. The broadcast revenues of the Football League clubs increased from around £16 million in 1996 to over £30 million per season from 1997. Amidst a blaze of publicity, ITV recovered the live Football League rights by bidding £315 million in the next auction, held in 2000. Live match transmissions were accorded flagship status in the promotion of a terrestrial pay-TV digital service ONDigital, co-owned by the two largest ITV companies Carlton and Granada. The British public, however, were unenthused, and the company struggled to raise subscriptions. Following an abortive rebranding as ITV Digital in July 2001, the company was liquidated in April 2002, with only £135 million having been paid to the Football League. BSkyB snapped up the rights for the next four seasons, 2003 to 2006, for a reported £95 million. Many Football League clubs endured a period of financial hardship following the sudden disappearance of anticipated TV revenues. Between 2007 and 2009 BSkyB and ITV shared the Football League rights, with the former screening live matches and the latter highlights, for a combined fee of around £110 million. BSkyB formed a similar partnership with the BBC for seasons 2010 to 2012, with the BBC screening ten live matches per season, and BSkyB showing sixtyfive live matches. The 2010 season thus became the first since 1996 in which English league football was screened live and free-to-air in the UK. The BSkyB–BBC package, which also covered the League Cup, generated significantly enhanced proceeds of £264 million for the Football League. Implications for competition and welfare

The transactions between the football industry and the broadcast media that are recounted in the previous subsection, and other similar arrangements operative in other European countries, have drawn the attention of the regulatory bodies responsible for competition policy and the courts, at both national and European level (Cave and Crandall, 2001; Hoehn and Lancefield, 2003; Jeanrenaud and Késenne, 2006; Parlasca, 2006). The following are the main issues of concern. Is the migration of top-level sports broadcasting from free-to-air to pay-TV in the public interest, and are there any grounds for intervention by the public authorities to inhibit or prevent this migration from taking place? Is the collective sale of broadcast rights by sports governing bodies anticompetitive, and should clubs be required to market and sell their own rights individually? Should broadcast rights be sold on a basis that grants exclusivity to one broadcaster, or should the rights be divided between more than one? Is the cross-ownership of football clubs and media companies anticompetitive, and if so should cross-ownership be prevented? Many of the arguments in legal cases concerning the application of competition law to the market for sports broadcast rights are complex and finely balanced; and as a consequence, a patchwork of arrangements for the organisation of this market has evolved across Europe. In Italy from the 2000 season onwards, the clubs were required to sell their own rights individually for pay-TV and overseas TV, while the league continued to sell the rights for

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public TV on behalf of the clubs (Baroncelli and Largo, 2006). Individual sale of broadcast rights also operated in Spain (Ascari and Gagnepain, 2006). In Germany the courts ruled against collective selling, but were overruled when parliament granted an exemption. In the UK the principle of collective selling has been upheld by the courts. The technical argument that the acquisition of broadcast rights by pay-TV broadcasters might be contrary to the public interest rests heavily upon the fact that televised broadcasts of sports events exhibit some, but not all, of the characteristics of public goods. Public goods are non-rivalrous, meaning that one person’s consumption does not diminish the amount of consumption that others are able to enjoy. Sports broadcasts share this characteristic. Public goods are also non-excludable, meaning that it is not feasible to exclude anyone from consuming the good if it is supplied. Prior to the development of encryption technology, sports broadcasts shared this characteristic; but in the era of pay-TV they no longer do so. Encryption technology renders it feasible to charge for access to sports broadcasts; but restricting some people’s access due to inability to pay still creates a welfare loss, since those people could have been permitted to consume without inhibiting anyone else’s ability to consume. It has also been argued, particularly in respect of major sporting events, that freely available televised sport generates positive externalities, through its capacity to bolster social cohesion and inculcate values of tolerance, respect and team work (Jeanrenaud and Késenne, 2006). If so, restricting some people’s access on the basis of inability to pay might create a welfare loss. Accordingly, the UK government has designated the Olympics, football’s World Cup and European Championship finals, the English and Scottish FA Cup finals, the Grand National and Derby (horse-racing), Wimbledon (tennis), the World Cup final (rugby union) and Challenge Cup final (rugby league) as events that must be broadcast freeto-air, known colloquially as the Crown Jewels. A further list specifies sports or events for which highlights must be shown free-to-air. Other European countries operate similar lists. Counter-arguments in favour of pay-TV sports broadcasting assert that viewers do not avoid paying when watching on free-to-air channels; they simply pay differently, through their willingness to tolerate exposure to advertising. Free-toair broadcasters do not receive the price signals that enable pay-TV broadcasters to gauge viewers’ preferences accurately, leading to a possible misallocation of resources. Pay-TV makes it feasible for minority sports, or less popular teams in popular sports such as football, to receive coverage that would not attract sufficient audiences for free-to-air broadcast. While there is public distaste for the lavish remuneration of top footballers, fuelled as it is mainly by revenues extracted directly from the bank accounts of pay-TV subscribers, the sport itself has also benefited during an era of profligacy, through (for example) investment in stadium redevelopment, and improvements in playing standards due to the ability of English clubs to attract and reward many of the world’s top footballers.

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Many of the issues discussed in the very early economics of sports literature, reviewed in Chapter 1, resonate through contemporary debates over the issue of the collective versus individual sale of broadcast rights. Are the clubs or the league the relevant economic entity that should assume responsibility for the sale? Proponents of collectivity argue that without the league, or without each other, no club would have a viable product to sell by itself. Proponents of individuality express concerns over the inhibition of competition if the rights are sold collectively. The league might act as a cartel in order to raise the price by exploiting its market power as a monopoly supplier. Proponents of collectivity counter that the matches of each club individually are not close substitutes for each other:  fans of Manchester United wish to watch their team’s matches, and do not regard those of Liverpool as an acceptable substitute. Therefore individual selling simply creates more monopoly sellers. This debate hinges on a question of market definition: in order to determine whether a monopoly exists, and if so whether it is being abused, the boundaries of the relevant market must first be defined. The same issue is also key to the debate surrounding exclusivity (see below). In favour of collective selling, a saving in transaction costs might be achieved if the rights are sold by one entity, averting the need for broadcasters to enter into costly and time-consuming negotiations with each club individually. The league can develop uniform branding, and thereby present a stronger product, than can the clubs individually. More contentiously, the collective sale of broadcast rights favours a more equitable division of the proceeds than would be achievable if each club sold its own rights individually; and an equitable division may create a positive externality for the clubs through a reduction in competitive inequality. This latter argument is rejected by some economists, such as Szymanski (2009), who argues that the question as to whether or how revenues should be shared is conceptually separate from the question of how the rights that generate the same revenues should be marketed. From a practical perspective, however, it seems likely that an equitable division of revenues is easier to administer and defend if the sale is conducted and the proceeds are collected centrally, than would be the case with individual sales followed by a round of punitive taxation and redistribution. The European Commission has objected to the practice of selling broadcast rights on a basis that grants exclusivity to one broadcaster. The Commission’s stance is reflected in the arrangements that have evolved for the sale of both the Premier League broadcast rights, as described above, and the rights for the Champions League. The latter must be divided between at least two broadcasters in each country, one of which must be free-to-air. In England the Champions League rights have been split between BSkyB and ITV since 2002. In the absence of regulatory intervention, exclusivity might be attractive not only to broadcasters, but also to the sports themselves. Exclusive rights might be worth more to a winning bidder than non-exclusive rights to two or more bidders combined, if competition between the latter to attract viewers or subscribers prevents them from extracting the full economic surplus. Therefore the sport might

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be able to realise higher proceeds if exclusivity is permitted. But exclusivity might be harmful to consumers if, for example, it reduces the number of matches that are televised. Under present arrangements only 138 of the 380 Premier League matches played in each season are screened. However, this argument ignores the practical difficulties in scheduling matches that would arise from any further extension of live coverage. Alternatively, allowing transmissions on Saturday afternoons while other matches are underway, would reduce attendances at matches that are not televised. This would be detrimental to the quality of a ‘product’ which relies, at least in part, upon the atmosphere generated by the crowd. In any event, most viewers have only so many hours’ leisure time available to devote to televised sport, and many would feel that coverage already far exceeds the saturation level. When tested in the courts or subjected to the scrutiny of the competition authorities, judgements as to whether exclusivity arrangements are anticompetitive rest heavily on questions of market definition. Should televised sport in general be viewed as the relevant market? If so, the award of exclusive rights in one sport is not anticompetitive, because broadcasters compete within a general market for sports or other programming content. This interpretation tends to evoke scepticism from football fans who would not regard snooker or volleyball as close or acceptable substitutes. Should the broadcast rights for individual sports, or individual competitions within sports, be seen as separate markets? This approach, adopted by the European Commission, may be problematic if, as suggested above, the contents of different packages are not perceived by viewers as close substitutes. Under present arrangements, to receive the maximum possible coverage of his or her team’s matches, the committed supporter needs to purchase subscriptions with each broadcaster. Such reasoning suggests that markets within sports subdivide to the level of individual teams, or even individual fixtures (Fikentscher, 2006; Jeanrenaud and Késenne, 2006). The issue of vertical integration between football clubs and broadcasters came to a head in England in 1998, when BSkyB launched a £623 million takeover bid for Manchester United. The bid was referred to the Monopolies and Mergers Commission (MMC), the predecessor of the Competition Commission. In 1999 the MMC delivered its findings, that the merger would damage competition between broadcasters, and be detrimental to the wider interests of British football (Monopolies and Mergers Commission, 1999). Accordingly the UK government blocked the takeover. Specific grounds for rejection of the bid included concerns that allowing the same company to operate simultaneously on both sides of the market for the broadcast rights would damage competition between broadcasters. Assurances that the company’s broadcasting arm would refrain from influencing the football arm were considered unenforceable. BSkyB would have an unfair advantage over rival bidders in future auctions, because a proportion of its bid would return to the company via the football club. BSkyB’s influence over the

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organisation of English football (for example, the scheduling of fixtures) might be exploited to the detriment of Manchester United’s competitors. A successful takeover might encourage retaliatory mergers involving other media groups and major clubs, widening the financial gap between the latter and the less marketable members of the Premier League and the Football League (Lee, 1999; Michie and Oughton, 1999). BSkyB also played a central role in a landmark case brought to the Restrictive Practices Court (RPC) by the Office of Fair Trading (OFT) in 1999. The OFT sought to demonstrate that the Premier League acted unlawfully as a cartel in negotiating the sale of broadcasting rights on behalf of its member clubs. It was argued that the Premier League’s decision to award exclusive live broadcasting rights to BSkyB unfairly restricted the number of live matches screened on television and inflated the price paid by subscribers. In a judgement published in July 1999, the RPC took the view that on balance these arrangements did not operate against the public interest. The outcome of this case depended heavily upon issues of market definition. Did exclusivity confer monopoly power upon BSkyB as sole suppliers to a distinct market for a specific programme type, or did it merely enable BSkyB to compete more effectively with other broadcasters within a wider market for TV programming in general? The RPC was sympathetic to this latter argument, suggesting that exclusivity could be helpful in promoting competition through enhanced programme quality (Cave, 2000). A more recent challenge to BSkyB’s supremacy emerged from a proposal from Ofcom, the UK’s media regulator, to require BSkyB to sell content from its premium sports and movies channels wholesale to other pay-TV broadcasters at regulated and significantly reduced prices. At the time of writing the cable TV company Virgin Media is the only wholesale purchaser of BSkyB programming; but the proposal could enable others, such as BT Vision (transmitted via broadband internet and digital terrestrial) to enter this market. Wholesale business is estimated to account for only a small proportion, around 4 per cent, of BSkyB’s total revenues. More significantly for consumers, however, the Ofcom proposal raises the prospect that a price war might break out between pay-TV broadcasters. If this proposal is implemented, rivals are expected to undercut BSkyB’s prices for premium content; and BSkyB might be forced to follow suit in order to deter subscribers from defecting to rival platforms. 6.6  Football’s labour market: players’ salaries and the transfer system

The retain-and-transfer system and the maximum wage were key features of English football’s labour market from the very earliest days of professionalism. Both were designed to prevent the clubs with the most resources from acquiring all of the most talented players simply by outbidding other clubs for their services; the outcome, it was argued, that might occur if the football players’ labour market

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operated without any restrictions. Both survived in their original form until the maximum wage was abolished in 1961, and the retain-and-transfer system was substantially overhauled in 1963. The retain-and-transfer system originated in a Football Association (FA) regulation introduced in 1885, requiring clubs to register their players annually with the FA. Player registrations immediately became tradeable commodities between clubs, since unregistered players were not permitted to appear (Morrow, 1999). All player contracts were renewable annually at the club’s discretion, and clubs were entitled to retain a player’s registration even if his contract was not being renewed. In theory and sometimes in practice, this enabled a club to prevent an out-of-contract player from earning a living. A player could only move if his present club was prepared to sell or release his registration. Under this system all clubs had the discretion to retain individual players for as long as they wished, as well as the guarantee of financial compensation when players were eventually permitted to depart. The incentive for players to seek to move was also restricted by the existence of the maximum wage, originally fixed at £4 per week when it was introduced in 1901. FA rules introduced simultaneously to outlaw bonus payments were regularly flouted during the next decade, resulting in many players receiving more than the maximum and a number of clubs being punished by the FA (Russell, 1997). By 1922 the official maximum had risen to £8 per week (£6 during the summer); meanwhile, the average weekly earnings of male employees in engineering in 1924 were £2.65. By the time the maximum had risen to £20 per week (£17 during the summer) in 1958, the differential had narrowed further: average weekly earnings for male manual employees in 1958 were £12.83 (Department of Labour and Productivity, 1971). By restraining both the growth in players’ salaries, and divergences between the remuneration of players at the top and bottom of the league, the maximum wage helped maintain a degree of uniformity in the financial structure of professional football at all levels. Between the early 1920s and the late 1950s the proportionate increases in the minimum and average admission price, and the maximum wage, were similar. Clubs appear to have responded to fluctuations in attendances and revenues primarily by adjusting the number of players employed on professional terms. For example, the total number of professional players in England and Wales increased from 5,000 in 1939 to 7,000 by the end of the 1940s, at the height of the post-war attendance boom (Fishwick, 1989). Roughly 4,000 of these were registered with league clubs. By 1961 the number of professionals registered with league clubs had fallen to just over 3,000 (Sloane, 1969). Circumstantial evidence also suggests that a uniform financial structure helped restrain growth in competitive inequality (see Section 6.1). Towards the end of its lifetime, the main economic beneficiaries of the maximum wage were the paying spectators. As late as the 1960 season, the average admission price was only 23 per cent higher in real terms than in 1926, despite the

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much larger rise in real disposable incomes that had taken place in the meantime. It is no coincidence that the pressure for abolition mounted progressively as the post-war economic recovery gathered pace, and as the magnitude of the spectators’ implicit consumer surplus also increased. As soon as the maximum wage was lifted and players’ salaries started to escalate, especially at the top end of the league, admission prices also started to rise. Much of the surplus then began to shift away from the spectators towards the players (Dobson and Goddard, 1998b). With both proven and suspected cases of illegal payments to players on the increase, and with the football authorities under pressure from a campaign organised by the Professional Footballers Association (the players’ union), the maximum wage was eventually abolished in 1961. In 1963, a High Court ruling in the case of the player George Eastham versus his employer Newcastle United, adjudged the retain-and-transfer system to be an unreasonable restraint on trade. From then on, the club holding the player’s registration had to offer a new contract at least as remunerative and of the same duration as the expired contract (which could be for one or two years) in order to retain his registration. If such a contract was not forthcoming, the player became a free agent. Transfers, however, were still at the discretion of the selling club, which retained the ultimate power to frustrate a player’s desire for a move, so long as it was prepared to continue to pay at the same level as under the old contract. As anticipated, the immediate consequence of these changes was salary inflation. Famously, the weekly salary of Fulham and England captain Johnny Haynes was increased to £100: a rise of more than 400 per cent relative to the old maximum. For the large majority of professionals, the immediate effect on salaries was less dramatic. According to Russell (1997) several leading clubs, including Liverpool and Manchester United, attempted to maintain their own unofficial maximum during the 1960s. Many clubs also responded to the increase in costs by reducing the number of professionals employed: the total fell to 2,400 in the 1967 season (Sloane, 1969). Nevertheless, over a period of years the cumulative effect on football’s finances of the decision to lift the lid on players’ salaries was profound. According to data reported by Szymanski and Kuypers (1999), the inflation-adjusted increase in salaries during the 1950s for clubs with complete records was less than 10 per cent. Between 1961 and 1974 the corresponding inflation-adjusted increase for the same clubs was around 90 per cent. Revenues had fallen by about 5 per cent in real terms during the 1950s. Between 1961 and 1974 the real increase was over 30 per cent. Between 1961 and 1974 growth in salaries appears to have outstripped growth in revenues among both the larger and the smaller clubs; but the growth in both was much faster for the larger clubs than for the smaller. The adjustment of football’s financial structure to the removal of the maximum wage appears to have been virtually complete by the mid-1970s. Between 1974 and the late 1980s, the rates of increase in revenues and salaries were similar. Having crept from below 40 per

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cent in the 1950s to above 50 per cent by the mid-1970s, the average ratio of total salaries to total revenues remained stable thereafter. Naturally, however, the average data tend to mask considerable intra-club and year-on-year variation. A further key change to the transfer system was introduced in 1978, when players were awarded the right to decide themselves whether to move on the expiry of their contracts. Though the new system was termed freedom-of-contract, in practice the out-of-contract player was still constrained to some extent. If his existing club offered a new contract at least as rewarding as the expired contract, it could still demand a compensation fee, either to be agreed between the two clubs, or (in cases where agreement could not be reached) to be decided by an FA tribunal. Arbitration was binding on both parties. This meant that in order to move, an out-of-contract player had to find a new club that would either agree a fee with his existing club, or be willing to accept the risks of arbitration. The 1978 ‘freedom-of-contract’ system survived intact in England and Wales until the landmark 1995 European Court of Justice ruling in the Jean-Marc Bosman case, which prompted further movement towards the complete acceptance of the principle of freedom of movement for out-of-contract players. The requirement for the payment of compensation to the former club of an out-ofcontract player signing for a new club was found to be incompatible with provisions in Article 48 of the Treaty of Rome for the freedom of movement of labour. The existing ‘three-foreigner’ rule, which had the effect of limiting the number of individuals from countries outside the jurisdiction of each national football federation allowed onto the field of play at any one time, also contravened Article 48, by restricting the opportunity for European Union (EU) nationals to play for clubs located in other EU countries. The Bosman ruling concerning out-of-contract players applied originally only to player transfers that crossed EU national boundaries. But many European governing bodies quickly brought into line the regulations governing transfers between clubs within their national jurisdictions. Since the end of the 1998 season, all transfers of out-of-contract players over the age of 24 between English clubs have been uncompensated. The retention of the fee element for out-of-contract players below the age of 24 recognises that in a completely free player labour market, clubs that invest in player development might be unable to realise the proceeds of their investment due to poaching. The post-1998 English arrangements attempt to preserve some element of compensation for clubs that discover or develop talented young players. The European Court of Justice was unconvinced that the entire pre-Bosman transfer system had been justified by the ‘compensation’ argument; instead, it took the view that transfer fees often bore little or no relation to the efforts or costs incurred in developing players (Simmons, 1997; Morrow, 1999). Following the Bosman ruling, protracted discussions led eventually to an agreement between the EU and the European and international football governing bodies UEFA and FIFA, which took effect from 2003. The new system involved

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compensation for clubs for the training and development of young players moving before the age of 24; the creation of a ‘transfer window’ before the start of each season, and a further limited mid-season window, with transfers not permitted outside these windows; players permitted to move only once per season; a minimum contract duration of one year and a maximum of five years; and contracts only enforced for a period of three years up to the age of 28 and two years after that age, but with financial compensation payable if a contract is breached outside these limits by either player or club (Goddard, Sloane and Wilson, 2010). Fifteen years after the original Bosman ruling, it is clear that the players’ labour market has changed fundamentally, and in ways that were, for the most part, predictable at the time. First, the removal of all restrictions on the eligibility of players from EU countries, as well as non-EU players of international standing, has led to a huge influx of foreign players now being employed by English clubs, especially in the Premier League (see Chapter 8, Section 8.1). Many have been attracted by remuneration perhaps much higher than they would expect to attain elsewhere. While the post-Bosman influx was spectacular, the trend was already underway before 1995. The success achieved by Eric Cantona, first at Leeds United and then at Manchester United, following his transfer from Nimes in 1991, seems to have been influential in raising awareness within the traditionally insular British game, of the potential contribution of gifted overseas players. Second, since the price of acquiring an out-of-contract player is now paid entirely to the player (rather than shared between the player and his former club), salary inflation is a predictable consequence of Bosman. Players seeking a new club are in a stronger position to bargain for high remuneration if their acquisition is not encumbered with the obligation to pay a transfer fee. As Table 6.5 shows, salary inflation in English football was exceptional during the immediate post-Bosman period of the mid to late 1990s, outstripping even what was also explosive and historically unprecedented revenue growth. Bosman clearly assisted many players, especially at the highest level, to capture a much larger share of the burgeoning financial rewards. For Germany, Feess, Frick and Muehlheusser (2004) report evidence that the higher the remaining length of a player’s contract, the higher the transfer fee if the player is sold, and the lower the player’s salary at his new club. These effects were similar, however, in both the pre- and postBosman periods. Tervio (2006) suggests that restricting the length of enforceable contracts to three years (or less for older players) would further increase salaries for all types of player, with the salaries of the most talented increasing the most. Third, many clubs attempted to protect themselves against the possibility of losing their best players without compensation by offering longer-term contracts, especially to their younger stars. Morrow (1999) suggests that this development may also have contributed to salary inflation in the short term, if a higher initial level of remuneration is needed to persuade a player to commit for a longer period. Longer contracts may also be attractive to players, however, since they insure future earnings against the consequences of serious injury or loss of

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form. They may help restrain salary inflation over the longer term, if they are enforced over their full duration. There are nevertheless incentives for clubs to offer enhanced terms to their top stars far in advance of the expiry of their present contracts, to avoid involvement in an eventual bidding contest for the players’ signatures. The ‘insurance’ argument also provides incentives for risk-averse players to accept improved terms. A contracted player who declines an improved offer received within the lifetime of his existing contract cannot be certain his value to potential bidders will be as high when the contract eventually expires, since all athletes are constantly exposed to the hazards of loss of form or serious injury. Feess and Muehlheusser (2003a; 2003b) distinguish between pre-Bosman, Bosman and post-Bosman contracts, and find that each type leads to similar levels of player effort, investment incentive and payoffs, provided the payoffs to players can be adjusted by varying the contract length. Feess, Frick and Muehlheusser (2004) report that in Germany, the average contract length increased by about six months after the Bosman ruling, from around two-and-a-half years to three years. A final predicted consequence of Bosman, widely debated at the time, was its potential to cut off what was an important source of finance for clubs in the lower tiers:  proceeds from the sale of their most talented players to higher-tier clubs. At best, the erosion of the implicit cross-subsidy generated by the domestic transfer market might widen competitive inequaliy between rich and poor; at worst, the loss of transfer fee earnings might threaten the survival of many of the small-­market clubs. Ericson (2000) argues that free agency might reduce the quality of play because the marginal cost of talent increases for small-market clubs, which no longer receive adequate compensation for producing talent. While the European Court of Justice accepted that it was legitimate for the football industry to use various means of cross-subsidy to reduce competitive inequality, the Court felt that the transfer system as it had operated pre-Bosman was neither a necessary nor an effective means for achieving this objective (Morrow, 1999). According to Antonioni and Cubbin (2000), the majority of transfers before 1995 involved players who were under contract at the time. Such transfers were not directly affected by the Bosman ruling, which applied to transfers involving outof-contract players. In fact, there is no clear evidence that Bosman has impacted significantly upon the flows of transfer expenditure between the Premier League and Football League clubs. For selected three-season periods between the 1970s and 2000s, Table 6.11 reports data on the net expenditures of T1, T2, T3 and T4 clubs in transfer deals in which both the selling and buying clubs were English league members. During both the immediate post-Bosman period (1996–8), and long after the dust from Bosman had settled (2006–8), there were substantial net expenditure flows from the Premier League to the Football League. These flows appear to be comparable in magnitude (relative to either gate revenue or total revenue) to the net flows from T1 to T2, T3 and T4 combined that are reported in Table 6.11 during the­

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Table 6.11 Average net transfer expenditure within the Premier League/Football League per season, selected three-season periods, £m

1976–1978 1986–1988 1996–1998 2006–2008

T1

T2

T3

T4

1.0 3.6 13.7 47.3

−0.6 −1.9 −6.9 −38.8

−0.3 −1.1 −3.8 −6.1

−0.1 −0.6 −3.0 −2.4

Source: Deloitte

Table 6.12 Average flows of transfer expenditure within the Premier League/ Football League per season, 2006–2008 seasons, £m To → From ↓ T1 T2 T3 T4 All tiers

T1

T2

T3

T4

All tiers

115.0 18.6 1.6 0.0 135.2

64.1 20.6 0.7 0.3 85.7

2.9 6.3 1.1 0.2 10.5

0.5 1.4 1.0 0.4 3.3

182.5 46.9 4.4 0.9 234.7

Source: Deloitte

pre-Bosman period (1976–8, and 1986–8). For the 2006–8 period, Table 6.12 provides more detail on the gross flows of transfer expenditure between tiers on a pairwise basis. The data reported in Tables 6.11 and 6.12 do not include transfers in which one of the parties was a Scottish, Irish or overseas club. Table 6.13 reports gross expenditure on both domestic and foreign transfers for the Premier League and the Football League for individual seasons from 2001 to 2008. The English transfer market entered a temporary recession following the collapse of ITV Digital in 2002. Although the impact was felt most severely in the Football League, there was a knock-on effect for the Premier League as well. Revenue growth in the latter slowed sharply in the mid-2000s, for reasons not unconnected with the ITV Digital affair. As shown in Table 6.8, the total value of the Premier League broadcast rights for seasons 2005 to 2007 was less than in seasons 2002 to 2004. In this context it appears that transfer expenditure can act as a useful cushion, which can be reduced faster and more easily than other items of expenditure during periods of unanticipated austerity.

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Table 6.13 Gross transfer expenditure of Premier League and Football League clubs per season, 2001–2008 seasons, £m

2001 2002 2003 2004 2005 2006 2007 2008

T1

T2, T3, T4

All tiers

364 323 187 386 340 435 492 664

  59   84   16   28   28   48   86 115

423 407 203 414 368 483 578 779

Source: Deloitte

Table 6.14 Average gross transfer expenditure and average revenue per season, three-season periods, 1994–2008 seasons, £m

1994–1996 1997–1999 2000–2002 2003–2005 2006–2008

Gross transfer expenditure

Total revenues

Gross transfer expenditure as percentage of revenues

151 282 390 328 613

456 830 1314 1740 2115

33.2 34.0 29.7 18.9 29.0

Source: Deloitte

Table 6.14 identifies the longer-term trend in gross expenditure on both domestic and foreign transfers for the Premier League and football clubs as a whole, in the form of averages per season over three-season periods. The aftermath of the ITV Digital collapse is also reflected in these data, with the ratio of gross transfer expenditure to total revenues for seasons 2003 to 2005 dipping temporarily below 20 per cent. Over the longer term, however, this ratio has been relatively consistent: just above 30 per cent during the mid and late 1990s, and just below 30 per cent during the early and late 2000s. 6.7  Ownership, governance and finance

When the FA was founded in 1863, football operated on an amateur basis. However, the competitive nature of the FA Cup, and the potential to generate income from selling match tickets, created pressures for players to receive payments for playing.

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Professionalism was sanctioned in 1885; and a new competition, the Football League, was established in 1888. Though the FA was unable to prevent the move to professionalism, it did succeed in defining club ownership as essentially a notfor-profit activity. English football’s non-profit ethos was underpinned by FA regulations limiting the amounts that could be remitted to shareholders and directors in the form of dividends or salaries; requiring existing chairmen to approve any major transfer of shares, eliminating the possibility of hostile takeover; and stipulating that a club’s assets would revert to the FA in the event that it ceased playing football, preventing any club from being taken over and closed in order to realise a quick profit by selling its stadium (Conn, 1998; Horrie, 2002). Although business interests would on occasions manifest themselves in the management of English clubs, the rules were largely successful in ‘protecting’ the clubs from profit-taking and asset-strippers (Vamplew, 1988). At the origins of professionalism, football clubs were voluntary organisations, administered by committees elected by voting members. The development of professionalism led to further growth in gate revenues, and in the costs of player compensation and stadium construction. This in turn created pressures for clubs to acquire limited liability status. According to Russell (1997), Small Heath (later, Birmingham City) was probably the first club to become a private company in 1888. By 1921, all but two of the league’s eighty-six member clubs had followed suit. From then until recently, professional football’s traditional methods of commercial and financial management seemed virtually impervious to pressures for modernisation emanating from a multitude of social and economic pressures. For most of the twentieth century, the ownership structure and the financing and administration of the average football club retained many features originally acquired during the late Victorian era. Traditionally, the major shareholders and the majority of directors of football clubs were individuals drawn from the local business community. Ownership and control were often handed down through the generations, from father to son. Most clubs were small, privately owned companies, which tended to be undercapitalised with little finance raised either from issues of new equity (because owners were unwilling to dilute their personal control) or from retained profit (because usually there was no profit). In many cases, however, club owners or directors provided additional long-term finance through personal loans, which for practical purposes were similar to equity finance. Bank loans and overdrafts were the other principal source of (mainly short-term) finance. Although share ownership sometimes extended beyond the well-heeled middle classes, working-class shareholdings were usually too small to confer influence over the running of the club, and seem to have existed primarily as a token of loyalty (Russell, 1997). The ‘true’ motives of those wealthy individuals who injected large amounts of personal finance into the local football club, often in return for little more than a seat on the board of directors, have been debated by academic economists and sociologists. The economist’s usual profit-maximising assumption seems untenable

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given the woeful financial performance of most football clubs, and because directors were, for many years, prohibited by FA regulations from receiving dividends, until this rule lapsed in the 1980s (Conn, 1997). No doubt some individuals have attempted to exploit their influence in football for ends such as political advancement, or to win contracts for their own businesses. In many cases, however, personal enthusiasm provides sufficient motivation, and success in business provides the means, to acquire an ownership stake and intervene in the running of the local football club. Eventually, historical restrictions on the exploitation of football’s commercial potential were eased or lifted. The ban on directors’ remuneration was revoked in 1981. At the time, North London property developer Irving Scholar was representative of a new generation of hard-headed, commercially minded club chairmen. During the early 1980s Scholar initiated a low-key campaign to buy out small Tottenham Hotspur shareholders. Legend has it that Scholar signalled his assumption of control by turning up at a directors’ meeting to announce himself as the new chairman, much to the astonishment of other board members. He set about refinancing the debt-ridden club by floating a new holding company, Tottenham Hotspur PLC on the London Stock Exchange. The holding company would circumvent FA regulations on dividend payments by owning the football club as a subsidiary, together with a number of other leisure, clothing and catering businesses. The flotation in October 1983 raised £3.3 million: a sum that appeared considerably larger at the time than it may seem when judged by present-day standards, and sufficient to eliminate the debts inherited from the previous ownership. Indifferent results in several of the other diversified businesses over the next few years, however, meant that the flotation was considered to have been somewhat less than an unqualified success. Perhaps because the holding company’s financial performance did not offer strong encouragement to others, Tottenham remained the only club with a Stock Exchange listing for several years. Other clubs eventually followed suit, however. Millwall raised £4.8 million in a flotation in October 1989, and Manchester United £6.7 million in June 1991. Again, the early experiences of the quoted companies were discouraging. Within two years, Millwall shares were trading at around one-tenth of their original value. The team’s relegation from T1 in May 1990, followed by a further decline in its fortunes within T2, led investors to scale back drastically their assessment of the company’s value, before trading in the shares was eventually suspended. Manchester United shares were more than 50 per cent undersubscribed at the time of flotation in June 1991. Meanwhile, other clubs were experimenting with alternative methods of raising external finance, such as bond schemes guaranteeing the right to purchase a season ticket for a specific seat in perpetuity. Such schemes were not popular with fans, however, and were soon dropped.

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Despite the indifferent results of these early attempts to expand and diversify English football’s capital base, by the early 1990s events and sentiment were starting to move in a direction more favourable to the sport’s commercial development. Decisive action on the part of the sport’s governing bodies, clubs and the government over issues such as safety and hooliganism had raised hopes that the stadium disasters and other problems of the 1980s could finally be lain to rest. Following a perceptible change of mood, watching football was once again perceived as a fashionable leisure activity. As the Premier League got underway, a surge of optimistic sentiment concerning future prospects led to massive appreciation in the share prices of the two T1 clubs that had already floated. Between December 1994 and December 1996, Tottenham Hotspur and Manchester United shares increased in value by around 300 per cent and 400 per cent, respectively. Meanwhile, the costs of stadium redevelopment and spiralling player salaries and transfer fees were creating urgent pressures for clubs to tap new sources of finance. Circumstances were favourable for the spate of fifteen further flotations on the London Stock Exchange Official List and Alternative Investment Market that took place between September 1995 and October 1997. By far the largest flotation, worth over £50 million, was that of Newcastle United in April 1997. Deloitte (2009) estimate that Premier League clubs raised approximately £175 million in total through stock market flotations. The combined capitalisation of the nineteen listed English clubs was £651 million in June 2002. Including clubs listed on the more loosely regulated Ofex market (subsequently renamed Plus Market), twenty-three English clubs (and four Scottish clubs) experimented with some form of stock market listing. During the 2000s, however, many of the clubs that were listed at the start of the decade eventually took the decision to de-list. By the end of 2009, only Preston North End (listed on the London Stock Exchange), Millwall, Tottenham Hotspur, Watford (Alternative Investment Market) and Arsenal (Plus Market) retained their listed status. Several clubs de-listed under severe financial duress: for example, Queens Park Rangers and Leicester City did so upon entering administration in 2001 and 2002, respectively. Several others de-listed following the acquisition of their equity by a single purchaser: prominent examples include Aston Villa, Chelsea, Manchester United and Newcastle United. With hindsight, it is clear that major inconsistencies existed between the governance of the typical English football club, and the model of corporate governance under public ownership to which listed companies are required to adhere. Critical comment on the governance of Newcastle United figured prominently in the financial press throughout the decade of the club’s existence as a listed company, but many of the issues raised were relevant to listed clubs in general. Prior to its acquisition by Mike Ashley in June 2007 and subsequent stock market de-listing, Newcastle was routinely criticised for the dominance on its board of representatives of the families of the two major shareholders, Sir John Hall

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and Freddy Shepherd. The pre-2007 board was characterised by a lack of independence, and a tendency for family interests to ride roughshod over the interests of smaller shareholders. Directors’ salaries and bonuses were disproportionate to the financial performance of the company, and were not reviewed by an independent remuneration committee. The tendency to signal to supporters an imminent change of team manager through none-too-subtle hints dropped via the local and national media, apparently standard issue in the media relations toolkit of many football club chairmen and chief executives, sat uncomfortably with stock market regulations requiring immediate disclosure of information concerning the turnover of senior company officials. For financially motivated shareholders, of course, the bottom line was profitability. Once again, the capability of most listed football clubs to satisfy stock market expectations was found to be deficient, especially following a few years’ investor experience of football’s fickle competitive and financial fortunes. The issue of vertical integration between media companies and football clubs first attracted headline attention in Britain in September 1998, when BSkyB’s takeover bid for Manchester United was announced (see Section 6.5). The MMC ruling and the UK government’s subsequent decision to block the Manchester United takeover also torpedoed an agreement for the cable pay-TV company NTL to take a controlling interest in Newcastle United. Although the direct ownership of major English football clubs by media companies has since been ruled out, several media companies acquired minority stakes in more than one club, subject to an FA regulation restricting parties with multiple interests to a maximum 10 per cent shareholding in each club. Accordingly, BSkyB acquired minority shareholdings in Manchester United, Leeds United, Chelsea, Sunderland and Manchester City; Granada Media invested in Liverpool; and NTL in Newcastle United, Middlesbrough, Aston Villa and Leicester City. Several clubs entered into arrangements with media companies to broadcast programmes over broadband internet, which subsequently turned out to be of little or no commercial value. For example, ITV built up a 9.9 per cent ownership stake in Arsenal with sucessive investments in 2000 and 2005, and a 50 per cent stake in Arsenal Broadband. These interests were eventually sold to the US billionaire investor Stan Kroenke in 2008. By this time, ITV had also divested itself of similar shareholdings in Liverpoolfc.tv (Liverpool) and MUTV (Manchester United). Deloitte (2009) estimate that strategic media investment contributed around £300 million to the finances of Premier League clubs during the late 1990s and early 2000s; but by the end of the 2000s the model of direct strategic investment in football clubs did not figure prominently on the agendas of media companies. At the height of football’s stock market flirtation, several clubs experimented with new mechanisms for raising non-equity finance from institutional investors (Gerrard, 2006). Securitisation involves the capitalisation of future anticipated streams of ticket or other commercial revenue. Bonds are issued, giving the purchasers a prior claim on the designated revenue stream for interest and

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capital repayments. The assets against which the bonds are secured remain in the ownership of the originating company (the football club). Newcastle United was the first English club to raise finance using this method, in December 1999. £55 million was raised by means of securitisation of the club’s gate and hospitality income over the next seventeen years. This capital sum was used primarily to finance redevelopment of the club’s St James Park stadium, with the seating capacity raised from 36,000 to 55,000. Other clubs that undertook similar transactions between 2000 and 2003 were Southampton (£25 million), Leicester City (£28 million), Ipswich Town (£25 million), Leeds United (£60 million), Everton (£30 million), Manchester City (£44 million), Tottenham Hotspur (£75 million) and Norwich City (£15 million). In several of these cases, the securitisation proceeds were employed to finance stadium redevelopment or the construction of new stadia; but in others the proceeds appear to have been used to finance player acquisitions or general working capital. Securitisation creates a heightened risk of insolvency, in the event that the securitised revenue stream drops below the level that is required to service the debt. While many football clubs’ future income streams are perceived to be rather stable and predictable, thanks to the loyalties of fans, some of the securitisation deals seemed analagous to mortgaging the house in order to fund lavish current consumption. Furthermore, few football clubs are entitled to consider themselves as realistically exempt from the dangers of relegation. As seen above, relegation from the Premier League entails a large drop in revenue for even the most keenly supported club, due to the loss of broadcast revenue. Among the clubs listed above, Leicester City entered administration in 2002, and Ipswich Town followed in 2003, both having been recently relegated from the Premier League. Following Leeds United’s failure to qualify for the Champions League in 2002, the club entered a rapid and spectacular spiral of decline that included relegation from the Premier League in 2004, and a default on the capital and interest payments on the £60 million bond issue in the same year. Bondholders reportedly incurred substantial losses in the subsequent settlement (Gerrard, 2006). Against this background, it is unsurprising that only one further football club securitisation took place between 2004 and 2009. The £260 million capitalisation of the future revenues of Arsenal’s whole business, undertaken in 2006 to finance the construction of the club’s Emirates stadium, is something of an outlier in terms of both timing and magnitude. It was claimed that even in the event that Arsenal failed to maintain its status as a regular Champions League qualifier, the debt was structured in a manner that would allow the servicing of the debt to continue. Over the longer term, however, the need to divert a substantial portion of the club’s revenue towards interest and capital repayments, rather than expenditure on players, seems to increase the likelihood that this theory may eventually be put to the test. Player sale-and-leaseback was a further form of financial innovation that was popular in English football in the late 1990s and early 2000s (Gerrard, 2006).6 For

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the duration of his contract with his current club, a player’s registration is an asset that might be used by the club as security for a bank loan, with the lender enjoying recourse to other assets in the event of default on the loan or a downgrade in the value of the player’s registration due to loss of form or injury. Typically, the lender took out credit insurance against the risk of default. Most arrangements of this kind were effected in order to spread the upfront cost of a player’s transfer over the full duration of the contract. Deloitte (2009) estimate that finance amounting to around £150 million was raised between 1999 and 2002. With several such arrangements also ending in default, however, player sale-and-leaseback appears to have fallen out of favour with investors after the early 2000s. In some ways, the acquisition of Chelsea by the Russian billionaire Roman Abramovich in June 2003 heralded a return to a more traditional model of football club ownership and finance, albeit on a far more extravagent scale than had ever been witnessed previously, in English football or elsewhere. According to Deloitte (2009), Abramovich’s total investment in Chelsea to the end of the 2008 season totalled £760 million in the form of non-interest bearing ‘soft’ loans. Accordingly, Chelsea’s balance sheet is heavily laden with debt; but since there are no interest or capital payments, the club’s expenditure on players’ salaries and transfers is constrained only by the extent of its benefactor’s extraordinary largesse. Chelsea’s salary expenditure for the 2008 season was £172 million, 42 per cent higher than that of the next-highest spender, Manchester United on £121 million. Chelsea’s pre-tax loss of £85 million was easily covered by a £123 million injection of new investment during the same season. At the time of writing, Sheik Mansour bin Zayed Al Nahyan of Abu Dhabi, the billionaire purchaser of Manchester City in September 2008, appears intent on emulating and perhaps even usurping Roman Abramovich’s position as English football’s most prolific benefactor. The Chelsea/Manchester City ownership model faces a future challenge, however, in the form of the Financial Fair Play proposals being developed by UEFA at the time of writing, and planned for implementation from the 2013 season onwards. Aimed at preventing clubs with wealthy backers from attempting to ‘buy success’ by spending beyond their means, the proposal seeks to force clubs operating above a certain expenditure threshold to limit their expenditure on salaries and transfers so as to break even over time. Critics have argued that by entrenching differentials in market size this proposal would, in common with the G14 payroll cap discussed in Chapter 2, Section 2.5, have the effect of increasing (rather than reducing) competitive inequality. Several decades’ experience of attempts to impose restraints on salary expenditure in North American major league sports suggest significant monitoring and enforcement challenges, as well as employment opportunities for lawyers, may lie ahead if this proposal is implemented. Manchester United, meanwhile, was the subject of a leveraged buyout in 2005 by the American entrepreneur Malcolm Glazer. The £810 million cost of purchasing the company’s equity, which relieved the previous shareholders of the property

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rights to the club’s future anticipated revenue or profit streams, was part-financed through loans from banks and hedge funds, some of which were secured against the club’s assets. In contrast to the situation at Chelsea and Manchester City, the Glazer family’s acquisition of Manchester United appears to have been commercially motivated. During the remainder of the 2000s, increased ticket prices contributed to sustained growth in revenue, accompanied by (relative) restraint in salary and transfer expenditure. For the 2008 season the interest payment on the debt was around £69 million, sufficient to wipe out a large proportion of the club’s operating profit. The Glazers claimed they could manage Manchester United’s cash flows in a manner that would meet their obligations to lenders, and provide sufficient financial resources to sustain a successful team. The revenue flows upon which this model depends, however, are sensitive to team performance. If the flow of trophies were to dry up, it seems that a highly leveraged financial model requiring the generation of large revenue flows in order to service the club’s heavy debt, could unravel. Liverpool, reputedly Manchester United’s fiercest rivals on the field of play, have also operated under American ownership since 2007, in the form of George Gillett and Tom Hicks. Like the Glazer family, Gillett and Hicks both hold ownership stakes in North American major league sports franchises. As in United’s case, their £435 million acquisition of Liverpool was highly leveraged, leaving the club burdened with debts that incurred interest charges of £35 million during the 2008 season. Many of the smaller-market Premier League and Football League clubs are financed along more traditional lines, through some combination of ‘soft’ loans from benefactors, and bank loans and overdrafts. As the gradient of the relationship between each team’s competitive position within the ninety-two-club league hierarchy and the scale of its finances (on both the revenue and cost sides) has become steeper, it is unsurprising that the number of clubs mismanaging their finances in a manner culminating in insolvency proceedings, was higher during the 2000s than ever before. During the 2010 season Portsmouth became the first Premier League member club to enter administration; although several others had previously experienced this fate soon after relegation. Deloitte (2009) report that seventeen Football League clubs underwent insolvency procedings between 1992 and 1999, and a further thirty-five between 2000 and 2009. These figures include a few clubs that became insolvent more than once. No fewer than sixteen Football League club insolvencies were recorded in 2002 and 2003, following the demise of ITV Digital. From the start of the 2005 season, the Football League introduced an automatic penalty, in the form of a deduction of ten league points, for any club entering administration.7 The aim was to deter clubs from gaining an unfair competitive advantage by overspending on players, and then escaping the full financial consequences by declaring insolvency. Points deductions have proven onerous on the majority of occasions they have been applied: seven of thirteen clubs punished in this manner between the 2005 and 2009 seasons (inclusive) were relegated at the end of the season in which league points were deducted.

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A radically different ownership model, which has proved successful in some cases at the lower end of the financial scale, is the supporters’ trust. The UK government’s Supporters Direct initiative, launched in 2000, provides legal and practical support to supporters seeking to form a trust as a vehicle for involvement in the ownership and management of a football club. Supporters’ trusts are cooperatives, which operate on a one-member one-vote basis. A trust might seek to gain influence by purchasing shares, or by securing representation on the club’s board. During the 2000s trusts were formed at more than 150 clubs at all levels in Britian, with 120,000 members in total, and £20 million raised and invested. Prominent examples include AFC Wimbledon, FC United of Manchester, Ebbsfleet United and AFC Telford United. AFC Wimbledon was founded at the base of football’s pyramid by supporters who refused to accept the relocation in 2004 of the former-Premier League club Wimbledon to its new home in Milton Keynes. At the end of the 2009 season, the newly formed club achieved promotion to the Conference, the tier immediately below T4 of the Football League. FC United of Manchester, the club formed by Manchester United supporters affronted by the Glazers’ takeover, regularly attracted 2,000 supporters to home matches played at a level three tiers below T4 during the 2010 season. Another Conference member-club of the late 2000s, Ebbsfleet United (formerly known as Gravesend and Northfleet United) was acquired for £700,000 in 2007 by the website MyFootballClub. The acqusition was funded through member subscriptions. Payment of the subscription fee entitled each member to vote on matters such as team selection and player transfers. Telford United, former members of the Conference, were one of the few financially stricken clubs to go into liquidation. In 2004 supporters set up their own club, AFC Telford United, to take its place. Not all supporters’ trusts have been successful, however. Notts County supporters’ trust relinquished its majority stake in the club in the summer of 2009. Stockport County, supporter-owned since 2005, overspent on either side of its 2008 promotion to T2, and entered administration in April 2009. Supporters’ trusts at Brentford, Chesterfield and York City lacked either the wherewithal or the financial resources needed to enable the clubs to flourish, and eventually ­relinquished ownership to private investors. At the time of writing, Exeter City is the only Football League club that is wholly owned by its supporters. Conclusion

Chapter 6 has presented a historical and current analysis of English club football’s commercial, financial and economic structure. From the origins of professionalism in the late nineteenth century until the early 1960s, considerable uniformity in professional football’s financial structure at all levels was preserved through regulation of both admission prices (which determined the main component of revenue) and players’ salaries (the principal item of cost). By the end of the 1950s, however, as the post-war recovery gathered momentum and general

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living standards rose dramatically, the pressure for relaxation of these regulations was mounting. The abolition of the maximum wage in 1961, and the reform of the retain-and-transfer system in 1963, heralded a period of rising financial inequality between clubs operating at different levels within the league hierarchy, as football made the transition towards a new and radically different economic structure. During the 1970s and most of the 1980s, English club football’s economic fortunes were in steep decline on a number of fronts. Pressures emanating from social and demographic changes, the hooligan phenomenon and the failure of football clubs themselves to maintain their own physical infrastructure, had taken their toll on attendances over many years, to the extent that the future survival of large numbers of clubs (both large- and small-market) seemed to be in jeopardy. Tragically, however, it was only after the stadium disasters of Heysel, Bradford and Hillsborough in the mid to late 1980s that the momentum for fundamental reform became irresistible. Football’s rehabilitation during the 1990s and 2000s as the most popular and fashionable national sport in England and elsewhere, has coincided with a further sharp rise in financial and competitive inequality between English clubs. This increase has taken place against a background of rising rather than falling spectator demand at all levels, which has done much to offset the most adverse financial consequences for the league’s smaller members. The wholesale reconstruction and conversion of all major stadia to all-seated status, together with the marginalisation of the hooliganism phenomenon, have strengthened football’s appeal as a middle-class spectator sport. Mainly as a consequence of technological change in broadcasting, football’s dual status as both spectator sport and television spectacle has become more realistically reflected in the balance between the revenues it derives from both sources. By showering unprecedented riches upon the Premier League, but relatively meagre returns for the Football League, the dispersion of broadcast income has opened up a financial chasm between the leading clubs and the rest. Meanwhile the market for TV broadcast rights continues to attract the critical scrutiny of the competition authorities. The Bosman ruling heralded the arrival of free agency in the European footballers’ labour market. An influx of talented overseas players is generally perceived to have led to marked improvements in playing standards in England, especially in the Premier League. However, the liberalisation of the rules governing football’s labour market has greatly widened disparities between the earnings capability of the top players and the rest. Many football clubs have become financially unstable, drawn into competitive bidding wars in order to attract better players they realistically cannot afford. Two decades of experimentation with alternative models of ownership, finance and governance began in the early 1980s, following the removal of several longstanding restrictions on the personal remuneration and activities of English football club owners. At the time of writing it appears, in some quarters at least, that a reversion to a more traditional model of ownership and control is

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underway, albeit with foreign billionaires rather than local merchants, builders and factory-owners assuming the status of English football’s latest and most prolific financial benefactors. Notes 1 There were fewer opportunities to win a European trophy after the cancellation of the Cup Winners’ Cup in 1999. However, the English clubs’ haul of three trophies during the 2000s looks especially meagre in comparison with the 1970s (nine trophies) and the 1980s (seven up to and including the 1985 season, after which English teams were banned from European club competition for the rest of the decade). 2 Post-war league entrants from the south were Colchester United (admitted in the 1951 season), Peterborough United (1961), Oxford United (1963), Cambridge United (1971), Wimbledon (1978), Maidstone United (1990), Barnet (1992), Wycombe Wanderers (1994), Cheltenham Town (2000), Yeovil Town (2004) and Dagenham and Redbridge (2008). Entrants from the North and Midlands were Scunthorpe United and Shrewsbury Town (both in the 1951 season), Hereford United (1973), Wigan Athletic (1979), Scarborough (1988), Macclesfield Town (1998), Kidderminster Harriers (2001), Rushden and Diamonds (2002), Boston United (2003) and Morecambe (2008). These lists do not include several clubs that exited and re-entered. 3 For comparative data based on surveys carried out in Britain, France, Spain, Austria and Belgium, see Waddington and Malcolm (1998). 4 In the 2006 season a fifth English club, Everton, also participated in the Champions League. 5 First-degree price discrimination, which is rarely encountered in practice, would involve charging a price for each ticket that would depend upon both the identity of the spectator and the total number of tickets purchased. 6 Solberg and Taylor (2010) examine the lucrative and rapidly-growing market in exported broadcast rights to foreign countries. 7 Technically these deals were not true sale-and-leaseback arrangements, because under Football Association regulations the club was required to retain the ownership of the ­player’s registration. 8 The Premier League, in which fewer matches are played per club per season, imposes a ­nine-point penalty.

7

Determinants of professional footballers’ salaries

Introduction

Since the early 1960s there has been a series of major institutional reforms to the organisation of the players’ labour market in English football, starting with the abolition of the maximum wage in 1961, and culminating in the 1995 European Court of Justice ruling in the Jean-Marc Bosman case. Some of the broader consequences of these changes are obvious and widely recognised. Spiralling salaries, especially for superstar players, are a consequence of the progressive shift towards freedom-of-contract that has been underway throughout this period. Although the chronology and detail of institutional reform varies between countries, the same long-term trend has been evident worldwide. This chapter examines explanations for the exceptionally high salaries earned by the leading stars in modern-day professional football. Above-inflation increases in players’ salaries, especially at the highest level, have been a permanent feature of English football since the abolition of the maximum wage in the early 1960s. Section 7.1 reports some recent data on footballers’ compensation, and considers to what extent the standard textbook microeconomic theory of wage or salary determination in labour markets is capable of explaining the patterns that are observed. Section 7.2 argues that scarcity in the supply of the highest talent can only form part of the explanation. Before the introduction of pay-TV, football reached large TV audiences but could not appropriate the full economic value of the service provided to individual audience members. Since the late 1980s, however, this situation has been transformed. The changing composition of effective demand for football has played a central role in creating the explosion in both ­revenue and salaries in football (and several other sports) in recent years. Salary inflation at the aggregate level has been accompanied by rapidly increasing differentials between the earnings of individual football players, even within the same club. Section 7.3 reviews a model of intra-team earnings distributions. To an economist, it seems reasonable to assume that football players, like other economic agents, respond to incentives. If players’ compensation is related to their performance, players will exert more effort and invest in developing their 197

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skills. The payment of extremely high salaries to certain superstar players may be a rational strategy for clubs to adopt, if it provides an incentive structure which maximises effort and investment in skills development by all players, especially in the early stages of their careers. According to the rank-order tournament model, the margin of performance between players determines their rank in a hierarchy of remuneration, but it does not determine the margin of compensation. Players’ salaries at any point in time therefore do not necessarily reflect directly their individual contribution to the club’s revenue-earning capability at the same time. Empirical evidence on levels of football players’ compensation is rather thin on the ground, due to restrictions on disclosure. In several North American sports, in contrast, there is sufficient disclosure to permit empirical investigation of the determinants of salaries at the micro level. Section 7.4 reviews some recent European evidence on the determinants of footballers’ salaries, and provides a brief treatment of the North American literature. 7.1  The compensation of professional footballers

Both the levels and the rapid growth of earnings of the top professional football players are issues of occasional public concern or irritation. According to estimates reported by Deloitte (2009), for the 2008 season the total wages and salaries bill of the twenty English Premier League clubs was £1.196 billion: a figure that represents an increase of 290 per cent on the 1998 season figure of £305 million. In the 2008 season, three clubs (Chelsea, Manchester United and Arsenal) each reported a total payroll in excess of £100 million. Table 7.1 reports data from the most authoritative survey of individual Premier League and Football League footballers’ salaries, compiled by The Independent newspaper in 2000 and 2006. For the 2006 season, the average reported Premier League footballer’s salary was £676,000. Of course, this average figure masks large differences between youth- and reserve-team players on the one hand and the top star players on the other. The average reported earnings in The Independent survey do not include performance-related bonuses, which typically increase a player’s earnings by between 60 and 100 per cent. Neither do they include the top players’ earnings outside football, from sources such as advertising and sponsorship. Various unofficial listings of the world’s highest-earning footballers, taking account of all sources of income, can readily be found on the Internet. According to one such list, Lionel Messi (Barcelona and Argentina) was the world’s most highly remunerated footballer in 2009, with total reported earnings of £29.5 million. David Beckham (LA Galaxy and England, £27.2 million) and Christiano Ronaldo (Real Madrid and Portugal, £26.8 million) were placed second and third. In seventh and ninth places respectively, Carlos Tevez (Manchester City and Argentina, £13.7 million) and Frank Lampard (Chelsea and England, £12.6 million) were the two highest-placed players employed at the time by English Premier League clubs.

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Table 7.1 Average basic footballer’s salary by tier, English League, 2000 and 2006 seasons, £ T1

T2

T3

T4

2000 season All players

409,000

128,000

54,600

38,800

2006 season All players

676,000

195,750

67,850

49,600

Age: 17–18 19–20 21–22 23–24 25–26 27–28 29–30 31–32 33+

24,500 95,000 139,000 582,500 653,000 899,500 806,000 586,000 660,500

22,500 43,700 79,000 79,200 136,000 261,850 247,000 247,000 195,700

— 18,950 52,000 61,650 67,600 71,750 69,300 87,000 72,000

— 16,000 32,350 43,650 46,300 47,300 50,500 45,800 49,600

Position: Goalkeeper Defender Midfield Forward

533,000 653,000 754,000 806,000

179,500 167,000 185,950 292,900

53,500 61,000 79,000 75,000

45,900 44,400 46,800 67,900

Source: The Independent

Public concern about football players’ earnings tends to have two dimensions: one relating to the implications for the competitive and financial structure of football itself; and one questioning the appropriateness, or even the morality, of such disproportionately high rewards accruing to participants in what is seen as an essentially frivolous occupation. The first of these areas is considered elsewhere in this volume (see, especially, Chapters 2 and 6). The second is the principal ­subject of this section. Even allowing for the fact that career durations at the highest level in professional sports are often brief, is it appropriate that the leading professional sports stars achieve earnings so obviously disproportionate to those of other occupational groups, including doctors, nurses, teachers and police officers? To most observers, of course, the contributions of these latter groups to society’s well-being appear much more important than those of even the most popular sports personalities. Without necessarily attempting to resolve the moral debate to everyone’s satisfaction, economists can perhaps make a significant contribution to the discussion, by proposing explanations for observed patterns of professional sports stars’ earnings that are grounded in axioms of rational, optimising behaviour on the part of players and the clubs that employ them. Two of the most influential theoretical

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contributions, written by economists during the early 1980s (Lazear and Rosen, 1981; Rosen, 1981), are reviewed in the following two sections. One way to approach the subject of sports stars’ salary determination is simply to consider the market for football players in the same way as any other labour market, by analysing the interaction between the supply and demand for players. Market mechanisms allocate players to clubs by matching bids and offers for the players’ services. If clubs seek to maximise profits, the highest salary a club is prepared to offer a player is the amount he would add to the club’s revenue if he were signed: his Marginal Revenue Product (MRP). If the player is paid more than his MRP, the club’s profit is lower than it is if it does not sign the player. If the club can get away with paying the player less than his MRP, the club’s profit is higher than it is if it does not sign the player. The question as to whether a player is paid his MRP depends partly on the institutional characteristics of the players’ labour market. Under a reserve clause (see Chapter 1), players do not generally receive salaries equal to their MRP. Because the player can only negotiate with the club that owns his contract, effectively there is only one bidder for the player’s services, and the market structure is monopsonistic. The player’s reservation wage is the next highest salary he can achieve in alternative employment outside the sport. Provided the salary on offer is equal to or higher than the reservation wage, the theoretical models predict that the player will accept this salary offer. Salaries tend to be held down, therefore, to the extent that the players’ compensation may only capture a small proportion of the clubs’ total revenues. In contrast, under free agency each player is expected to play for the club for which he has the highest MRP; in other words, the club to which he is most valuable. His salary should lie between his MRP with that club and the next highest MRP that would be attainable if he were to sign for another club. The club to which the player is most valuable can outbid other clubs for his services, and still increase its profit by signing him. The theoretical models predict that under free agency, each player should capture at least his MRP with the club that would place the second-highest value upon him out of all clubs in the league. Salaries tend to be bid up to the point where most of the clubs’ revenues are absorbed by players’ compensation (Quirk and Fort, 1992). One possible objection to this type of analysis when applied to football clubs arises from its reliance on the profit-maximisation assumption. As seen in Chapter 1, Sloane (1971) argues that it is more appropriate to model the club’s objectives using a utility-maximising framework. Football clubs seek to maximise utility, subject to a financial solvency constraint. Arguments in the utility function include playing success, attendance and profit. In this case, even under a reserve clause, clubs that attach high value to playing success relative to profit may choose to sign players for salaries higher than their MRP, in an attempt to increase playing success even though it is not profitable to do so. Nevertheless, departures on the part of some clubs from profit maximisation do not seem likely to account for the highly skewed patterns observed in

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the distributions of sports stars’ earnings. If the earnings of star players are to be explained using marginal productivity theory within a traditional supply-anddemand framework, it therefore seems necessary to confront head-on the question of whether the MRPs of leading football players could conceivably be so high as to justify annual salaries of several million pounds. 7.2  The economics of superstars

Rosen (1981) provides an influential explanation as to how not only sports stars, but also superstars in other fields such as acting, publishing and music can indeed generate extremely high MRPs when they reach the pinnacle of their respective professions. Although Rosen’s analysis is presented in terms of professionals selling their services directly to the public, many of the insights are relevant at a general level in the case of professional team sports, in which individual sellers contract with one another (or with a club) to form a team before their services are sold collectively to the public. It is important to note at the outset, however, that when the superstars model is applied to team sports, a further set of complexities that arise in explaining intra-team earnings distributions are not addressed. This theme will be pursued in the next section. Rosen’s objective is to explain not only the highly skewed distribution of earnings within certain professions, but also the unusually high levels of seller concentration that appear to coexist with skewed earnings. In other words it is important to explain not only the high levels of earnings, but also why employment in the fields concerned often tends to be restricted to relatively small numbers of individuals. According to figures reported by Deloitte (2009), for the 2008 season the annual turnover of English Premier League and Football League clubs was slightly less than £2.5 billion; but only slightly more than 3,000 professionals were employed in the clubs’ core activity of playing football. Rosen’s account of these phenomena rests on two key aspects of consumer tastes and production technology, as follows: • Imperfect substitution between sellers of certain services. The very best talent is in scarce supply. For consumers lesser talent is not perfectly substitutable for greater talent, even if there is compensation in terms of quantity. For example, Manchester United might be three times more talented than Birmingham City, but watching Birmingham City on three occasions is not equivalent to watching Manchester United once. • Scale economies in joint consumption of certain services. The technology of production enables very large audiences to be serviced at the same time. The effort and therefore the production costs incurred by Manchester United’s players are much the same if they are playing in a half-empty stadium, or in front of a capacity crowd, or additionally before a large TV audience. The technology, in other words, has characteristics similar to that employed to supply certain

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public goods like street lighting and national defence: production costs depend only slightly, or not at all, on the number of people consuming the service. But in contrast to these examples, in football there are no free-rider problems preventing the seller from appropriating a charge for providing the service. Would-be audience members who are unwilling to pay (by purchasing a match ticket or a pay-TV subscription) can easily be excluded from consumption. The implications of these attributes of tastes and technology for the distribution of earnings and employment opportunities depend on the precise nature of the relationship between production costs and audience size. Rosen suggests two reasons why marginal costs of production may eventually start to increase as the audience size increases. First, internal diseconomies include all the usual reasons why marginal costs rise as output increases. In professional football, marginal costs start to rise when players become tired or injured as the number of matches played increases, or perhaps as a result of increased stress or psychological pressure in matches played before a large audience. Second, external diseconomies are factors that reduce the quality of the product as the audience size increases. A stadium with a capacity of 50,000, for example, might provide a better viewing experience than one twice that size, due to excessive distance from the pitch in the latter case. Beyond the stadium capacity, the TV audience consumes a product that is presumably inferior to that obtained by ‘live’ spectators, though one whose characteristics do not vary further as the TV audience size increases. Rosen demonstrates first that imperfect substitution between sellers, combined with internal diseconomies, induces a skewed distribution of earnings, even if there are no joint consumption economies. The more talented sellers charge each consumer a higher price and capture a larger share of the market than their less talented counterparts. But in the absence of joint consumption economies, talent differentials do not lead to extremely high seller concentration: all sellers are able to capture some market share. Under certain simplifying assumptions, both the price paid by each consumer and each seller’s audience share can be shown to be linear functions of the seller’s talent. This implies that sellers’ total earnings, the product of price and audience, are quadratic in talent. The distribution of earnings is therefore more skewed than the distribution of talent. To account for high seller concentration as well as a skewed earnings distribution, joint consumption economies are also required in the model. Suppose initially that there are no internal or external diseconomies at all, so joint consumption economies are not limited by the size of the audience. In other words, the audience size can be expanded indefinitely, without imposing additional costs upon the seller, and without causing any deterioration in the quality of the ­product obtained by the consumer. In this extreme case, the market has the characteristics of a natural monopoly. The most talented seller is able to drive all other sellers out of business, and in the long run services the entire market. The ­equilibrium price, however, is constrained by the threat of entry. The rent element

The economics of superstars

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in the equilibrium price, which is proportional to the talent differential between the most and second-most talented sellers, is modest. Crucially, the total rent obtained by the most talented seller is substantial, because the latter captures the entire audience. As Rosen and Sanderson (2001) observe, superstars achieve high earnings by operating at high volume (by servicing very large audiences) but at low margins (by charging each audience member only a modest mark-up relative to less talented suppliers). The ‘zero diseconomies’ case described above is somewhat unrealistic, but useful because it illustrates the main insight of the Rosen model. The most talented seller captures the entire market because the production technology permits limitless expansion of the audience at zero cost to the seller. This is in stark contrast to the experience of doctors, nurses, teachers and police officers, who find that the number of patients they can treat, schoolchildren they can teach and criminals they can catch on any one day is strictly finite. The key to the high earnings of superstars, in other words, lies in the vast extent of the audience they can reach at any one time, afforded by the existence of scale economies in joint consumption (Rosen and Sanderson, 2001). In practice, of course, one football team does not dominate the entire market. The Rosen model suggests that this is not solely due to considerations of jointness in production or concerns over competitive inequality (see Chapters 1 and 2). It is also to be expected if joint scale economies in consumption are eventually limited by internal or external diseconomies of the kind described above. In this case several sellers obtain market shares in long-run equilibrium. The price each seller charges is constrained by the (actual not potential) presence in the market of other sellers with less talent, and the rent element in the price is dependent on the talent differential. If the rate at which internal or external diseconomies increase varies inversely with talent, audience share and price both increase with talent, but audience share increases at a faster rate than does price. As before the high earnings of the most talented sellers derive principally from the vast size of their audiences, rather than from the modest price differential paid by each audience member. An extension of Rosen’s superstars model is discussed by MacDonald (1988), who considers the career progression of performers who eventually become superstars in their fields, despite the fact that in the early stages of their careers they may have imperfect information about their future performance and future earnings. Aspiring stars enter the profession at a young age and perform cheaply. The audience feedback they receive provides useful but incomplete information about their probable future performance. Those who receive negative feedback are persuaded to withdraw from the profession. Those who receive positive feedback are encouraged to continue, and as the favourable notices accumulate their audience rapidly expands. So too do their earnings, and as in the Rosen model at a faster rate than the talent gradient would suggest. Although MacDonald seems to have in mind primarily groups such as actors or musicians, the notion of a football apprenticeship as an information-gathering process, enabling individuals to take

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rational decisions at various stages as to whether to continue in pursuit of a career as a professional, seems an appropriate description of the path followed by many youngsters, including the majority that eventually do not make the grade as professionals. In summary, the contrast between the configurations of high earnings-low utility achieved by sports stars, and low earnings-high utility achieved by groups such as nurses and teachers is explained mainly by the technologies under which the former operate, which enable them to provide services, albeit of modest value, to very large audiences. The latter groups provide services of much higher value, but to a strictly finite number of users. The same technological conditions explain the high levels of seller concentration found in professional sports. Internal and external diseconomies of scale, however, impose limits on the audience share of the most talented sellers, enabling the less talented to capture some share of the market. The road from apprenticeship to stardom can be viewed as a type of sequential information-gathering process, in which cumulative feedback on performance enables the individual to take rational decisions on whether to continue or withdraw from the profession. Rosen’s essentially technological explanation for the high earnings of superstars is clearly relevant in explaining salary inflation in professional football during the 1990s and 2000s. Before the arrival of pay-TV (see Chapter 6, Section 6.5), English football reached large TV audiences via free-to-air services provided by the BBC and ITV. Constrained by this type of ‘public goods’ production technology, football was unable to appropriate the full economic price for providing the service to individual audience members. Since the early 1990s, technological innovation in broadcasting has transformed this situation. With further moves in the direction of free agency taking place simultaneously in the footballers’ labour market (see Chapter 6, Section 6.6), the leading players’ bargaining position in salary negotiations was strengthened immeasurably. The players were able to capture a large proportion of the rent element in the additional broadcast (and other) revenues, resulting in rampant salary inflation. 7.3  Rank-order tournaments and intra-team earnings distributions

As noted previously, Rosen’s insights on the economics of superstars do not address the complexities of intra-team earnings distributions. At first sight, these can seem as puzzling as the disparities between the earnings of sports stars in general and those of other groups. In the English Premier League, for example, the top players can earn many times more than the average first-team player, even though it seems doubtful whether this differential could be explained by a corresponding differential in MRP. In a competitive labour market, the intra-team salary structure is equivalent to a piece-rate system, since each player receives a salary equivalent to his MRP. Differences in salaries between players in the same club should reflect the fact

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that those contributing most to club revenues get paid the most. Casual observation, however, suggests that some players receive large salary increases even when there is no noticeable improvement in performance. Often, players who might be judged only a small fraction better than others appear to earn significantly more. In these cases, the intra-team salary structure seems to be hierarchical. The models outlined above are unable to explain why top stars can earn ‘n’ times more than other players, if the talent gradient is shallower than ‘n’, and if their contribution to revenue is not ‘n’ times as high. In a highly influential paper on the determination of executive salaries in corporate business, Lazear and Rosen (1981) argue by analogy that top executives’ high salaries are equivalent to the outcome of a rank-order tournament. In situations where it is costly to monitor or measure exactly the productivity of individual workers, it may be efficient for firms to rank workers according to their productivity, and reward them according to their rankings. In the corporate sector, the salaries of vice-presidents are typically much lower than those of presidents. Yet presidents are often promoted from the ranks of vice-presidents. On the particular day an individual is promoted, his salary might triple, but it is difficult to argue that his productivity has also suddenly increased by an equivalent amount. According to the Lazear and Rosen model, the individual who achieves promotion to president is like the winner of a contest for which there is a very large first prize. The president’s salary does not reflect his or her current productivity, but it does induce all junior employees (from the rank of vice-president downwards) to perform appropriately, in the hope that one day they too will win the prize and achieve promotion to president. In other words, the president earns a high salary not because he is highly productive as president, but because this type of salary structure provides incentives for all employees to be more productive throughout their entire working lives. Scully (1995) adapts this type of analysis in order to examine player salary determination in several North American sports. It is worth noting that in contrast to the situation in the corporate sector, the productivity of each player or ‘worker’ is relatively easy to measure (baseball being perhaps the most obvious case in point). Both the employer and the customer observe the joint output of the team, and have ample opportunity to form their own subjective assessments of the individual contributions of each team member. With reference to English football, this relationship is aptly described as follows: The first team player faces over forty public examinations a year before an attendance of thousands of spectators. He will be talked about, shouted at, criticised or praised, given extensive coverage in the press and radio … he is in the limelight and must be seen to behave as befits his profession. (PEP, 1966, p134)

Even so, professional team sports players do not appear to be paid on a piecerate basis. Scully argues that the rank-order tournament model may provide a

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more convincing explanation of compensation scales than the traditional supplyand-demand model. Clubs that are motivated either by playing success or by profit need players to develop their skills to their maximum potential, and to exert the maximum effort on behalf of the team. A compensation structure in which salaries depend upon each player’s ranking relative to others within the same club provides incentives for all players to compete (effectively against one another) in pursuit of these aims. Even in sports such as football, where there is high input complementarity and individual outputs are less easily identified, the rank-order tournament model may still be applicable. Historically, there were no restrictions on the number of players an English League club could register. Under proposals announced during the 2010 season for implementation at the start of the 2011 season, however, premier league clubs are subject to a maximum first-team squad size of 25 players, of which no more than 17 can be over the age of 21 and not home-grown (trained before the age of 21 in England or Wales). Each club’s first-team squad players compete against one another for a place in the team. At the start of each game the manager selects one goalkeeper, ten outfield players and up to seven substitutes, three of whom can be used to replace any of the eleven players on the field of play at any time during the game, either for tactical reasons or because of injury. The numbers of defenders, midfield players and forwards among the outfield players depends upon the tactical choices of the manager. Typical formations include 4 –3–3 (four defenders, three midfielders and three forwards), 4 – 4 –2, 5–3–2, 3–5–2 and 4 –5–1. For each playing position, the squad will include several players who can provide cover. Especially useful in this respect are utility players, able to play in more than one outfield position. Performance is related to athletic endowment such as speed, strength, agility, balance and coordination; intangible attributes of talent such as determination and concentration; and player and team investments in enhancing skill through coaching, tactical awareness and practice at passing, shooting, heading and tackling. Theoretical and empirical models of rank-order tournaments have been applied extensively to individual sports such as tennis and golf. Competitors face a fixed prize structure and achieve the next higher reward by moving up by one place in the ranking of competitors. Scully argues, however, that competition among sports players for a first-team place is not entirely dissimilar. Those in the first team are always threatened explicitly by the performance of lower-ranked reserve players, and implicitly by the possibility that the club might sign a replacement player for the same position from outside. If a first-team player experiences a slump in form, a reserve is substituted into the team or the club acquires a new player. Injury or suspension for disciplinary transgressions can also lead to the replacement of one player by another. A replacement who performs well can often capture a first-team place, until he in turn eventually drops out due to loss of form, injury or suspension. The rest of this subsection contains an exposition of the rank-order tournament model using mathematical notation. Apart from minor changes of notation, the

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model is as presented by Scully (1995). It is assumed that two players (i = 1,2) are competing for one first-team place. The performance of player i, denoted Qi, is determined by his athletic endowment and his investment in playing skill, denoted ti, plus a number of exogenous factors that affect performance randomly, denoted εi. Random factors include temporary fluctuations in form, fitness and fortune. The probability that player 1 defeats player 2 as part of the contest for a first-team place, denoted p, is the probability that player 1’s performance exceeds that of player 2: p = prob(Q1 > Q2 ) = prob(t1 − t 2 > ε 2 − ε1 ) = 1 − F(t1 − t 2 ) 

[7.1]

where Qi = ti + εi for i = 1,2; E(ε2 – ε1) = 0; and F( ) is the cumulative distribution function of ε2 – ε1. The intra-team salary structure pays SF to the first-choice player and SR to the reserve player, with SF > SR. The expected salaries of the two players, S1 and S2, are determined by the probability that player 1 beats player 2 for the first-team place (p) and the salaries for the two positions (SF, SR): S1 = pSF + (1 − p)SR ;

S2 = (1 − p)SF + pSR 

[7.2]

Players can improve their skills by means of investment. Because some attributes of playing talent are natural, the cost of investment, Ci(ti), is assumed to vary between players. It is assumed that the marginal cost of investment in further skill increases ∂C i with the level of skill already acquired, so > 0 ; and that marginal cost increases ∂t i ∂2 C i at a faster rate as the level of skill increases, so > 0 . If player 1 has more natural ∂t i 2 ability than player 2, player 1’s marginal cost of further investment in playing skill ∂C1 ∂C 2 (starting at any given level of skill) is lower than that of player 2, so . < ∂t 2 ∂t1 Players are assumed to invest in the development of playing skills to maximise expected net income, EYi = Si – Ci(ti). The first-order conditions are: ∂EYi = (SF − SR )f(t1 − t 2 ) − C i′ (t i ) = 0 ∂t i

(for i = 1,2) 

[7.3]

where f = F′ is the probability density function of ε2 – ε1. Equation [7.3] provides the Cournot-Nash solution for each player’s level of investment in skill (based on the assumption that the investment of the competitor is fixed at its current level) in terms of the salary levels, SF and SR. The equilibrium is illustrated in Figure 7.1. ∂C1 ∂C 2 . If the Player 1 has more natural ability than player 2, so MC1 = < MC 2 = ∂t1 ∂t 2 salary differential is (SF – SR)1, t*1 and t*2 represent the optimal investments in playing talent for each player. The greater the level of playing skill at the club’s disposal, the more valuable is each match to the club. By varying the intra-team salary structure (SF, SR), the

Determinants of professional footballers’ salaries MC2

Marginal cost and benefit to players of investment in talent

208

0

MC1

(SF − SR )1f ( t1* − t *2 )

(SF − SR )1f ( t1** − t *2* )

t *2*

t *2

t1**

t1*

t1, t2

Figure 7.1  Optimum investment in playing talent, rank-order tournament model

club can influence the level of investment by both players in their playing skills. Increased player investment adds to the value of the club’s matches, but there are lower and upper bounds to the range within which the club can vary the salaries. First, SR has a lower bound because player 2 has the option to earn a living outside the sport. If player 2’s potential earnings outside the sport are C8, this constraint implies that the lower bound of player 2’s expected earnings is equal to outside earnings plus player 2’s cost of investment in playing skill: (1 − p)SF + pSR = C 2 (t 2 ) + C 

[7.4]

Second, assuming that the club has a financial constraint which prohibits it from making a loss, there is an upper bound to the total salary bill, equal to the club’s total revenue. Scully simplifies the derivation of the equilibrium intra-team salary structure by introducing a parameter c (0 < c ≤ 1) to reflect the degree of competitiveness in the players’ labour market. c is the total salary bill expressed as a proportion of total revenue, as follows: SF + SR = cTR 

[7.5]

At the maximum value of c = 1, the players’ salaries capture all of the club’s revenue. This would apply with free agency in the players’ labour market, so the players’ bargaining power is maximised.1 The distance by which c falls below one is a measure of the degree of monopsony power held by the club as a buyer of players. Equations [7.4] and [7.5] can be used to derive the following expressions for the salary levels, SF and SR: SF = cTR[p/(2p − 1)] − [(C 2 (t 2 ) + C)/(2p − 1)] SR = [(C 2 (t 2 ) + C)/(2p − 1)] − cTR[(1 − p)/(2p − 1]

[7.6]

Determinants of players’ compensation

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Scully points out two key implications of the model: • The greater the degree of monopsony power in the players’ labour market, the narrower is the intra-team salary structure. This follows directly from [7.6], because SF – SR = cTR/(2p – 1). Conversely, a move towards free agency should increase the differential between the salaries of the top players and the rest. • A reduction in the differential between SF and SR reduces the level of investment in playing skills by both players, and narrows the differential in playing skills between the first-team and the reserve-team player. This is illustrated by ** the move from (t*1, t*2) to (t** 1 , t2 ) in Figure 7.1. Conversely, a move towards free agency should increase the level of investment in playing skills generally, and increase the differential between the playing skills of the top players and the rest. Clearly, the rank-order tournament model of salary determination generates a number of propositions that are relevant in the case of English football. In contrast to the traditional supply-and-demand model, the rank-order tournament model is capable of decoupling players’ salaries from their MRPs, thereby explaining highly unequal and hierarchical intra-team salary distributions. The model also predicts that moves towards free agency should lead to a widening of the gap in compensation between top players and the rest, and should lead to an increase in investment in playing skills all round. There is no doubt that the former has occurred in English football since movement towards free agency first started in the early 1960s. The latter is more difficult to verify conclusively, but there is overwhelming anecdotal evidence: video footage suggests, and most commentators agree, that modern-day players are much fitter, faster and stronger than their counterparts from earlier eras.2 7.4  Determinants of players’ compensation: empirical evidence Football players’ salaries

Empirical evidence on the factors that determine players’ salaries in European professional football is sparse, because individual players’ compensation details are considered confidential and are generally not disclosed. Reilly and Witt (2007) examine salary determination in North American Major League Soccer (MLS), using data for 361 players obtained from the MLS Players Union on base salaries prior to the start of the 2007 season, excluding bonuses and endorsements. A salary regression is estimated, with player characteristics, performance measures and team effects used as explanatory variables. Player characteristics variables include age, playing position, time at the current club, whether or not the player is a US citizen, and a player’s racial group. Racial group is determined by inspecting colour photographs; players are designated as ‘white’, ‘black’, or ‘mixed race’. Performance variables include the number of prior seasons in MLS, number of MLS games started in the previous season, number of MLS

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games as substitute in the previous season, and dummy variables for whether or not the player has international caps and whether or not the player has played in European professional football. In ordinary least squares (OLS) regressions, around two-thirds of the total variation in base pay is explained. The results show that playing experience (number of consecutive MLS seasons) is a more important determinant of salary than length of time at the current club. Experience of playing in European leagues produces an average mark-up of 70 per cent compared to a player without such experience. An international player obtains a mark-up of 67 per cent and strikers are more highly rewarded than players in other positions. Coefficients on the race dummies are insignificant. Similar results are obtained from quantile regressions for median salary. Using 2008 season data on 193 players, Kuethe and Motamed (2010) also examine the determinants of salaries in MLS. Superstar status is indicated by a ‘designated player’ dummy variable. In a concerted effort to recruit star players, MLS awarded to each team in 2007 a single designated player slot, which is not constrained by the league’s salary cap (known colloquially as the ‘David Beckham Rule’). Designated players can be traded, but no team can have more than two. Data on the salaries of individual players are published annually by the MLS Players Union. Age and experience are significant in salary regressions estimated using OLS, but performance measures are insignificant. The effect of country of origin dummy variables is weak, but the designated player dummy variable is highly significant, yielding a 928 per cent salary premium. In quantile regressions for percentiles towards the upper end of the salary distribution, designated player status yields a similar premium, while several performance measures are significant. For European football, several researchers have used sources that offer market valuations of players as a proxy for undisclosed salaries. Several studies have used valuations of German Bundesliga players obtained from the Kicker football magazine.3 The use of transfer market valuations data as a proxy for players’ salaries has been justified on the basis that in cases where the actual salary is known, the correlation between the actual salary and the published valuation is high. The Kicker player valuations are compiled by a stable panel of experts, who have established consistent practice over a period of years. There is a close correspondence between the aggregated valuations divided by a constant factor, and the aggregate salary expenditure for the top tier of the Bundesliga (Frick, 2003; Torgler, Schmidt and Frey, 2006). As in North American studies based on actual salary data, regressions are estimated in which the player’s valuation is assumed to depend on experience, performance and team characteristics. Lehmann and Schulze (2008) use Kicker player valuations data from the 1999 and 2000 seasons for 651 German Bundesliga players. Recognising the skewness in the distribution of valuations, the authors report quantile regressions in order to identify the determinants of the valuations at different points in the distribution.

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Performance measures, especially goal scoring and assists, are significant. The signs and magnitudes of some coefficients differ between different points in the distribution, validating the use of quantile regression. Media presence has a positive influence on valuations which diminishes over time, suggesting decreasing returns to popularity. This finding appears contrary to the hypothesis of a superstar effect. Battré, Deutscher and Frick (2009) use a German Bundesliga data set with Kicker player valuations, comprising 6,147 player-year observations for 1,993 different players over 13 seasons from 1996 to 2008. Performance measures include matches played, goals scored and international caps, recorded for the player’s entire career to date and for the most recent season. Other explanatory variables include age, a team captain dummy, playing position dummies and team-specific variables. Most of the explanatory variables are significant in OLS, random effects and quantile regressions, with the most recent performance indicators being far more important than entire-career indicators. The results support the hypothesis of a superstar effect. Bryson, Frick and Simmons (2009) examine the impact of two-footedness on player valuations. Most players are predominantly right-footed or left-footed, but some are considered equally effective with both feet. Two-footedness may enhance a player’s valuation for two reasons:  first, the player’s performance might be enhanced directly; and second, a two-footed player may be more versatile because he can play in several positions.4 OLS and quantile regressions indicate a premium for two-footedness, estimated at 15.4 per cent for the European cross-section and 13.2 per cent for the Bundesliga panel. The focus of the study by Ashworth and Heyndels (2007) is the relationship between month of birth and Kicker player valuations in the German Bundesliga. Professional footballers born after the cut-off date used to define each age group have higher valuations due to a selection effect:  survivors are revealed to be of above-average talent because they have overcome the tendency of the scouting system to discriminate against them; and they have benefited from a superior football education that requires them to compete with older (and therefore physically stronger) players. Estimation results show clear evidence of a month-of-birth­related bias: players born late in the year, after the cut-off date of 1 August, are valued more highly on average. The impact of the month of birth varies with playing position: the premium for being born late is highest for goalkeepers and defenders, and is absent for forwards. Lucifora and Simmons (2003) use 1995 data on Italian footballers to estimate an equation for salaries in which performance variables play a key role. Pre-season salary data on 533 outfield players, gross of tax, but net of bonuses and signing-on fees, is obtained from an annex to the newspaper Il Giornale published on 15 March 1996. Salaries are explained by experience (including age and number of appearances over the entire career and for the most recent season), performance (goal scoring and assists), reputation (international appearances)

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and team-specific variables. Most of the explanatory variables have a significant influence on salaries. A key finding is that salaries are highly convex in goalscoring rate and assists, consistent with a superstar effect generated by spectator enthusiasm for attacking play. Using 2007 data, Christiansen and Sievertsen (2008) also find evidence of a superstar effect in Italian football. Salary data on 444 players is obtained from La Gazzetta dello Sport. Explanatory variables in the salary equation include age, experience (minutes played in the current and previous seasons, and international caps), performance (goals scored, shots, assists, tackles and passes, all for the current and previous seasons), and team-specific variables. The average relationship between age and players’ salaries is non-linear, with a turning point at age twenty-four. International experience has a positive impact on salaries, and experience for national teams other than Italy has a larger effect. The results also show a positive superstar premium in salaries, of almost 70 per cent. Several performance criteria are used to identify superstars. In comparison, the estimated effect on the salary of scoring an extra goal per match over an entire season is around 67 per cent. Salaries in North American major league sports

For North American major league sports other than MLS, numerous studies have examined the determinants of player salaries, as well as closely related topics such as player exploitation and racial discrimination. One of the first and most influential studies in this literature is Scully (1974), in which a framework is developed for drawing comparisons between estimated MRPs for different categories of player in MLB, and the average salaries of players in the same categories. Scully’s study dates from the pre-free agency period when the reserve clause was still effective, so systematic divergence between salaries and MRPs is expected. Scully obtains estimated marginal productivities for baseball hitters and pitchers using the slope coefficients in a regression of team win ratios on team slugging averages (for hitters) and team strikeout-to-walk ratios (for pitchers). Dummy variables are also included in the regression to control for differences between the NL and the AL, and to differentiate teams according to the extent to which they were in contention to be divisional winners in the season concerned. Gross MRPs for hitters and for pitchers are imputed by multiplying the marginal productivity estimates by the slope coefficient obtained from a second regression of team revenues on win ratios. Various additional controls used in the second regression include an NL–AL dummy, home-town population and a variable reflecting underlying differences between teams in intensity of support. Net MRPs are calculated by deducting allowances for player training and other factor costs from the gross MRPs. Scully then estimates salary equations for hitters and pitchers, using individual data. Among the explanatory variables are personal career slugging averages and

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213

strikeout-to-walk ratios, career durations, and variables (such as population and intensity of support) that are also used in the revenue regression to control for demand factors contributing to monopoly rent. The latter are mainly insignificant in the salaries regressions, suggesting that the players failed to capture any share of the monopoly rents under the reserve clause. The comparisons between MRPs and salaries are drawn by substituting sets of explanatory variables describing representative hitters and pitchers of mediocre, average and star quality into the various estimated equations. The MRP-talent gradient is much steeper than the salary-talent gradient. Consequently, while mediocre players earned more than their net MRPs, the salaries of average players and star players were only around 20 per cent and 15 per cent of their net MRPs, respectively. This suggests there was substantial monopsony exploitation of players before free agency. Following Scully’s pioneering work, numerous authors have used the model as a benchmark for examining exploitation in North American sports (see, for example, Medoff, 1976; Raimondo, 1983; Zimbalist, 1992; MacDonald and Reynolds, 1994; Gustafson and Hadley, 1995; Krautmann, 1999; Mullin and Dunn, 2002). Pelnar (2007, chapter 6) reviews the post-Scully literature on exploitation. Using an empirical framework similar to that employed by Scully twenty years earlier, MacDonald and Reynolds (1994) use data on player performance and earnings in MLB in the 1987 season to show that following the introduction of free agency, players’ salaries matched their estimated career MRP more closely than they did during the pre-free agency period. There were still some anomalies, however. Young players were paid less than their MRP, perhaps due to institutional restrictions on their mobility within the labour market, and senior pitchers (but not senior hitters) were overpaid. MacDonald and Reynolds also present evidence that differences between the salaries of top- and middle-rank players are consistent with Rosen’s model of superstars. Scully (1995) uses data on the individual performance and salaries of baseball and basketball players before and after the introduction of free agency in both sports, to examine the impact of this change. It is clear that the salary-talent gradient became steeper during the free agency period, and for both sports the sensitivity of salaries to performance in the current season and to measures of past experience (included in the regressions to control for talent, investment and effort) is higher than it was before free agency. For baseball, an average individual performance index exceeds an average individual salary index for up to 547 career games; thereafter, the salary index exceeds the performance index. This finding seems consistent with the time-profile of salaries predicted by the rank-order tournament model. For the pre-free agency period, in contrast, the salary index is higher than the performance index for both inexperienced players (less than 405 games) and players nearing the end of their careers (1,550 games). Some empirical research has suggested that there are limits to the applicability of the rank-order tournament model to team sports. An intra-team salary distribution that is too unequal may be divisive, perhaps damaging team cohesion and

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Determinants of professional footballers’ salaries

spirit to an extent that outweighs the incentive benefit described above. It is certainly common enough for English football clubs to explain failure to reach agreement with a player they are seeking to sign in terms of a reluctance or refusal to overturn established internal remuneration structures. Richards and Guell (1998) argue on similar lines that a high intra-team variance in salaries may have a negative effect on performance, since it implies a dispersed level of talent and an inability to function at a high level as a team. One or two star players do not necessarily carry an entire team. In their empirical results for MLB over the period 1992–5, the mean salary has a positive effect on the win ratio and the propensity to win championships, but an increase in the variance of salaries reduces the win ratio (with a coefficient that is significant at the 10 per cent level). A greater dispersion of salaries does not seem to affect the probability of winning the championship, however. Depken (2000) and Jewell and Molina (2003) report further evidence for MLB. Frick, Prinz and Wintelmann (2003) find that a higher degree of dispersion enhances the performance of NBA and NHL teams, but has the reverse effect in the NFL and MLB. Berri and Jewell (2004) fail to find any evidence of a relationship between salary dispersion and team performance in the NBA. Conclusion

Professional footballers’ pay is an issue of occasional public concern, irritation or outrage. By the end of the 2000s, the annual payrolls of the top English clubs were in excess of £100 million per club; while several of the world’s very highestpaid footballers registered total annual earnings of more than £20 million each, taking into account salaries, bonuses, sponsorship and income from other commercial activities. This chapter considers theoretical explanations, put forward by economists, for the exceptional remuneration that is enjoyed by the leading stars in modern-day professional football, and other professional team sports. The theoretical analysis of the economics of superstars addresses the apparent paradox between the high earnings achieved by sports stars whose contribution to society’s well-being is perhaps rather modest (despite the adulation they receive), and the low earnings achieved by groups such as nurses and teachers, whose contribution is far more important. The discrepancy is explained by the fact that especially since the advent of pay-TV, sports stars are capable of servicing very large paying audiences simultaneously, incurring little or no incremental cost as the audience size increases. Nurses and teachers, in contrast, service strictly finite number of users. The potential for high salary inflation in football is therefore created by changes in the level and composition of effective demand, driven in turn by technological change in broadcasting. Meanwhile successive moves towards free agency in the players’ labour market have increased players’ bargaining power in their salary negotiations, enabling them to capture a large proportion of the rent element in the extra revenues that are being generated.

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215

Another feature of sports stars’ compensation is described by the rank-order tournament model, which examines intra-team salary distributions. Clubs have an interest in providing incentives for footballers to maximise investment in their playing skills, and to maximise their level of effort. High performance arises from innate ability and from investment in skills and effort. According to this model, large salary differentials provide all players with the incentive to invest in the development of their skills, in the hope of securing a first-team place and a higher salary. In contrast to the traditional microeconomics textbook supply-anddemand model of the labour market, the rank-order tournament model is capable of decoupling players’ salaries from their MRPs, thereby explaining highly unequal and hierarchical intra-team salary distributions. Notes 1 Implicitly for c = 1, there is also an assumption that the club seeks to maximise revenue or playing success, subject to a zero-profit constraint. 2 It is not at all clear, however, that the best modern-day players are more skilful on average than players of earlier periods. Natural skill is, of course, mainly an endowed rather than an acquired attribute, and is therefore not sensitive to changes in the structure of players’ compensation. 3 German-language studies include Lehmann and Weigand (1999), Lehmann (2000), Huebl and Swieter (2002) and Frick and Deutscher (2009). 4 Data on two-footedness and player valuations at the start of the 2006 season for players in England, France, Germany, Italy and Spain were obtained from the website www.transfermarkt.de. The German sample was supplemented by valuation data from Kicker magazine for several earlier and later seasons.

8 Professional footballers: employment patterns and racial discrimination

Introduction

The previous chapter has examined the topic of footballers’ remuneration. Chapter 8 discusses several other topics concerned with the economics of the professional footballers’ labour market. Section 8.1 presents an analysis of patterns of migration, mobility and career development among English club football’s regular workforce: the players employed by the ninety-two member-clubs of the Premier League and Football League. The coverage of the analysis extends from the mid-1980s to the late 2000s, a period during which the character of English football has been transformed by the arrival of a large contingent of overseas players. During this period there appears to have been a shift in the overall burden of responsibility for the development of young players away from the smaller English clubs towards their larger counterparts; and some sharp regional disparities have emerged in the prospects for locally born youngsters to become professional footballers. Patterns of migration by footballers across national borders reflect a wide range of influences, which are reviewed in Section 8.2. An analysis of the employment profile (by country of employment in club football) is presented for the international footballers who participated in the Finals of the 2000 and 2008 European Championships. Despite the England national team having failed to qualify for the Euro 2008 Finals, the English league was the largest single host-country provider of footballers in these Finals, reflecting England’s recent ascendancy within Europe as an importer of top-level footballers. Section 8.3 reviews empirical evidence on racial discrimination in English football and elsewhere. A bias in the employment of indigenous black footballers in favour of teams of higher divisional status may suggest that a form of hiring discrimination affects the opportunities for indigenous black players of average talent to progress to professional status. It seems likely, however, that any such effect has diminished over time. Possible sources of discrimination include prejudicial attitudes on the part of club chairmen or team managers, a lack of opportunities for youngsters from disadvantaged backgrounds to participate in competitive 216

Employment mobility, migration and career structure

217

football, and geographical variations in the ethnic composition of the population combined with barriers to mobility in the footballers’ labour market. 8.1  Employment mobility, migration and career structure in English football

Section 8.1 presents an analysis of patterns of migration, mobility and career development among English football’s regular workforce:  the players employed by clubs participating at all levels in the Premier League and Football League. The principal data source for the empirical analysis is the retained list, published annually in Sky Sports Football Yearbook (known as Rothmans Football Yearbook prior to 2003). This source provides an annual snapshot of the employment history and current status of all players employed with the ninety-two English league member clubs at an end-of-season (May) census point, enabling career progression to be tracked at the micro (individual player) level. In addition, the comprehensive post-war listing of players’ career records compiled by Hugman (1998) is used to cross-check the data for the earlier years, and to complete some of the early-career details for players whose records would otherwise have been left-censored. Table 8.1 reports the number of players recorded at each end-of-season census point from 1986 to 2009, in total and disaggregated between the four tiers (divisions). Over this period there was a large growth in the numbers of players employed in all four tiers. Total employment increased by 46.0 per cent, and the rates of growth by tier were 55.2 per cent for T1, 55.4 per cent for T2, 38.5 per cent for T3 and 31.9 per cent for T4. Much of the employment growth in the Football League (T2, T3 and T4) took place during the late 1980s, while employment growth in the Premier League (T1) took place mainly during the 1990s. Employment of professional footballers by English clubs peaked between 1999 and 2002. Between 2002 and 2009, total employment fell by around 10 per cent, with most of the decline concentrated on the Football League (T2, T3 and T4). Table 8.2 reports an analysis of changes in the age distribution of professional footballers, based on comparisons drawn at four-year intervals using the 1989, 1993, 1997, 2001, 2005 and 2009 end-of-season censuses. These data suggest that during the 1990s and 2000s there was a shift in the burden of responsibility for youth player development away from clubs in T3 and T4, and towards clubs in T1 and T2. During the mid to late 1990s, much of the growth in employment in T1 was concentrated among footballers in the younger age groups. During the 2000s the trend in the employment share of the under-21 age group in T1 has stabilised (but with some significant year-on-year variation). Over the period 1989–2009 as a whole, the employment share of the under-21 age group fell by 2.6 per cent in T3 and 6.7 per cent in T4. This shift may be related to the introduction of free agency through the Bosman ruling. Despite the existence of safeguards in the form of financial compensation when players below the age of 24 move between clubs, it has become more difficult for lower-tier clubs to realise large windfall financial gains in the transfer market; and it seems likely that the incentive for these clubs

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Footballers’ employment, and racial discrimination

Table 8.1 Employment totals for professional footballers by tier, English League, 1986–2009

1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 % growth, 1986–2009

T1

T2

T3

T4

Total

Mean age

SD age

623 649 613 610 627 679 749 779 779 846 830 825 859 980 937 944 952 958 881 803 815 834 939 967

509 522 574 655 717 721 718 727 792 753 820 812 884 848 910 946 924 848 776 785 771 765 797 791

501 546 579 600 630 634 670 617 634 654 675 688 732 767 804 785 776 728 676 726 715 659 700 694

476 536 585 595 616 626 581 546 622 596 686 691 704 728 741 733 772 687 680 714 686 645 651 628

2109 2253 2351 2460 2590 2660 2718 2669 2828 2849 3011 3016 3179 3323 3392 3408 3424 3221 3013 3028 2987 2903 3087 3080

24.0 23.9 24.1 24.1 24.1 24.2 24.3 24.3 24.5 24.5 24.4 24.4 24.3 24.2 24.2 24.3 24.3 24.4 24.4 24.6 24.4 24.5 24.2 24.2

4.7 4.7 4.8 4.8 4.8 4.8 4.9 4.9 5.0 5.1 5.2 5.2 5.3 5.3 5.4 5.3 5.3 5.3 5.2 5.3 5.3 5.2 5.1 5.0

+55.2

+55.4

+38.5

+31.9

+46.0

Note: SD age denotes standard deviation of footballers’ ages. Source: Rothmans/Sky Sports Football Yearbook

to invest in the training and development of young footballers has been reduced (see Chapter 6, Section 6.6). At the opposite end of the age distribution, between 1989 and 2005 the proportion of professional footballers aged over 32 increased from 5.4 per cent to 9.6 per cent. This increase may reflect the effects of improvements in training regimes and the treatment of injuries, which have enabled more footballers to extend their playing careers into their mid or late 30s. By the end of the 2000s, however, there were signs of a reversal of this trend towards career prolongation. Between 2005 and 2009 the proportion of footballers aged over 32 fell back to 6.6 per cent. Further analysis of professional footballers’ dates of birth reveals a feature of the data that is quite striking, and consistent throughout the observation period. Table 8.3 reports the percentage distribution of all players by month of birth. This reveals that a large majority (around 60 per cent) of professional footballers

Employment mobility, migration and career structure

219

Table 8.2 Percentage distribution of professional footballers in England by age band and tier, English League, selected years T1

T2

T3

T4

All

1989 under 21 21–24 25–28 29–32 over 32

35.9 24.3 23.9 12.8 3.1

28.7 28.1 23.2 15.0 5.0

30.0 26.0 22.0 15.2 6.8

29.2 27.7 23.0 13.4 6.6

30.9 26.5 23.0 14.1 5.4

1993 under 21 21–24 25–28 29–32 over 32

34.5 25.3 19.6 15.5 5.0

25.4 28.5 24.6 14.6 6.9

25.0 30.0 21.6 15.6 7.9

27.8 30.2 20.9 13.4 7.7

28.5 28.3 21.7 14.8 6.7

1997 under 21 21–24 25–28 29–32 over 32

38.5 20.6 21.6 12.8 6.4

29.3 22.2 22.3 17.5 8.7

26.5 26.3 25.4 15.4 6.4

26.6 29.8 19.2 13.0 11.3

30.6 24.4 22.1 14.7 8.2

2001 under 21 21–24 25–28 29–32 over 32

42.4 19.8 17.7 13.8 6.4

34.9 20.4 18.6 18.5 7.6

26.8 29.8 19.4 14.9 9.2

25.6 25.5 20.3 16.9 11.6

33.1 23.5 18.9 16.0 8.5

2005 under 21 21–24 25–28 29–32 over 32

31.9 21.0 22.9 16.2 8.0

30.1 24.2 18.0 16.6 11.2

29.1 27.8 20.7 12.4 10.1

24.1 32.9 21.6 12.2 9.2

28.9 26.3 20.8 14.4 9.6

2009 under 21 21–24 25–28 29–32 over 32

40.7 20.1 20.6 13.9 4.8

28.7 25.0 24.0 15.9 6.3

27.4 27.5 23.6 14.7 6.8

22.5 30.3 24.7 12.9 9.7

30.9 25.1 23.0 14.4 6.6

Source: Rothmans/Sky Sports Football Yearbook

were born during months that fall within the first half of the school year, from September to February. Children whose birthdays fall in these months are physically bigger and stronger, and therefore more likely to succeed in school sports, than children in the same school year with birthdays between March and August,

220

Footballers’ employment, and racial discrimination

Table 8.3 Percentage distribution of professional footballers in England by month of birth, English League, selected years

January February March April May June July August September October November December

1989

1993

1997

2001

2005

2009

8.9 7.2 7.1 6.3 6.1 6.2 6.0 6.6 12.0 13.0 11.1 9.6

8.0 7.4 7.0 6.7 5.6 6.2 5.7 6.7 12.9 13.3 11.2 9.3

8.1 7.3 7.5 6.6 5.9 5.6 4.9 8.7 12.1 12.6 11.1 9.6

8.5 7.9 7.5 6.7 6.8 6.0 5.4 8.0 12.7 12.1 10.2 8.3

9.9 8.0 7.9 6.3 7.8 5.9 5.8 6.9 12.4 10.8 9.5 8.7

11.2 7.6 8.5 6.6 7.3 5.8 5.4 7.2 11.2 10.6 9.7 8.8

Source: Rothmans/Sky Sports Football Yearbook

who nevertheless play in the same school sports teams as their older counterparts. Although the physical disadvantage of the latter is most pronounced at the youngest ages, it seems likely that an aversion to sport acquired early in life would effectively terminate an individual’s prospects of becoming a sports professional. Table 8.4 reports the numbers of players recorded at each end-of-season census point from 1986 to 2009, disaggregated by country of birth. The categories are England and Wales, Scotland, Northern Ireland, Republic of Ireland and the rest of the world. It is worth noting that growth in the employment of players born outside the British Isles (the rest of the world category) had been underway for a number of years prior to the Bosman ruling, starting from an exceptionally low base. The double signing by Tottenham Hotspur in 1978 of the star Argentinian players Osvaldo Ardiles and Ricardo Villa was hailed as revolutionary at the time, but would be considered routine today. By the end of the 1993 season, the first since the formation of the Premier League, each of the leading clubs had a handful of star foreign players on its books. The following players all featured prominently in the 1993 season: for Arsenal, John Jensen (Denmark) and Anders Limpar (Sweden); for Liverpool, Stig Inge Bjornebye (Norway), Jan Molby (Denmark) and Ronnie Rosenthal (Israel); for Manchester United, Eric Cantona (France), Andrei Kanchelskis (Ukraine) and Peter Schmeichel (Denmark); and for Tottenham Hotspur, Nayim (Morocco), Eric Thorstvedt (Norway) and Pat Van Den Hauwe (Belgium). Even as recently as the mid-1990s, however, the playing rosters of all English clubs were dominated by British players. Subsequently the trend in the employment of foreign-born players has been almost relentlessly upward, with only a temporary lull in the rate of growth for a few years in the early 2000s. A record total of 744 foreign-born players (24.2 per cent of total employment) was recorded in 2009.

Employment mobility, migration and career structure

221

Table 8.4 Employment totals for professional footballers by birthplace (country), English League, 1986–2009

1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 % growth, 1986–2009

England & Wales

Scotland

Northern Ireland

Republic of Ireland

Rest of world

All

1820 1949 2038 2126 2218 2288 2328 2277 2408 2415 2514 2443 2486 2517 2521 2427 2407 2268 2129 2098 2084 1993 2086 2057

157 160 160 169 174 167 153 144 156 140 134 140 144 153 152 153 147 133 126 121 103 98 102 104

39 41 40 44 49 40 40 46 48 48 51 61 67 69 69 71 81 72 67 65 68 53 58 48

33 41 48 50 54 62 69 61 60 64 76 79 98 105 133 155 165 153 135 124 122 124 122 127

60 62 65 71 95 103 128 141 156 182 236 293 384 479 517 602 624 595 556 620 610 635 719 744

2109 2253 2351 2460 2590 2660 2718 2669 2828 2849 3011 3016 3179 3323 3392 3408 3424 3221 3013 3028 2987 2903 3087 3080

+13.0

−33.8

+23.1

+284.8

+1140.0

+46.0

Source: Rothmans/Sky Sports Football Yearbook

Among the other categories reported in Table 8.4, employment opportunities for footballers born in England and Wales grew significantly between 1986 and 2000, but most of this gain has subsequently been reversed. The number of Scottish-born players playing in England has declined, gradually during the 1990s and more sharply during the 2000s. For Northern Ireland there was employment growth up to 2002, followed subsequently by a sharp decline. For the Republic of Ireland the pattern is similar, but with faster growth up to 2002 followed by a slower decline. Table 8.5 reports a more detailed analysis of changes in the distribution of players by country of birth and by tier (division), based on comparisons drawn at four-year intervals using the 1989, 1993, 1997, 2001, 2005 and 2009 end-of-season censuses. Most of the employment growth of overseas players is concentrated in

222

Footballers’ employment, and racial discrimination

Table 8.5 Total numbers of professional footballers by birthplace (country) and tier, English League, selected years T1

T2

T3

T4

All

1989 E+W Scotland NI Ireland RoW Total

484 47 18 28 33 610

546 64 12 8 25 655

557 20 8 7 8 600

539 38 6 7 5 595

2126 169 44 50 71 2460

1993 E+W Scotland NI Ireland RoW Total

612 55 19 27 66 779

639 30 11 12 35 727

535 39 10 11 22 617

491 20 6 11 18 546

2277 144 46 61 141 2669

1997 E+W Scotland NI Ireland RoW Total

586 42 22 40 135 825

639 46 20 23 84 812

600 23 11 11 43 688

618 29 8 5 31 691

2443 140 61 79 293 3016

2001 E+W Scotland NI Ireland RoW Total

527 52 23 67 275 944

657 46 23 50 170 946

601 36 18 28 102 785

642 19 7 10 55 733

2427 153 71 155 602 3408

2005 E+W Scotland NI Ireland RoW Total

392 33 14 28 336 803

541 36 23 58 127 785

579 34 11 16 86 726

586 18 17 22 71 714

2098 121 65 124 620 3028

2009 E+W Scotland NI Ireland RoW Total

451 18 22 33 443 967

505 47 12 48 179 791

553 23 6 31 81 694

548 16 8 15 41 628

2057 104 48 127 744 3080

Source: Rothmans/Sky Sports Football Yearbook

Employment mobility, migration and career structure

223

Table 8.6 Percentage distribution of footballers by birthplace (region) and location of club (region), English League, 1989 Birthplace (region) London SE SW East EM WM YH NW NE Wales Scotland NI Ireland RoW All

Club location: Lon

SE

SW

East

EM

WM YH

NW

NE

Wal

Total

43.3 9.2 4.0 6.9 2.0 3.2 3.4 4.9 5.2 3.2 5.2 2.9 2.9 4.0

25.8 27.2 7.0 2.8 2.3 6.1 5.2 8.0 3.3 2.8 3.3 1.9 2.3 1.9

11.5 5.2 30.5 3.4 3.4 10.3 8.6 8.6 5.2 4.6 6.9 0.0 0.0 1.7

23.4 6.3 0.9 20.7 5.9 6.3 6.3 6.3 5.4 4.1 5.0 1.8 2.7 5.0

6.4 5.5 1.8 3.2 24.1 14.1 15.0 9.1 9.5 0.9 5.5 0.9 2.3 1.8

2.8 2.8 4.0 3.2 6.8 33.9 7.2 11.2 8.0 4.4 10.4 1.2 0.4 4.0

4.3 3.4 0.9 2.0 6.9 4.3 42.0 10.9 10.9 2.0 7.1 1.4 2.3 1.7

3.2 1.3 2.3 1.3 4.6 4.9 8.9 46.4 7.4 4.4 7.4 2.7 2.3 3.0

2.9 5.1 0.7 0.0 2.9 3.6 11.6 8.7 38.4 2.9 14.5 2.2 2.9 3.6

5.8 7.2 1.4 0.0 4.3 7.2 11.6 11.6 1.4 44.9 4.3 0.0 0.0 0.0

337 13.7 162 6.6 114 4.6 110 4.5 154 6.3 220 8.9 316 12.8 389 15.8 214 8.7 110 4.5 169 6.9 44 1.8 50 2.0 71 2.9 2460 100.0

0 3 2 2 7

2 2 1 3 8

2 1 3 1 7

2 5 3 1 11

1 4 2 7 14

3 3 6 6 18

2 1 0 2 5

0 0 2 1 3

Number of clubs (by tier) T1 7 1 T2 2 3 T3 2 3 T4 1 0 All 12 7

%

20 24 24 24 92

Note: se = South East, SW = South West, East = East of England, EM = East Midlands, WM = West Midlands, YH = Yorkshire and Humberside, NW = North West, NE = North East, NI = Northern Ireland, RoW = Rest of the World. Source: Rothmans/Sky Sports Football Yearbook

T1, followed by T2, and then T3 and T4. By 2009, overseas players accounted for nearly one-half of all employment with Premier League (T1) clubs. Clearly the leading clubs have greater financial resources to allow them to search internationally for playing talent. While the financial rewards in T1 and (perhaps) T2 may be sufficient to induce the most talented players to relocate, the financial rewards in the lower tiers may be insufficient for the less talented. Furthermore, the rules governing the issue of visas and work permits to non-EU nationals tend to favour the most talented athletes, but are tilted against the less talented in order to protect the employment of locally born professionals. The data reported in Tables 8.4 and 8.5 suggest that there have been significant changes in employment opportunities for footballers born in England and Wales. The employment prospects of locally born players might have increased due to the increase in total employment, but any improvement has been offset by the arrival of the large overseas contingent. Tables 8.6–8.8 present a cross-tabulation of the

224

Footballers’ employment, and racial discrimination

Table 8.7 Percentage distribution of footballers by birthplace (region) and location of club (region), English League, 1999 Birthplace (region) London SE SW East EM WM YH NW NE Wales Scotland NI Ireland RoW All

Club location: Lon 32.2 12.3 1.5 9.3 2.3 3.2 2.1 2.8 1.7 3.4 2.1 2.8 2.3 22.0

SE

SW

East

EM

WM

YH

NW

NE

Wal Total

14.3 23.7 8.6 9.0 3.3 4.9 3.7 4.9 2.9 3.3 5.7 1.2 1.2 13.5

10.8 5.6 26.4 2.6 4.3 6.1 3.5 7.4 4.3 6.9 6.5 1.7 0.9 13.0

24.1 5.8 2.9 20.3 4.8 6.8 3.9 3.9 2.6 3.2 4.5 3.2 1.3 12.9

9.8 5.1 1.4 2.9 19.6 10.1 10.9 7.6 6.2 2.5 3.6 2.2 1.8 16.3

5.8 3.4 4.0 3.7 8.3 25.7 6.1 8.9 4.0 4.0 4.6 1.8 5.2 14.7

5.0 2.3 2.7 1.1 7.0 5.0 32.5 13.8 7.9 2.5 3.2 1.4 4.3 11.5

3.7 2.0 1.6 1.6 3.4 4.7 9.2 39.7 4.3 4.4 6.0 2.7 4.0 12.9

3.5 1.8 0.0 0.9 2.6 2.6 11.4 7.9 36.8 2.6 7.0 0.9 6.6 15.4

3.5 5.9 4.7 0.0 0.0 7.1 5.9 18.8 5.9 41.2 3.5 0.0 1.2 2.4

Number of clubs (by tier) T1 6 1 T2 2 2 T3 2 3 T4 3 1 All 13 7

0 2 2 3 7

0 3 2 3 8

3 0 4 2 10

2 4 2 0 8

2 5 1 5 13

4 5 7 3 19

2 1 0 2 5

0 0 1 2 3

%

392 11.8 205 6.2 142 4.3 173 5.2 186 5.6 241 7.3 329 9.9 479 14.4 217 6.5 153 4.6 153 4.6 69 2.1 105 3.2 479 14.4 3323 100.0 20 24 24 24 92

Note: For region definitions, see note to Table 8.6. Source: Rothmans/Sky Sports Football Yearbook

distribution of the employment of players by birthplace at the level of standard English regions (for those born in England), against the distribution by the standard region in which the player’s current employer is located, for three selected years: 1989, 1999 and 2009. A striking feature of Tables 8.6–8.8 is the strength of the association between birthplace and the geographical location of employment for locally born footballers. Perhaps this pattern is to be expected among the youngest professional footballers, who are most likely to be spotted and signed by a local professional club when playing at school or junior level. At all ages, however, the geographical influence is strong. The distribution of employment by region of birth looks very different in every region. In 2009, for example, 32.6 per cent of footballers employed by London clubs were born in London, and only 2.3 per cent were born in the North West. By contrast, 3.3 per cent of footballers employed by North West clubs were born in London, and 39.4 per cent were born in the North West. Tables 8.6–8.8 indicate some sharp differences by region of birth in the changes in the employment prospects of English-born players. The numbers of professional

Employment mobility, migration and career structure

225

Table 8.8 Percentage distribution of footballers by birthplace (region) and location of club (region), English League, 2009 Birthplace (region) London SE SW East EM WM YH NW NE Wales Scotland NI Ireland RoW All

Club location: Lon 32.6 7.5 1.0 5.4 1.9 1.2 2.7 2.3 1.2 1.9 0.4 0.4 2.5 38.9

SE

SW

East

EM

WM

YH

NW

NE

Wal Total

19.9 24.9 5.1 6.5 1.4 2.2 0.0 6.1 1.1 1.1 2.9 0.4 2.5 26.0

15.8 12.4 23.9 3.8 1.3 5.6 3.4 8.1 1.3 3.8 6.8 1.3 2.1 10.3

26.3 4.6 2.9 21.7 2.9 5.0 3.8 5.0 2.1 0.8 3.8 2.5 5.8 12.9

9.5 5.7 3.8 4.3 26.2 3.3 8.6 9.5 0.5 1.9 5.7 1.0 3.3 16.7

7.9 3.0 2.4 5.4 3.3 26.6 2.4 9.7 3.0 1.8 3.6 1.5 5.1 24.2

5.2 2.9 2.0 2.6 5.2 4.6 35.3 10.9 5.2 2.0 3.7 0.9 4.3 15.2

3.4 1.6 0.5 1.0 2.1 5.9 4.5 39.4 2.5 2.1 3.1 2.5 4.7 26.8

6.4 0.6 1.2 1.7 1.7 0.6 5.2 8.7 31.2 1.2 2.3 4.0 6.9 28.3

10.9 1.8 1.8 1.8 0.0 7.3 0.0 0.0 1.8 25.5 9.1 1.8 7.3 30.9

Number of clubs (by tier) T1 5 1 T2 3 2 T3 2 2 T4 3 3 All 13 8

0 2 4 2 8

0 3 3 1 7

0 2 2 3 7

3 3 2 2 10

1 4 3 3 11

7 3 5 6 21

3 0 1 1 5

0 2 0 0 2

%

418 13.6 191 6.2 112 3.6 152 4.9 125 4.1 196 6.4 221 7.2 452 14.7 119 3.9 71 2.3 104 3.4 48 1.6 127 4.1 744 24.2 3080 100.0 20 24 24 24 92

Note: For region definitions, see note to Table 8.6. Source: Rothmans/Sky Sports Football Yearbook

footballers born in the East, London, North West and South East regions increased, by 38.2 per cent, 24.0 per cent, 17.9 per cent and 16.2 per cent, respectively, between 1989 and 2009; but the numbers born in the South West, West Midlands, East Midlands, Yorks and Humber, Wales and North East regions decreased by 1.8 per cent, 10.9 per cent, 18.8 per cent, 30.1 per cent, 35.5 per cent and 44.4 per cent, respectively. Some of these shifts might be explained by shifts in the fortunes of each region’s football clubs. For example, the number of North West clubs in T1 increased from three in 1989 to seven in 2009. The sharp reduction in the employment of players born in the North East is noteworthy, in view of this region’s historical tradition as a producer of high-quality playing talent. In this respect there are some affinities between the recent experience of the North East and Scotland. Tables 8.1–8.8 provide snapshots of the characteristics of the population of footballers employed by English clubs at moments in time. It is also possible to track the career progression of individual players over time. Tables 8.9–8.13 report empirical transition probabilities based on comparisons between the divisional status (T1, T2, T3 or T4) of players employed at each of five start-years 1989,

226

Footballers’ employment, and racial discrimination

Table 8.9 Four-year employment transition probabilities by tier, English League, 1989–1993 1993 employment status: T1

T2

1993 employment status:

T3

T4

Not emp.

T1

T2

T3

T4

Not emp.

1989: T1 T2 T3 T4 All

all ages in 1989 .359 .206 .154 .222 .047 .135 .024 .114 .145 .170

.090 .178 .191 .090 .138

.054 .094 .118 .163 .107

.291 .352 .508 .610 .440

ages 25–28 in 1989 .523 .189 .053 .144 .205 .247 .053 .168 .221 .015 .110 .096 .182 .169 .156

.038 .096 .099 .199 .108

.197 .308 .458 .581 .385

1989: T1 T2 T3 T4 All

ages under 21 in 1989 .248 .182 .117 .156 .231 .134 .061 .100 .150 .047 .124 .094 .135 .161 .124

.065 .118 .122 .135 .108

.388 .360 .567 .600 .472

ages 29–32 in 1989 .296 .254 .085 .076 .185 .196 .000 .080 .125 .000 .013 .050 .085 .130 .118

.056 .076 .136 .087 .091

.310 .467 .659 .850 .577

1989: T1 T2 T3 T4 All

ages 21–24 in 1989 .444 .254 .085 .213 .282 .184 .065 .214 .279 .024 .176 .121 .180 .231 .169

.042 .086 .143 .224 .126

.176 .236 .299 .455 .294

ages over 32 in 1989 .056 .056 .111 .094 .031 .031 .000 .000 .077 .000 .026 .000 .031 .023 .047

.111 .031 .026 .051 .047

.667 .813 .897 .923 .852

Source: Rothmans/Sky Sports Football Yearbook

1993, 1997, 2001 and 2005, and the status of the same players four years later in 1993, 1997, 2001, 2005 and 2009, respectively. Transition probabilities are reported for all players, and for players in the under 21, 21–24, 25–28, 29–32 and over 32 age bands. Using the first row of Table 8.13 as an example, 29.8 per cent of players who were employed by a T1 club in 2005 were again employed by a T1 club in 2009; 21.0 per cent of those employed in T1 in 2005 were employed in T2 in 2009; 9.4 per cent and 6.6 per cent of those employed in T1 in 2005 were employed in T3 and T4 in 2009, respectively; and 33.2 per cent were not employed by any English Premier League or Football League club in 2009. Among those players who remain in employment, there is a consistent tendency for divisional status to decline with career duration. Players who eventually become unemployable at the highest level are able to prolong their playing careers by moving to a lower tier. Throughout Tables 8.9–8.13, the probabilities of playing in a lower tier after four years (above the main diagonal) exceed the probabilities of playing in a higher tier (below the main diagonal). The probability of not being employed at the end of each four-year period is directly related to the player’s divisional status at the start of the period: T1 players are the most likely and T4

International migration of professional footballers

227

Table 8.10 Four-year employment transition probabilities by tier, English League, 1993–1997 1997 employment status: T1

T2

1997 employment status:

T3

T4

Not emp.

T1

T2

T3

T4

Not emp.

1993: T1 T2 T3 T4 All

all ages in 1993 .316 .231 .110 .205 .030 .131 .021 .034 .131 .159

.093 .156 .155 .172 .141

.083 .150 .165 .152 .135

.278 .379 .519 .621 .434

ages 25–28 in 1993 .382 .324 .110 .138 .269 .234 .000 .228 .157 .009 .037 .174 .141 .226 .173

.022 .174 .197 .202 .147

.162 .186 .417 .578 .314

1993: T1 T2 T3 T4 All

ages under 21 in 1993 .261 .136 .086 .111 .167 .133 .048 .096 .116 .027 .040 .167 .134 .116 .120

.105 .122 .144 .187 .134

.412 .467 .596 .580 .497

ages 29–32 in 1993 .262 .272 .087 .030 .149 .099 .000 .096 .117 .014 .014 .071 .084 .144 .095

.117 .208 .170 .114 .155

.262 .515 .617 .786 .522

1993: T1 T2 T3 T4 All

ages 21–24 in 1993 .385 .297 .110 .148 .250 .173 .061 .133 .233 .031 .043 .248 .160 .186 .189

.077 .138 .183 .124 .131

.132 .291 .389 .553 .334

ages over 32 in 1993 .257 .114 .000 .021 .063 .021 .000 .042 .042 .000 .000 .053 .059 .053 .030

.086 .104 .063 .053 .077

.543 .792 .854 .895 .781

Source: Rothmans/Sky Sports Football Yearbook

players are the least likely to remain employed after four years. Over the entire period, employment growth has been accompanied by a rise in employment turnover. Of 2,460 players employed in 1989, 44.0 per cent were not employed in 1993. Of 3,028 players employed in 2005, 52.3 per cent were not employed in 2009. The transition probabilities are non-linear in age. By age band, the five-year transition probabilities out of employment between 1989 and 1993 were 0.472 (under 21), 0.294 (21–24), 0.385 (25–28), 0.577 (29–32) and 0.852 (over 32). The corresponding probabilities between 2005 and 2009 were 0.575, 0.383, 0.398, 0.606 and 0.880. The relatively high rates of transition out of employment for the lowest and highest age bands reflect the fact that the under-21 age band contains a high proportion of youngsters who will eventually fail to make the grade as professionals; while the over-32 age band contains older professionals most of whom are approaching retirement. 8.2  International migration of professional footballers

The migration of professional sports labour at international level, both in football and in other sports, is examined by Maguire (1994, 2004), Maguire and Stead

228

Footballers’ employment, and racial discrimination

Table 8.11 Four-year employment transition probabilities by tier, English League, 1997–2001 2001 employment status: T1

T2

2001 employment status:

T3

T4

Not emp.

T1

T2

T3

T4

Not emp.

1997: T1 T2 T3 T4 All

all ages in 1997 .286 .178 .076 .209 .028 .138 .008 .027 .101 .140

.084 .174 .177 .105 .135

.093 .113 .175 .186 .140

.359 .429 .482 .674 .483

ages 25–28 in 1997 .476 .238 .056 .066 .375 .243 .019 .196 .253 .000 .016 .071 .130 .214 .165

.040 .112 .259 .294 .178

.190 .204 .272 .619 .313

1997: T1 T2 T3 T4 All

ages under 21 in 1997 .189 .121 .094 .074 .161 .148 .046 .120 .137 .017 .022 .117 .095 .111 .121

.138 .109 .103 .100 .116

.458 .509 .594 .744 .557

ages 29–32 in 1997 .304 .304 .089 .032 .119 .190 .010 .070 .140 .000 .012 .070 .074 .120 .130

.025 .167 .190 .198 .151

.278 .492 .590 .721 .524

1997: T1 T2 T3 T4 All

ages 21–24 in 1997 .338 .200 .110 .148 .265 .181 .035 .159 .194 .010 .057 .161 .121 .163 .163

.103 .103 .188 .238 .164

.248 .303 .424 .534 .389

ages over 32 in 1997 .186 .093 .000 .015 .031 .062 .000 .071 .071 .000 .000 .027 .040 .040 .040

.023 .046 .071 .067 .053

.698 .846 .786 .907 .827

Source: Rothmans/Sky Sports Football Yearbook

(1998), Maguire and Pearton (2000), McGovern (2002), Poli (2006, 2009) and Taylor (2006). Section 8.2 reviews the main findings of this body of work. For economic historians and sociologists, patterns of international migration of football players are ‘socially embedded’. The transactions of football clubs in the transfer market are heavily influenced by cultural and social ties, and by established historical and economic relationships. According to McGovern (2002), for example, migration patterns are mediated through social structures in ways that cannot be explained by a pure ‘market’ approach to economic action. Taylor (2006, p19) adds: it is difficult to deny that the ‘historical and cultural roots’ so often alluded to but rarely examined in detail continue to underpin many of the contemporary systems and networks of football player migration. Indeed it remains clear that where these players choose to go – and where the clubs decide to look for players – is not indiscriminate, but often determined by long-established colonial, cultural, linguistic, social and personal connections.

Maguire (1994, 2004) and Maguire and Stead (1998) also acknowledge the importance of social, historical and cultural influences, but emphasise economic factors. Patterns of migration of professional sports players across national borders reflect the following influences:

International migration of professional footballers

229

Table 8.12 Four-year employment transition probabilities by tier, English League, 2001–2005 2005 employment status: T1

T2

2005 employment status:

T3

T4

Not emp.

T1

T2

T3

T4

Not emp.

2001: T1 T2 T3 T4 All

all ages in 2001 .227 .184 .091 .180 .013 .104 .001 .058 .083 .133

.118 .117 .167 .074 .119

.090 .125 .141 .152 .127

.381 .486 .575 .715 .538

ages 25–28 in 2001 .425 .310 .069 .125 .289 .141 .008 .147 .171 .000 .069 .130 .114 .194 .133

.034 .164 .163 .145 .135

.161 .281 .512 .656 .425

2001: T1 T2 T3 T4 All

ages under 21 in 2001 .154 .112 .133 .057 .141 .094 .016 .110 .115 .000 .077 .044 .071 .114 .102

.112 .094 .157 .160 .124

.489 .613 .602 .718 .589

ages 29–32 in 2001 .273 .312 .130 .055 .188 .156 .000 .072 .134 .000 .009 .026 .067 .135 .111

.052 .125 .113 .132 .111

.234 .477 .680 .833 .577

2001: T1 T2 T3 T4 All

ages 21–24 in 2001 .311 .197 .129 .176 .200 .121 .025 .118 .241 .006 .088 .123 .113 .146 .159

.114 .176 .153 .222 .168

.250 .327 .463 .561 .413

ages over 32 in 2001 .048 .214 .048 .034 .069 .086 .000 .000 .127 .000 .000 .012 .016 .053 .066

.024 .052 .048 .025 .037

.667 .759 .825 .963 .828

Source: Rothmans/Sky Sports Football Yearbook

• The degree of geographical proximity between countries and the ease of travel; • The residual impact of historical imperial or colonial ties; • Countries’ attitudes towards their own nationals seeking employment opportunities abroad; • Countries’ treatment of foreign nationals seeking employment opportunities within their own boundaries; • Salary differentials, offering players the opportunity to increase their earnings by playing abroad, or (the other side of the same coin) clubs the opportunity to recruit talented players more easily or cheaply than is possible in the domestic transfer market; • The reputation, status and characteristics (including, for example, tactics, styles of play or the strength of physical competition) of the sport in different countries; • The extent to which media exposure raises interest and awareness in the sport across countries; • Inter-personal links, which might influence players from the same nation to play in the same foreign country or join the same club simultaneously.

230

Footballers’ employment, and racial discrimination

Table 8.13 Four-year employment transition probabilities by tier, English League, 2005–2009 2009 employment status: T1

T2

2009 employment status:

T3

T4

Not emp.

T1

T2

T3

T4

Not emp.

2005: T1 T2 T3 T4 All

all ages in 2005 .298 .210 .076 .211 .030 .091 .008 .054 .088 .137

.094 .141 .141 .131 .129

.066 .099 .173 .135 .122

.332 .473 .566 .672 .523

ages 25–28 in 2005 .519 .291 .051 .108 .342 .225 .040 .095 .190 .000 .043 .177 .127 .173 .171

.038 .045 .230 .163 .131

.101 .279 .444 .617 .398

2005: T1 T2 T3 T4 All

ages under 21 in 2005 .195 .170 .130 .065 .159 .107 .030 .086 .137 .025 .063 .107 .082 .123 .121

.075 .079 .168 .069 .099

.430 .589 .579 .736 .575

ages 29–32 in 2005 .182 .236 .091 .042 .146 .115 .028 .014 .056 .000 .000 .053 .054 .094 .081

.091 .177 .169 .200 .165

.400 .521 .732 .747 .606

2005: T1 T2 T3 T4 All

ages 21–24 in 2005 .475 .242 .071 .115 .309 .176 .028 .156 .194 .005 .092 .175 .111 .188 .165

.061 .139 .194 .175 .154

.152 .261 .428 .553 .383

ages over 32 in 2005 .059 .118 .059 .014 .028 .069 .015 .000 .000 .000 .000 .032 .017 .026 .038

.059 .042 .030 .032 .038

.706 .847 .955 .935 .880

Source: Rothmans/Sky Sports Football Yearbook

Based upon an analysis of the nationalities of all players participating in the highest tiers of thirty-two European countries in the 1993 season, Maguire and Stead (1998) report that 1,295 players, or 11.4 per cent of the total workforce, were employed by clubs located in countries other than their country of nationality. Of these, the proportions from non-European countries, non-EU European countries and EU countries were 27 per cent, 54 per cent and 19 per cent, respectively. Flows of players into and out of Europe were concentrated most heavily on Latin American countries. In 1994, there were 297 transfers (at all levels) involving moves from non-European to European countries. Of these, 46 per cent were from Latin America, 22 per cent from North and Central America and the Caribbean, 20 per cent from Asia, 7 per cent from Africa and 5 per cent from Oceania. European countries located around the Mediterranean rim were the principal destinations for players imported from Latin America. Intra-European trade in players was dominated by flows from Eastern Europe into the EU. According to Maguire and Stead, 47.3 per cent of all non-EU players playing in the EU were from Eastern Europe. Such flows increased significantly

International migration of professional footballers

231

following the collapse of communism at the end of the 1980s. Previously the majority of former-communist countries permitted only a handful of players to move to the west, and in most cases not until the latter stages of their careers. During the 1990s, apart from the ‘pull’ factor of the higher earnings available in Western Europe, significant ‘push’ factors include the brutal ethnic conflicts in the former Yugoslav territories, and political and economic turmoil elsewhere, mirrored at the sporting level by the disappearance or wholesale reconstruction of various leagues and individual clubs. Players from Croatia and the rump Yugoslav Federation formed the two biggest groups among non-EU Europeans playing in the EU in 1993. Their principal destinations (in descending order) were Greece, Spain, Austria and Portugal. One of the most striking aspects of Maguire and Stead’s analysis of the intraEuropean player flows is the imbalance between the number of players moving from north to south and the number moving in the opposite direction. In the 1995 season, there were twenty-nine northern Europeans playing in the south, but only five from southern Europe playing in the north. Speculating on the causes of this asymmetry, Maguire and Stead suggest that the (actual or perceived) professionalism, adaptability, language competence and high educational standards of Dutch and Scandinavian players, together with their physical attributes, tend to make them attractive targets for leading clubs in any country. In contrast, northern European perceptions of southern Europeans tend to focus on concerns about temperament or the ability to adapt to the physical demands of the northern style of play. Whether such attributes are imagined or real is beside the point, since it is the perception that counts in determining clubs’ recruitment policies. Poli (2006) examines the geographical origin of migrant footballers to leagues under the jurisdiction of UEFA using data for the 2003 season. Eastern Europe was the largest originator of migrant footballers (29.7 per cent), followed by Western Europe (28.7 per cent), Africa (19.6 per cent) and Latin America (16.9 per cent). The largest exporter country was Brazil (9.5 per cent of all migrants in UEFA countries). After Brazil, other prominent exporter countries were Serbia-Montenegro, France, Argentina, Nigeria, Ukraine, Croatia and Cameroon. The largest importer of migrant footballers was England: 718 migrants (13.5 per cent of all migrants in UEFA countries) played for English clubs. After England, other prominent importer countries were Germany, Italy, Portugal, Belgium, France and Spain. The recruitment of foreign players is influenced by the standard of football. This relationship also depends upon the continent of origin. In a five-level hierarchy of European leagues based upon UEFA rankings, the proportion of migrant footballers from Latin America decreases from the top level to the bottom. However, migrant footballers from Africa are more heavily represented in the lower four levels than in the highest level. For example, 53.3 per cent of migrant footballers in Romania were from Africa. For Malta, Belgium, Switzerland and Albania, the corresponding figures were 52.6 per cent, 43.4 per cent, 33.7 per cent and 33.3 per cent. These data reflect a need for the less affluent clubs to recruit foreign talent from relatively low-cost sources (Poli, 2006).

232

Footballers’ employment, and racial discrimination

Poli (2009) reports that the presence of foreign players in the major European leagues increased significantly between 1996 and 2006. The percentage of non-EU players has increased both with respect to the total number of players and relative to the total number of foreign players. In the 2006 season, 38.4 per cent of players in the big-five European leagues, England, France, Germany, Italy and Spain, were migrants (20.2 per cent in the 1996 season). The concentration of foreign players tends to be heaviest with the top-ranked teams in each league. In the 2008 season, 52.6 per cent of players employed by teams ranked in the top five in their domestic leagues were foreign. For middle-ranked teams and bottom-ranked teams, the corresponding figures were 37.1 per cent and 42.2 per cent, respectively. Darby and Solberg (2010) and Poli (2010) present further evidence on the experience of African migrant footballers. The distribution of foreign-born players by origin in the 2006 season varied widely among the big-five leagues. For Italy and Spain, the pattern was similar. The proportions of foreign-born players from Latin America were 50.8 per cent for Italy and 62.2 per cent for Spain. In both cases, Western Europe was the next highest source (20.2 per cent for Italy and 25.5 per cent for Spain). For Germany, the two principal sources were Western Europe (34.9 per cent) and Eastern Europe (33.1 per cent). For France, the two main sources were Africa (48.3 per cent) and Latin America (23.3 per cent). For England, the two main sources were Western Europe (63.6 per cent) and Africa (10.7 per cent). Tables 8.14 and 8.15 present an analysis of the home countries and countries of employment of the members of the sixteen national team squads which took part in the finals of the 2000 and 2008 European Championships (Euro 2000 and Euro 2008), staged jointly by Belgium and the Netherlands in 2000, and by Austria and Switzerland in 2008. The analysis, along the same lines as that of the 1998 World Cup reported by Maguire and Stead (2000), provides a snapshot of patterns of intra-European player migration at the highest level. At Euro 2000 22 players were permitted in each squad, or 352 players in total. At Euro 2008 the squad sizes were increased to 23 (368 players in total). In Euro 2000, 177 players were foreign-based (50.4 per cent of the total). In Euro 2008 this proportion was slightly lower: 176 players were foreign-based (47.8 per cent of the total). The columns of Tables 8.14 and 8.15 show the sixteen participating countries, arranged from left to right in ascending order of the numbers of foreign-based players included in their squads, shown in the final row. In 2008, for example, Russia selected a squad in which only one player was foreign-based. At the other extreme, the Czech Republic selected twenty-one foreign-based players. The rows of Tables 8.14 and 8.15 show the countries of employment of the squad members of each country. The first sixteen rows report the data for the participating countries in each tournament; the remaining rows show players employed in non­participating countries. Each group of countries is arranged in descending order of the total numbers of imported players employed, shown in the final column. The numbers of home-based players in each squad, shown in italics in the relevant cells of Tables 8.14 and 8.15, are not included in the final row and column totals.

0

22

Ita

0

22

Spa

Home country

1

21 1

Eng

Source: World Soccer (June 2000)

Scotland Austria Greece US Croatia Switzerland Japan All

England Spain Italy Germany Netherlands Belgium France Portugal Turkey Denmark Norway Yugoslavia Czech Rep Romania Sweden Slovenia

Country of employment

3

1

19

1 1

Tur

4

1

1 18

2

Ger

11

1 1 11

1 4 4

Por

12

1 4 3 10 1 1

2

Bel

14

1

8

1

1

3 1 2 5

Cze

15

7

3

1 6 1 1 2 1

Rom

15

1

1

1 7

1 1

9 1

Nor

15

7

6 2 5 2

Fra

16

1 1

5 1

6

1

3 1

3

Slov

17

2

5

2 1

4 3 3 2

Swe

17

2

5

5 7 3

Net

Table 8.14 Cross-tabulation of squad players’ home countries and countries of employment, Euro 2000

1 18

4

1 1

7 5 1 2

Yug

19

1 1

3

1

4 4 3

5

Den

6 6 3 2 1 1 1 177

39 33 29 22 10 7 5 4 3 3 1 1 0 0 0 0

All

1

22

1

Rus

4

2

19 2

Ger

Home country

5

5

18

Spa

5

1 3 18 1

Ita

7

2

16

1 1 1

1 1

Tur

8

1

1

1 1 15 1

2

1

Aus

9

2

1

14

4 2

Gre

1 11

1 1

12

1 1 3 2 1

Rom

11

4

12

2 5

Por

Source: www.thebesteleven.com/2008/06/club-breakdown-for-euro-2008-squads.html

England Belgium Scotland Ukraine Denmark Norway Bulgaria All

Germany Spain Italy France Russia Greece Austria Portugal Romania Netherlands Turkey Switzerland Czech Rep Sweden Poland Croatia

Country of employment

13

6

2 3 2 10

Fra

14

3 1 1 1

9

1

1 2 1

2 1

Pol

14

1

7

9

3 3

Net

16

3

7

1

2 4

6

Swit

17

1 1

5

6

1 1

1

1

1 4

1

Swe

Table 8.15 Cross-tabulation of squad players’ home countries and countries of employment, Euro 2008

20

1

2

3

1

3 3 2 1 1

6

Cro

21

2

4 3

2

5 1 4 1 1

Cze

46 4 3 3 3 2 1 176

36 22 17 16 7 6 3 2 2 1 1 1 0 0 0 0

All

International migration of professional footballers

235

Based on the data for both tournaments, England (a non-participant in 2008) was by some distance the leading importer of players at this level. This position reflects the financial rewards the leading English clubs are able to offer the leading players, as a result of the commercial vibrancy of the Premier League. The number of foreign-based players based in the English league who participated in the finals increased from thirty-nine for Euro 2000 to forty-six in Euro 2008. The equivalent figure for Germany also increased, from twenty-two to thirty-six; but the figures for Spain and Italy fell, from thirty-three to twenty-two (Spain), and from twentynine to seventeen (Italy). In Euro 2000, all members of the Spanish and Italian squads were home-based; in the case of the latter, the absence of foreign-based players appears to have been a conscious policy decision, and may not reflect a complete lack of suitably skilled foreign-based talent. The tendency for the majority of the leading Spanish and Italian players to remain home-based is reflected in the Euro 2008 data as well; although by then five Spanish squad members were employed by teams in the English Premier League, and five Italian squad members were based in Spain, Germany or France. England’s apparent ascendancy within Europe as an importer of footballers is a relatively recent phenomenon, but several longer established features of intraEuropean migration patterns are also apparent in Tables 8.14 and 8.15. These include the popularity of England as a destination for Swedes and the Dutch; the ability of Swedes to find employment across a wide range of European countries; and the importance of geographical proximity or historical links in determining migration flows, especially for players from nations with less economically powerful domestic leagues. In Euro 2008 Switzerland, for example, had six squad members based in Germany, and the Czech Republic had five; while Portugal had five squad members based in Spain. Finally, it is interesting to note that the two participant countries whose domestic leagues hosted the highest numbers of foreignbased players from other Euro 2008 squads, Germany and Spain, were also the two finalists of this tournament. Using data similar to those presented in Tables 8.14 and 8.15, Frick (2009) presents an econometric analysis of the impact of the Bosman ruling on player migration, using data on the percentage of players under contract in a foreign country at the time of a World Cup or European Championship. To explain the variation in this percentage he estimates a regression model with a Bosman dummy (before 1997 = 0; after 1997 = 1) and random country effects. After controlling for the tournament (World Cup or European Championship) and for a (linear) time trend, the Bosman ruling is found to have produced a statistically significant increase in the percentage of squad players under contract in a foreign country. The time trend is also statistically significant, indicating that the Bosman ruling had the predicted positive impact on player migration. Frick (2009) also analyses the impact of the ‘internationalisation’ of national teams on their performance. The playing strength of the national teams is measured using their performance in World Cup and European Championship tournaments

236

Footballers’ employment, and racial discrimination

staged between 1978 and 2006. A binary team performance measure (based on qualification for the semi-finals or the final of the tournament) is explained by the (normalised) percentage of players under contract abroad at the time of the tournament, with controls for the tournament (as above) and the number of participating teams. The estimation method is random effects logit. The probability of reaching the semi-final or the final of either tournament is unaffected by the percentage of players employed abroad. According to Frick (2009 p 96) the increasing competitive pressure exerted on players migrating from Eastern Europe, Africa, Asia, and South America to the better paying leagues in Western Europe has not yet resulted in a better performance of their national teams

Similarly, Baur and Lehmann (2008) analyse whether a country’s success is influenced by the number of national team players that do not play in the home league and by the number of national team players from other countries that play in the home league, using data for all thirty-two national teams that qualified for the 2006 World Cup. Both the number of players that play in a foreign league (exports) and the number of foreign players that play in the home league (imports) are positively associated with the country’s FIFA ranking. This suggests that all countries benefit from trade. For example, Brazil and Italy are both highly ranked, even though Brazil is a net exporter and Italy is a net importer of footballers. 8.3  Racial discrimination in professional team sports

The investigation of discrimination in professional team sports has motivated many empirical studies of the determinants of player compensation, especially in the US. This issue has been of particular interest in North American sports. Before the Second World War, racial segregation at professional level operated in a number of sports: the teams in the top leagues employed only white players. The colour bar was lifted for the first time in both baseball and basketball during the late 1940s, but there is no doubt that discriminatory practices continued for many years afterwards. Empirical evidence on the extent of racial discrimination in professional team sports outside North America is more limited, mainly because data on the remuneration of individual professional sports players are, for the most part, not publicly available. In professional team sports, the forms that discrimination can take include inequality in the level of compensation; inequality in hiring standards; inequality in the allocation of playing positions; inequality in the prospects for retention or career progression; and inequality in the availability of opportunities for endorsements or sponsorship. Possible perpetrators of discrimination are employers, ­co-workers or customers. Although in principle it is possible to distinguish between the different forms and sources of discrimination, in practice the boundaries may be blurred. A derisory salary offer, for example, may be tantamount to a refusal to hire. An employer practising hiring or salary discrimination may attempt to attribute blame to the attitudes of customers.

Racial discrimination in professional team sports

237

Becker (1971) argues that eventually, economic competition between teams as employers should eliminate employer discrimination. Teams that discriminate should be forced out of business because they are inefficient. In contrast, co-worker discrimination should result in equally competitive segregated teams. Using the ‘joint economies of scale in consumption’ argument (see Chapter 7, Section 7.2), Rosen and Sanderson (2001) suggest that customer discrimination is likely to have especially adverse consequences for black athletes. Each customer may demonstrate only a trivial prejudice, reflected in a small reduction in the price they are willing to pay to watch a team containing black athletes. But from the team’s perspective, the total loss of revenue that has to be compensated (by paying black athletes a salary that reflects customer prejudices) may be huge, because of the large audience sizes involved. In this case a feasible salary may not exist, and the black athlete is effectively forced out of the market altogether. Empirical evidence on racial discrimination: North American professional team sports

Kahn (1991, 2000) reviews a substantial body of empirical literature on discrimination in professional team sports. Empirical tests for salary discrimination normally use a cross-sectional regression of individual salaries on various productivity indicators, and a dummy variable for race or any other characteristic that is thought to be the subject of discrimination. The availability of accurate productivity indicators is vital, since as Kahn points out, any correlation between race and the measurement error in the productivity component will lead to bias in the estimated discrimination effect. Another key issue in detecting discrimination in salary equations concerns the skewness that is often present in athletes’ salary data. If the salary distribution for blacks and whites reveals significant disparity in the compensation of each group above or below the mean, an estimation method that focuses on the conditional mean may misrepresent the relationship between salary and race. Quantile regression permits the impact of race to be established at different points of the salary distribution, not just at the mean (Hamilton, 1997; Berri and Simmons, 2009). For the NBA, there is extensive evidence to suggest that prior to the 1990s, black players were paid lower salaries than white players at comparable levels of productivity (Kahn and Sherer, 1988; Koch and Vander Hill, 1988; Brown, Spiro and Keenan 1991). Using NBA data for the 1995 season, Hamilton (1997) finds evidence of a 1 per cent across-the-board salary differential between white and black players. At the lower end of the salary range, whites earned less than blacks; though when the number of matches is included in the regressions as a control, the effect reverses. At the upper end of the salary range, whites earned more than equally qualified blacks. The premium was the same regardless of the race of the team’s manager, and so is attributed by Hamilton to customer rather than employer discrimination.

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Bodvarsson and Brastow (1998) use salary regressions to test for employer discrimination in the NBA in the 1986 and 1991 seasons. Again the race of the team’s manager is assumed to convey information about team owners’ attitudes: owners that employ black managers are assumed to be non-discriminators. The test therefore examines whether black players working for white managers experienced discrimination. The salary regressions include the percentages of team members and of the local population that were black, as controls for coworker and customer discrimination respectively. Salary discrimination, present in 1986, had disappeared by 1991. This finding is consistent with the hypothesis that two important structural changes in the interim increased competition between teams as employers, and reduced the discretion for team owners to discriminate as monopsony purchasers in the labour market. These were the 1988 NBA Collective Bargaining Agreement, which introduced free agency; and the addition of four new teams, which stimulated competition between teams as employers of players. By contrast, Jenkins (1996), Dey (1997), Gius and Johnson (1998) and Eschker, Perez and Siegler (2004) find little evidence of salary discrimination in the NBA. Berri and Simmons (2009) find evidence of performance-related salary discrimination against black quarterbacks in the top half of the salary distribution in the NFL. Several studies of discrimination against Francophone players in the NHL offer mixed results (Jones, Nadeau and Walsh, 1999; Lavoie, 2000; Curme and Daugherty, 2004). Speaking generally, it is apparent that evidence of discrimination in North American major league professional team sports has become weaker over time (Rosen and Sanderson, 2001). Direct tests for discrimination in hiring in North American professional team sports are less common than tests for salary discrimination, primarily because of the difficulties in obtaining data on players who were not hired, as well those who were. Indirect testing, mostly based on comparisons between the performance of black and white players, is more common. If blacks tend to outperform whites on average, this is interpreted as evidence of discrimination in hiring: on average a black needs to attain a higher standard to be hired than a white. Similar methods can be used to test for discrimination in the allocation of specific team positions between whites and blacks. Empirical studies of hiring discrimination have reported mixed findings. Bellemore (2001) reports evidence of discrimination against black players in promotion from minor league baseball to MLB between the 1960s and 1990s. The level of discrimination was lower in years when the number of major league teams was increased. Discrimination against Hispanics was evident at the start of this period, but had disappeared by the end. McCormick and Tollison (2001) report that black players in the NBA were assigned more playing time than comparable white players. Burdekin, Hossfield and Kilholm-Smith (2005) find evidence of a correspondence between the racial composition of NBA teams and of the populations of the cities in which the teams were located.

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Jiobu (1988) reports evidence of retention discrimination in MLB during the 1970s and early 1980s, in the form of a tendency for team owners to retain underperforming white players for longer than black players. Similarly for the NBA, Hoang and Rascher (1999) report evidence of retention discrimination favouring white players. Using more recent MLB data, however, Groothuis and Hill (2008) find no link between race and career duration. Finally, tests for customer discrimination normally focus on the relationship between match attendances or revenues and team racial composition. The use of attendance data can be problematic, because many teams routinely sell all of their seats, especially in the NFL and NBA. However, accounting for the truncation of the data, Berri, Schmidt and Brook (2004) find that customer discrimination was widely prevalent in the NBA in the 1980s, but less so subsequently. Foley and Smith (2007) suggest that MLB attendances in the cities of Boston, Cleveland, Houston, San Diego and Saint Louis were reduced when the home team added Hispanic players to its line-up. Tainsky and Winfree (2010) examine the impact of foreign-born players on MLB attendances. Using TV audience data for televised NBA matches, Kanazawa and Funk (2001) find that the number of white players in both the home and visiting teams influenced ratings. Hanssen and Andersen (1999) and Depken and Ford (2006) examine the voting records for baseball’s All-Star game. There is evidence of racial discrimination in the 1970s, but not subsequently. Todd, Brown and Miles (2002) and Todd (2003) find that race did not influence a player’s prospects for induction into the National Baseball Hall of Fame between the 1960s and 1990s. Empirical evidence on racial discrimination: English and European football

Szymanski (2000) reports the first empirical test for employer discrimination against black players in English football. Although football has never operated a formal colour bar, instances of black players appearing in the Football League before the 1970s were isolated. There is abundant anecdotal or circumstantial evidence of discrimination against black players throughout the 1970s and 1980s, on the part of some club officials as well as spectators. As Szymanski reports, the rate at which first-team opportunities opened up for black players appears to have varied between clubs, to a degree that seems difficult to attribute to chance. Since the 1980s the situation appears to have improved, with crowd abuse of black players becoming a rarer phenomenon than it was in earlier times. Even recently, however, there is no shortage of anecdotal evidence to suggest that the longstanding tradition of racism in English football is not completely defunct. Sir Norman Chester Centre for Football Research (2002) notes a catalogue of occasions when senior officials and football club managers have referred to black players as ‘lacking bottle’, ‘having no stamina’ and ‘exhibiting a lack of discipline and consistency’. In 2004 Ron Atkinson, a high-profile former football manager, left his job as a TV commentator after a racist comment about Chelsea’s Marcel Desailly was

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broadcast on a live feed to several Middle East TV channels while the UK transmission was off-air (Goddard and Wilson, 2009). In the Szymanski (2000) study, the difficulties created by the non-availability of individual salary data for football players are circumvented by testing for discrimination using data at team rather than at individual level. Total wages and salaries per team are available from annual football club company accounts. Using data on thirty-nine clubs for which complete data were available for the period 1978–93, Szymanski finds that teams that used a below-average proportion of black players achieved inferior playing performance (measured by league position) after controlling for salary expenditure and for the total number of players used in each season. Perhaps surprisingly, this finding is stronger for the period 1986–93 than it is for 1978–85. The test, however, is more powerful for the later period because by then more black players were employed. The evidence of discrimination is also stronger for the larger clubs (measured by stadium capacity) than for the smaller ones. How is the finding that teams that under-recruited black players also under­performed on the pitch to be interpreted? It appears that by refraining from recruiting the most talented players available for a given salary spend, team owners or managers with a taste for discrimination indulged their preferences by accepting a lower standard of team performance than they could otherwise have achieved. The proportion of black players used turns out to be insignificant in attendance or revenue regressions, suggesting that discrimination originates with the teams as employers rather than with spectators as customers. A crucial assumption underlying the test is that the market for playing talent is efficient, so all teams recruit from the same pool of players. This may rest uneasily with the evidence that player recruitment is, in practice, geographically highly segmented (see Section 8.1). Szymanski suggests that a relatively weak market for corporate control of football clubs may explain why the more efficient, non-discriminating teams did not drive the less efficient, discriminating ones out of business through competition. In a separate study, Preston and Szymanski (2000) find no evidence of a link between the selection of black players and match attendances, suggesting that customer discrimination is not responsible for the racial influence on the salary expenditure-performance relationship. However, the ethnic composition of the local population is a significant determinant of the team-level proportion of appearances made by black players. It is not clear whether the racial factor in the salary-performance relationship truly reflects employer discrimination, or a geographically segmented labour market, which confers advantages on teams able to hire from an ethnically diverse pool of talent at local level. Pedace (2008) reports evidence that English teams with more players of South American origin performed less well than those with fewer such players. However, teams fielding South American players also attracted higher attendances. For countries other than England, Wilson and Ying (2003) present a analysis constructed along similar lines to the Szymanski study, using data for the postBosman period from the highest divisions of several top European leagues. It

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is suggested team performance could be improved by hiring more players from under-represented regions, such as eastern Europe and Latin America. There is no evidence that spectators react adversely to the selection of non-domestic playing talent. Frick (2006) estimates that German Bundesliga footballers from other western European countries, from eastern Europe and from Latin America received salary premiums of 15 per cent, 30 per cent and 50 per cent respectively, relative to native players born in Germany. Frick’s (2007) survey article reports little or no evidence of salary discrimination against foreign footballers in the European leagues. Using the Premier League and Football League retained list data published annually in Rothmans Football Yearbook, Goddard and Wilson (2009) report an analysis of hiring and retention discrimination in English football. Patterns of career progression for white and black players are compared, by examining the career progression of three cohorts of players over the five-year intervals 1986–91, 1991–6 and 1996–2001. The choice of sample period is dictated by the timing of the publication in the Yearbook of playing-squad photographs of English league clubs. Publication of these photos started in 1986, and ended in 1998. The photos allow a binary classification based on skin colour of the large majority of professional footballers who were employed during this period.1 The same source was also used in the earlier Szymanski (2000) study. The remainder of this section describes the empirical model used in the Goddard and Wilson study in some detail, and presents some of the estimation results. The econometric model for the conditional probability that a professional footballer is retained within the data set over a five-year period and, for those that are retained, the conditional probability distribution for the possible transitions in divisional status, comprises three equations. The dependent variables are initial divisional status, retention and divisional transition. The dependent variables in the initial divisional status and divisional transition equations can each take one of four possible values, depending on the player’s divisional status (T1, T2, T3 or T4) at the start and end of the five-year period. The specification of these two equations is therefore analogous to ordered probit. The dependent variable in the retention equation is binary, so the specification is analogous to binary probit. Ignoring the interdependence between the three equations, the specification of the ordered probit regression equation for initial divisional status is as follows: Probability (initial divisionalstatus is T1) = 1 − Φ(µ3 − x i,t ) Probability (initial divisional status is T2) = Φ(µ3 − x i,t ) − Φ(µ 2 − x i,t ) Probability (initial divisional status is T3) = Φ(µ 2 − x i,t ) − Φ(µ1 − x i,t ) Probability (initial divisional status is T4) = Φ(µ1 − x i,t )  [8.1] The specification of the binary probit regression equation for retention is as follows:

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Probability (player is retained) = Φ(y i,t ) Probability (player is not retained) = 1 − Φ(y i,t ) 

[8.2]

Finally, the specification of the ordered probit regression equation for divisional transition, conditional on initial divisional status = j for j = 4, … ,1 (j = 4 for T1; j = 3 for T2; j = 2 for T3, j = 1 for T4), and the player being retained, is as follows: Probability (final divisional status is T1) = 1 − Φ(δ j,3 −  j z i,t ) Probability (final divisional status is T2) = Φ(δ j,3 −  j z i,t ) − Φ(δ j,2 −  j z i,t ) Probability (final divisional status is T3) = Φ(δ j,2 −  j z i,t ) − Φ(δ j,1 −  j z i,t )  [8.3] Probability (final divisional status is T4) = Φ(δ j,1 −  j z i,t ) In [8.1], [8.2] and [8.3] Φ is the cumulative Normal distribution function. xi,t, yi,t and zi,t are vectors of covariates. α, β and γj are vectors of coefficients to be estimated. β includes an intercept; α and γj have no intercept. In [8.1], μk (for k = 1,2,3) are cut-off parameters to be estimated. Equation [8.3] is parameterised so that the divisional transition equation contains a separate set of coefficients and cut-off parameters for each possible state of the initial divisional status variable. δj,k (for j = 1,2,3,4 and k = 1,2,3) are cut-off parameters to be estimated.2 The covariates appearing in xi,t, yi,t and/or zi,t are as follows: CLUBSEA = Total number of different teams the player has been employed by up to and including his present club at the end-of-season census point, divided by the number of times the player has appeared in the end-of-season census. APSEALL = Total number of league appearances in the player’s career to date, divided by the number of times the player has appeared in the end-of-season census. DIV18 = Divisional status (T1 = 4, T2 = 3, T3 = 2, T4 = 1) of the club the player was employed by at the end-of-season census immediately following his eighteenth birthday. DUM18 = 0–1 dummy variable identifying players not in the data set when aged 18 (for whom DIV18 = 0). SCOTIRE = 0–1 dummy variable identifying players born in Scotland, Northern Ireland or the Irish Republic. O’SEAS = 0–1 dummy variable identifying players born overseas. RACE = 0–1 dummy variable identifying non-white players. AGE = Player’s age in years at the time of the end-of-season census. AGESQ = Square of AGE. DFR, MFR and FWD = 0–1 dummies identifying outfield playing positions (defender, midfield and forward). OUTF’LD = DFR + MFR + FWD. T2, T3, T4 = 0–1 dummy variables identifying players’ initial divisional status. The model is estimated separately over the three five-year intervals: 1986–91, 1991–6 and 1996–2001. The data set for each five-year interval includes those players

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Table 8.16 Estimation results: initial divisional status

CLUBSEA DIV18 DUM18 SCOTIRE O’SEAS RACE O’SEAS × RACE

1986–1991

1991–1996

1996–2001

−1.2254*** −7.53 .2696*** 7.72 .8509*** 6.82 .3683*** 4.11 .8647*** 3.79 .1313 1.06 −.5388 −1.45

−1.3713*** −9.98 .1875*** 5.90 .6031*** 5.44 .2964*** 3.58 1.2870*** 8.77 .3387*** 3.84 −1.4061*** −4.70

−1.5602*** −11.48 .1973*** 6.20 .5342*** 4.98 .5005*** 5.29 1.2039*** 11.40 .2499*** 3.28 −.2753 1.24

Notes: Table 8.16 reports the estimation results for α in [8.1]. *** = significantly different from zero, two-tail test, 1% level; ** = 5% level; * = 10% level. z-statistics for significance of estimated coefficients are reported in italics. Source: Adapted from Goddard and Wilson (2009)

who were employed by a league club and aged over 21 at the start of the five-year interval, and for whom the RACE variable is observed. Players aged under 21 are excluded to permit the construction of covariates which proxy for player quality, using data on the player’s divisional status at age 18 (see below). The estimation results reported by Goddard and Wilson (2009) are summarised in Tables 8.16 (initial divisional status), 8.17 (retention) and 8.18 (divisional transition). Positive and highly significant coefficients on DIV18 in [8.1] reflect the expected association between natural talent and initial divisional status.3 Several covariates play an important role in [8.2] or [8.3], but are unimportant and are therefore excluded from [8.1]. AGE and AGESQ, APPSEA, and the positional dummy variables DFR, MFR and FWD are virtually irrelevant in [8.1]. Clubs in all four tiers have similar proportions of old and young players, similar proportions of experienced and inexperienced players, and similar proportions of players in each playing position. All of these attributes, however, are highly significant determinants of retention and divisional transition. In [8.2] the dummy variables for T2, T3 and T4 control for the tendency (also apparent in Tables 8.9–8.13) for the retention probabilities to vary with divisional status. The parameterisation of [8.3], which allows separate equations for each of the four possible values of initial divisional status, effectively interacts the T2, T3

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Table 8.17 Estimation results: retention 1986–1991 APPSEA AGE AGESQ DFR MFR FWD SCOTIRE O’SEAS RACE O’SEAS × RACE T2 T3 T4 Constant

.0307*** 6.67 .0038 0.02 −.0035 −1.25 −.4066*** −2.99 −.3290** −2.35 −.6384*** −4.54 −.1147 −1.01 −.5788** 2.15 .3191* 1.95 .1378 0.31 −.1513 −1.42 −.5608*** −5.28 −1.0975*** −9.81 2.7861 1.32

1991–1996 .0657*** 14.6 −.1904* −1.76 −.0002 −0.11 −.7483*** −5.82 −.8297*** −6.34 −.8221*** −6.21 −.4560*** −4.01 −.2386 −1.35 .4271*** 3.54 −.5292 −1.35 −.4822*** −4.99 −.8402*** −8.14 −1.5957*** −13.78 5.3444*** 3.61

1996–2001 .0571*** 13.93 .4300*** 4.33 −.0113*** −6.28 −.4228*** −3.64 −.4832*** −4.12 −.5486*** −4.61 −.2319* −1.91 −.6978*** −5.51 −.0382 −0.39 .1703 0.61 −.2669*** −3.04 −.5014*** −5.43 −.9183*** −9.45 −3.4855*** −2.57

Notes: Table 8.16 reports the estimation results for β in [8.2]. *** = significantly different from zero, two-tail test, 1% level; ** = 5% level; * = 10% level. z-statistics for significance of estimated coefficients are reported in italics. Source: Adapted from Goddard and Wilson (2009)

and T4 dummy variables with each of the other covariates, allowing maximum flexibility in the specification of the divisional transition probabilities. Several covariates (AGESQ, SCOTIRE, O’SEAS and O’SEAS×RACE) are excluded from the reported versions of [8.3], and the three positional dummies DFR, MFR and FWD are consolidated into a single outfield dummy, OUTF’LD. In [8.2], APPSEA is a significant predictor of a player’s prospects for remaining in employment. Naturally, players who have made regular first-team appearances throughout their careers are more likely to be retained than those who have not.

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Table 8.18 Estimation results: divisional transition

1986–1991 APPSEA AGE OUTF’LD RACE 1991–1996 APPSEA AGE OUTF’LD RACE 1996–2001 APPSEA AGE OUTF’LD RACE

T1

T2

T3

T4

.0343*** 4.08 −.0783*** −2.71 .0906 0.47 .2484 1.08

.0286*** 3.29 −.1396*** −5.00 −.4601* −1.96 .6796*** 2.60

.0023 0.21 −.1332*** −4.84 .1702 0.59 .0329 0.10

.0367*** 3.06 −.1904*** −3.02 −.0971 −0.28 .1277 0.40

.0316*** 3.95 −.0551*** −2.71 −.2501 −1.31 .1800 1.00

.0259*** 3.55 −.0903*** −4.68 −.3757* −1.92 .0200 0.11

.0087 0.96 −.1432*** −4.43 −.0951 −0.38 −.1630 −0.70

.0364** 1.93 −.1758*** −3.31 −.6666* −1.85 .5797* 1.82

.0381*** 3.93 −.0349 −1.30 −.0817 −0.39 −.1511 −0.91

.0345*** 4.21 −.1374*** −5.73 −.6604* −1.75 −.0307 −0.11

.0210** 2.36 −.1332*** −4.53 −.3410 −1.53 −.0996 −0.43

.0181 1.45 −.1202*** −3.30 −.4361 −1.15 .3035 1.12

Notes: Table 8.16 reports the estimation results for γj in [8.3]. *** = significantly different from zero, two-tail test, 1% level; ** = 5% level; * = 10% level. z-statistics for significance of estimated coefficients are reported in italics. Source: Adapted from Goddard and Wilson (2009)

APPSEA is also significant in most of the estimations of [8.3]. The inclusion of AGE and AGESQ in [8.2] allows for a possible quadratic relationship between age and retention probability. There is some variation in the signs and magnitude of these coefficients between the three estimations, but in all cases there is a negative age-retention gradient, which becomes steeper as age increases. In most of the estimations of [8.3], AGE has negative and significant coefficients, reflecting the tendency for older players to accept a reduction in divisional status in order to prolong their professional careers.

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The coefficients on the playing position dummies DFR, MFR and FWD are all negative and significant in [8.2], reflecting the tendency for outfield players’ careers to be of shorter duration than those of goalkeepers. While playing position has a large impact on the retention probability, among those players who are retained it has little further effect on divisional transition. The coefficients on the birthplace dummies SCOTIRE and O’SEAS in [8.1] suggest a tendency for players born outside England and Wales to gravitate towards higher-tier clubs (see Section 8.1). The coefficients in [8.2] are negative and in several cases significant. Employment with an English club may represent a temporary phase in the careers of many players born outside England and Wales, who are less likely to be retained over any five-year interval than their locally born counterparts. Significant coefficients on O’SEAS in the 1986–91 and 1991–6 estimations of [8.1] may reflect the fact that pre-Bosman, overseas players employed in the English league were few in number but typically high-profile. In contrast the insignificant 1996–2001 coefficient reflects much-increased post-Bosman overseas representation at all levels. The relatively large coefficient in the 1996–2001 estimation of [8.2] may be attributable (as before) to reduced mobility barriers post-Bosman. The coefficients on RACE in the estimations of [8.1] for 1991–6 and 1996–2001 are positive and significant. The coefficient for 1986–91 (reflecting the experience of a smaller number of black players) is insignificant. These findings are similar to those for the SCOTIRE and O’SEAS dummies, but suggest another, perhaps less benign, type of selection effect. Black players who appear in the league tend to gravitate towards teams of higher divisional status and are therefore of above average talent. This is suggestive of a form of hiring discrimination, affecting opportunities for black players to become professionals. While the most talented black players are able to overcome the barriers, the less talented are less likely to become professionals than their (equally talented) white counterparts (Goddard and Wilson, 2009). Possible explanations for a selection effect of this kind are discussed below. The 1986–91 and 1991–6 coefficients on RACE in [8.2] are positive and significant, while the 1996–2001 coefficient is insignificant. The 1986–91 coefficients on RACE in [8.3] are positive throughout, and significant in the equation for players starting in T2. For 1991–6 three of the four coefficients are positive, and one is significant (at the 10 per cent level). For 1996–2001 three of the four coefficients are negative and none is significant. Allowing for the smaller numbers of observations used to estimate the equations in [8.3], these results seem consistent with a pattern of selection bias associated with race, perhaps diminishing over time. Negative coefficients on an O’SEAS×RACE interaction in [8.1], one of which is significant and the other two narrowly short of being so, suggest hiring discrimination appears to affect black UK and Irish footballers more than their overseas counterparts. Most overseas players who appear in the English league are established professionals, whose ability to perform at first-team level is already revealed at the point of hiring. In contrast, young indigenous players undergo a lengthy period of

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training and development before their ability to perform at first-team level is revealed, leaving greater scope for prejudicial attitudes on the part of team owners, managers, coaches or scouts to be obscured by uncertainty (Conlin and Emerson, 2006). The O’SEAS×RACE interaction is insignificant, however, in both [8.2] and [8.3]. Uncertainty concerning players’ abilities at the point of hiring is not the only conceivable source of a selection bias that has a greater impact on hiring decisions for indigenous black players than on those for their overseas counterparts. For example, Vasili (2000) argues that a decline in the provision of competitive football in UK state schools since the 1980s has had a disproportionate effect on the professional career prospects of youngsters from disadvantaged backgrounds, including a high proportion of black youngsters. According to this interpretation, the ultimate source of the selection bias lies beyond the confines of the professional sport altogether. Alternatively, customer discrimination could underlie a selection effect. The geographical distribution of employment in football does tend to reflect local population characteristics to some extent, presumably due to mobility barriers within the players’ labour market. Higher-tier clubs are predominantly located in the larger cities, most of which also have sizeable non-white populations, while many lowertier clubs are located in smaller provincial towns where the opposite is true. The ultimate source of the selection effect affecting the recruitment of indigenous black footballers is unresolved, but it is nevertheless apparent that the results point in a similar direction to those of a number of other sports discrimination studies. Football teams that discriminate against black players by failing to recruit from the complete pool of available talent are likely to bear a cost in the form of reduced performance (Szymanski, 2000). Several US studies report that black athletes outperform their white counterparts on average (Kahn, 1991). This finding is commonly interpreted as evidence of hiring barriers. The results reported by Goddard and Wilson (2009) are consistent with such an effect. Conclusion

Chapter 8 describes the employment patterns of professional footballers with English clubs between the mid-1980s and 2009. During this period, the character of English football was transformed by the arrival of a large contingent of overseas players. While the employment of players born in the UK also increased during the 1990s, it declined during the 2000s. Meanwhile the size of the overseas contingent continued to increase relentlessly. During this period there appears to have been a shift in the overall burden of responsibility for the development of young players away from the smaller English clubs towards their larger counterparts. Within the UK there are some sharp regional disparities in the potential for locally born youngsters to become professional footballers. Employment prospects have improved for youngsters born in regions with a preponderance of top-level professional clubs, such as London and the North West; but prospects

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have diminished, in some cases substantially, for youngsters born elsewhere. The employment prospects of youngsters born in certain regions, such as the North East and Scotland, with a strong historical reputation for producing high-quality footballing talent, have been especially hard hit. Patterns of migration by footballers across national borders reflect a wide range of influences, including:  geographical proximity or distance between countries; historical links between countries; home-country attitudes towards nationals seeking employment abroad; host-country attitudes towards foreign nationals seeking employment; salaries and remuneration; the standard and style of play of football in the home and host countries; the level of media exposure football receives in each country; and footballers’ personal relationships and social networks. Despite the England national team having failed to qualify for the Finals of the 2008 European Championships, the English league was the largest single host-country provider of footballers in the Finals. England’s ascendancy within Europe as an importer of top-level footballers is a relatively recent phenomenon. The migration flows that have produced this situation, however, form part of a larger, more complex and long-standing model of international mobility among professional footballers throughout (and beyond) Europe. Empirical evidence on racial discrimination in English football suggests a bias in the employment of indigenous black footballers in favour of teams of higher divisional status. This suggests that a form of hiring discrimination may affect the opportunities for indigenous black players to become professionals. While the most talented tend to be able to overcome whatever barriers exist, less talented black footballers find it harder to do so than their (equally talented) white counterparts. Prejudicial attitudes on the part of those making the hiring decision are a possible source of an effect of this kind. Other sources might include a lack of opportunities for youngsters from disadvantaged backgrounds to participate in competitive football, and geographical variation in the ethnic composition of the population combined with barriers to mobility in the footballers’ labour market. Happily, the available evidence suggests that the extent of discrimination in English football has diminished over time. Notes 1 The conflation of skin colour with race is common practice in the economics literature on racial discrimination. 2 The inclusion of the initial divisional status and retention equations controls for sample selection effects that would otherwise bias the estimation of the divisional transition equation. If common unobservable factors affect both retention and transition, a single-equation transition equation would be subject to selection bias (Heckman, 1979). Similarly, divisional transition probabilities may depend on initial divisional status, but initial status and transition are also affected by common unobservables. A third set of common unobservables may affect initial divisional status and retention. See Goddard and Wilson (2009) for full details of the estimation procedure that corrects for these sample selection effects. 3 DUM18 identifies players not in the data set at age 18, for whom DIV18 is unavailable.

9

The football manager

Introduction

For many years economists have recognised the manager’s role in the production process. In classical and neoclassical theory, individual firms and consumers are the fundamental building blocks of the market economy. The theoretical distinction between the owners, entrepreneurs and managers of firms tends to be rather blurred, because all are assumed to pursue the same objective of profit maximisation. In a highly influential contribution, Coase (1937) reinvented the theoretical role of the firm, by asking why it is that in a free market economy, certain transactions take place outside the domain of the market, within centrally planned and hierarchical organisations known as firms. Coase’s answer was that for certain types of transaction, the costs of gathering information and negotiating contracts prohibit the use of market mechanisms; instead it is more efficient for such transactions to be planned and coordinated consciously. The manager is the individual within the firm who takes responsibility for this coordinating function. In the context of team sports, whatever the outcome of the debate as to whether the league or the individual club is the relevant unit of observation (Neale, 1964; Sloane, 1971; see also Chapter 1), it is clear that the Coasian story has some merit in explaining why sports team production is organised outside the market domain. One can easily imagine that transactions costs would be prohibitive if each football player had to enter into a network of bilateral contracts with ten other players to form a team, and each team (or each set of individuals) had to contract bilaterally with the individuals in other teams to formulate a set of rules and produce a series of fixtures. Section 9.1 discusses the historical development and present-day characteristics of the football manager’s role as the principal planner and coordinator of team affairs. According to the behavioural theory of the firm, the separation of ownership from control is crucial to understanding the way modern corporations operate (Berle and Means, 1932). Here the key insight is that the interests of the owner and the manager may diverge, with implications for the behaviour and performance of the firm. While the owner is concerned with profit maximisation, the manager may 249

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pursue other objectives. In businesses generally, this conflict of interest is important because once hired, the manager cannot necessarily be monitored effectively. If monitoring is imperfect, the manager may devote less than the maximum level of effort towards attainment of the owner’s objectives:  there is a moral hazard problem (Alchian and Demsetz, 1972; Jensen and Meckling, 1976). Agency problems (in this case, managerial shirking) seem likely to be less severe in football than elsewhere. The club’s owners are able to observe the performance of the team each time a match is played, at least once a week. Monitoring is direct and regular, and performance is transparent and easy to measure. In professional football, if the output of the team (measured by its win ratio) is below the maximum that should be attainable given the playing and financial resources at the manager’s disposal, this could be because the manager is not exerting maximum effort. Perhaps more likely, this could simply reflect bad ‘matching’, caused by the owner not having full information about the manager’s characteristics prior to hiring, or by the manager sending misleading signals during the hiring process, overstating his true abilities. Production frontier estimation is an empirical technique for the objective measurement of the manager’s performance while controlling for team quality. Section 9.2 describes the production frontier approach to measuring the managerial input, and reviews the literature on production frontier estimation for professional sports teams. While the measurement of managerial efficiency is an interesting exercise, it does not necessarily capture every aspect of a manager’s performance. Many times, a manager who was deemed a hero yesterday has been transformed into a villain today. All football followers know that one of the defining characteristics of the football manager’s position is its chronic insecurity. The rest of this chapter examines the relationship between managerial change and team performance. Section 9.3 reports tabulations describing a number of salient features of this relationship. The factors that are critical in triggering the decision, taken either by the club or by the manager himself, to terminate a manager’s appointment are investigated more systematically in the next two sections. Section 9.4 reviews findings from the previous academic literature on this topic, and Section 9.5 reports estimations of empirical managerial job departure hazard functions for English football, using match-level data. Section 9.6 examines the relationship between managerial change and team performance from the opposite direction, by considering the extent to which the removal of a manager influences the team’s performance subsequently. According to one view, it is simple common sense for a manager to be replaced when his team is performing badly. Assuming that a more effective replacement can be appointed, team performance should improve post-succession. An alternative view is that a change of leadership is usually disruptive, especially if it occurs while the season is in progress, and tends to make matters worse rather than better. A third view suggests that on average, the appointment of a new manager has no effect whatever on team performance, because performance depends primarily on the playing

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talent available to the team, and not on the managerial input. In this case managerial dismissal is simply a form of scapegoating. Section 9.7 presents an empirical analysis of managerial succession effects in English football. 9.1  The role of the football manager

Most football managers are former professional players. For many football managers, a playing career is the only source of previous work experience; although some enter management having served an informal apprenticeship as a coach or assistant manager. Few football managers come into the job without some previous professional involvement in the sport. The careers of most professional players start at age 16. Many players therefore have only limited educational attainment, and few study in further or higher education. This is in marked contrast to the typical educational attainment of managers in other business sectors. Furthermore, while the majority of managers in industry or commerce are likely to have had formal training, only top-level football managers are required to hold a formal qualification. Since 2003 UEFA has stipulated that anyone employed as a manager in the top tier of any member nation’s league structure for more than twelve weeks, and anyone who manages a team in European competition, must hold a UEFA Pro-Licence.1 In the early days of professional football, the manager was the club secretary. Secretary-managers, as they later became known, ran the club on a day-to-day basis, while a trainer looked after the players. At this time the club secretary’s role was limited. In the nineteenth and early twentieth centuries, responsibility for team affairs rested primarily with the club’s directors and chairman. An ethos of amateurism still prevailed, even within the burgeoning professional sport. In 1903, for example, the directors of Newcastle United asked the senior players to select the team. Most early secretary-managers were from administrative or accounting backgrounds. They might have played football previously at some level, but they were employed because they knew how to run things. Unlike football managers in later periods, most were more highly educated than the players (Carter, 2006). The modern-day football manager role as the person responsible for team affairs first began to emerge during the inter-war period. During this period, it was quite common for a manager to see his players on match-days only. During the rest of the week, the manager would undertake scouting missions, watch other teams play, and carry out administrative duties. Walvin (1994) identifies the growth of a stronger ethos of professionalism within football during the 1920s and 1930s as instrumental in encouraging directors to begin shifting responsibility for performance on the pitch towards the professional manager.2 Two individuals from the inter-war period, Herbert Chapman (Huddersfield Town 1921–5, Arsenal 1925–34) and Major Frank Buckley (Wolverhampton Wanderers 1927–44) typify the evolving new breed of professional, hands-on team manager. Before Chapman’s arrival, Huddersfield and Arsenal were both

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under-achieving clubs. Having enjoyed only a modest career as a player himself, Chapman steered Huddersfield to the first two of three consecutive championships in 1924 and 1925, and then won further titles with Arsenal in 1931 and 1933. The latter was the first of three consecutive championships; tragically, however, Chapman died during the course of the 1934 season, aged 55. Chapman’s success at Arsenal (in particular) was based on a regime of physical fitness, strength and skill previously unseen in the English game. Chapman’s tactical acumen was also impressive: Arsenal are widely credited as the first team to adapt fully to the introduction of the present-day offside law in 1925.3 Arsenal came in with the idea of a stopper centre-half. Previously centre-halfs were allowed to wander, and it now became a pendulum. The stopper centre-halves stayed there and then the two full-backs were like pendulums on a clock. If play was on one wing, one full-back would take it and the other one came back to cover behind the centre-half. You had three forwards up front, two in the ‘V’ point of the ‘W’ with a lot of alternatives. One of those men had two men in front of him and one at the side. He’d got three alternatives with the ball. (Jack Curtis, quoted in Taylor and Ward, 1995, p27–8)

Although he won no major honours with any of the seven sides he managed, Major Frank Buckley is one of the best-known managers of all time. His military background, disciplined approach and personal demeanour seem to belong to a bygone era, but other aspects of his style, including his dealings in the transfer market and his astute handling of the media, mark him clearly as an early prototype of the modern-day football manager.4 I soon realised that Major Buckley was one out of the top drawer. He didn’t suffer fools gladly … his style of management in football was very similar to his attitude in the army … Major Buckley implanted into my mind the direct method of playing which did away with close interpassing and square-ball play. If you didn’t like his style you’d very soon be on your bicycle to another club. He didn’t like defenders overelaborating in their defensive positions  …  Major Buckley also knew how to deal with the press. (Stan Cullis, quoted in Taylor and Ward, 1995, p31–2)

As football’s popularity grew in the 1920s and 1930s, there was an expansion in press coverage. Critical press reports on the team’s performance could be transformed into abuse from the terraces. Increasingly, the secretary-manager came to act not only as a buffer between the directors and the players, but also as a scapegoat for a run of poor results. During the 1930s, the press regularly reported on the performance of teams in terms of the manager’s actions. This gave a certain legitimacy to his role, and fostered a growing sense of self-importance (Carter, 2006). During the post-war period, Matt Busby personified the arrival of the football manager centre-stage, as the guiding spirit behind the football club, which itself came to be seen increasingly as an institution of defining importance to a community, a city or even a nation’s self-identity (Ronay, 2009). Busby was appointed to the post of Manchester United manager in 1945, when the club’s Old Trafford stadium was still badly damaged from wartime bombing. Under Busby’s guidance,

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Manchester United became established as one of the strongest teams in Europe by the late 1950s, before eight players and three coaching staff were tragically killed in a plane crash at Munich airport in February 1958. An outpouring of public grief and sympathy at the time may have been pivotal in Manchester United’s subsequent emergence as the world’s most popular football club. Within another decade, Busby had constructed a second great Manchester United team, which became the first from England to lift the European Cup in 1968. Throughout his two-and-a-half decades as team manager, prior to his eventual retirement in 1971, Busby stood at the helm, exuding an air of calm but unassailable authority and dignity. Although Busby’s longevity as team manager at a major English club was unparalleled at the time, his career provided a template for a number of others who emerged during the 1950s and 1960s and went on to secure equivalent legendary status at their own clubs. In England Bill Shankly (Liverpool, 1959–74), Don Revie (Leeds United, 1961–74) and Brian Clough (Derby County, 1967–73; Nottingham Forest, 1975–93) all fall into this category, as does Jock Stein (Celtic, 1965–78) in Scotland. The charisma and media-awareness of Clough, in particular, formed the basis for a highly successful and sometimes controversial secondary career in TV punditry: a path also followed by many lesser managers who shared some of the same telegenic attributes. The irresistable growth in the popularity and ubiquity of televised football has undoubtedly impacted on the football manager’s job specification, with the capability to communicate effectively via the TV media becoming an essential prerequisite. It often seems that the manager serves as little more than a figurehead, satisfying the media’s insatiable demand for a narrative containing instant heroes and instant scapegoats. The consequences for the football manager’s job security in the television era, documented in some detail in Section 9.3 below, are predictable enough. Apart from media relations, the remit of most managers in modern-day professional football is the selection, supervision and coaching of playing staff, and devising the team’s tactics and strategies (King and Kelly, 1997; Lambert, 1997). During the post-war period, most managers have also taken responsibility for the buying and selling of players, salary negotiations, and various administrative duties. This multi-functional role of the manager still predominates in many lower-­tier clubs. Among the leading clubs, however, as the scale and complexity of the financial and administrative aspects of club management has increased, there has been a shift towards the division of responsibility among teams of specialists in the various functional areas of management, so that the team manager of a large-market club typically assumes full responsibility for first-team playing matters only. The extent of the manager’s influence over player transfers and contract negotiations varies from club to club. Responsibilities for reserve-team and youth affairs, as well as coaching for specialist positions such as goalkeeper, are often delegated among a roster of subordinate coaches and assistants.

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Against a background of chronic job insecurity for the typical football manager, the career trajectories of the two longest-serving contemporary managers at the time of writing, Alex Ferguson (Manchester United, appointed 1986) and Arsène Wenger (Arsenal, appointed 1996), can be deemed truly exceptional. Ferguson has often been characterised as the last representative of a dying breed (Ronay, 2009). This reputation rests upon Ferguson’s authentic working-class upbringing as an apprentice toolmaker in the Clyde shipyards; colourful tales of his persona as dressing-room disciplinarian; a string of prickly and sometimes absurd exchanges with rival managers conducted through the media; and a propensity for bearing grudges against individual journalists or media organisations (including the BBC) that can endure for years. Having accumulated eleven Premier League titles and two European championships with Manchester United to the end of the 2009 season, Ferguson’s credentials as a successful football manager are, of course, unequalled in English football, and may never be surpassed. While Ferguson’s Glaswegian roots, shared with several illustrious predecessors including Busby, Shankly and Stein, seem to hark back to a bygone age, Wenger exudes an aura of cosmopolitan sophistication that has proved challenging to many of English football’s more insular and workmanlike traditions. Despite having access to rather slender financial resources, in comparison with Manchester United at least, Wenger’s Arsenal teams had secured three Premier League titles to the end of the 2009 season. They will, however, perhaps be most fondly remembered for a fluid and skilful style of attacking play that, at its best, has rarely if ever been matched in English club football. 9.2  Measuring the managerial contribution: the production frontier approach

As discussed in Chapter 1, ‘production’ in team sports is unlike that in other business sectors because it cannot take place without the joint cooperation of at least two teams. The requirement that clubs simultaneously cooperate and compete with one another is almost unique to team sports, and has led to debate regarding the status of the sports team as a firm in the economist’s sense (Neale, 1964). Much of the North American professional team sports economics literature assumes an objective of profit or wealth maximisation, and many major league franchises consistently return large operating profits. In English football, as seen in Chapter 6, the story is very different. Sloane (1971) suggests it is more appropriate to think of English football clubs as utility-maximisers. Arguments of the utility function might include playing success, attendance, media recognition and sponsorship, as well as profit. Rottenberg (1956) first proposed the notion of a sporting production function: (T)he product is the game, weighted by the revenues derived from its play. With game admission prices given, the product is the game, weighted by the number of paying customers who attend … the players of one team [are] the factors and all others (management, transportation, ballparks, and the players of the other team), another. (Rottenberg, 1956, p255)

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Managers of professional sports teams can influence performance in two ways. First, taking the collection of playing inputs at his disposal as given in the short term, the manager seeks to maximise the level of performance achieved using these inputs. The manager’s direct contribution depends partly on the quality of his strategic input: the effectiveness of his team selections and tactics. The direct contribution also depends on the manager’s ability to inspire and motivate players. Second, the manager can attempt to improve the level of skill of his existing players over the longer term, or strengthen his squad by dealing in the transfer market. The manager’s indirect contribution depends partly on his effectiveness as a coach in training and developing his existing players, and partly on his skill and astuteness in deciding which players he should buy and sell. In theoretical terms, it is possible to conceive of each team as facing a production set, comprising all technologically feasible means of transforming a given set of playing inputs into a given level of output (measured by the team’s win ratio). Within the production set there is a maximum level of output that corresponds to a particular combination of inputs, or there is a minimum combination of inputs that can be used to produce a particular level of output. Both of these define the limit of technological possibility. A production function defined using the maximum efficiency assumption is known as a frontier production function or a production frontier. The quality of the managerial contribution, or the level of managerial efficiency, can be measured by examining the team’s actual performance relative to the maximum attainable performance (given the quality of its inputs) that would be predicted by the production frontier. If several different teams (or managers) are observed, it is likely that some will be found not to operate on the technologically feasible boundary (too many inputs are being used to produce the boundary level of output; or output is below the maximum that should be attainable). Compared to best practice, these managers are technically inefficient. Neoclassical production functions do not allow for suboptimal solutions, and so exclude the notion of inefficiency. In contrast, the production frontier approach acknowledges that most managers are inefficient, to some extent, relative to best practice. The production frontier approach identifies the frontier, and locates the position of each manager relative to the frontier. Empirical studies of team production begin with Scully (1974), who uses an average production function, rather than a production frontier, to model team output (win percent) in baseball, as a function of playing and non-playing (management, capital and team spirit) inputs. This method of modelling the sporting production process became the norm in early production function studies (Zech, 1981; Scott, Long and Somppi, 1985; Atkinson, Stanley and Tschirhart, 1988; Schofield, 1988; Carmichael and Thomas, 1995). All of these studies assume implicitly that team production takes place at maximum efficiency. In some cases, one or two managerial variables are included on the right-hand side of the estimated equation. Zech (1981), for example, includes the number of years spent managing in major league

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baseball and the manager’s lifetime win-loss ratio. Carmichael and Thomas (1995) include the number of years’ coaching experience. Two approaches to efficiency measurement using production frontiers are prevalent in the literature. One approach focuses on measuring managerial efficiency, while the other concentrates on estimating a team’s efficiency over an entire season. Production or cost frontiers can be fitted using either econometric (stochastic frontier analysis) or linear programming (data envelopment analysis, or DEA) techniques. Frontiers estimated using the former method are stochastic, and those estimated using the latter are deterministic. Among early North American studies, Porter and Scully (1982) find that the contribution of the coach to team performance in baseball is comparable to that of an individual star player. Scully (1994, 1995) compares coach efficiency in baseball, basketball and (American) football. Hofler and Payne (1996, 1997) examine coach efficiency in the NFL and in the NBA. Ruggerio, Hadley and Gustafson (1996) calculate efficiency scores for twenty-four coaches with four or more full seasons’ employment in MLB. Kahn (1993) and Singell (1993) attempt to separate the direct contribution of the manager to team performance (through team selection and tactics) and the indirect contribution (through enhancement of player quality by effective coaching). A conventional production function is used to measure the direct effect. Kahn proxies for managerial performance using the predicted salary, while Singell uses managerial experience. The indirect managerial effect is captured by running separate regressions that compare individual player performance for the season under review with the historical performance of the player. Kahn focuses on the effect of a new manager on player performance, while Singell concentrates on the performance of players once they have moved to a new club. Dawson, Dobson and Gerrard (2000a, 2000b) employ stochastic frontier ­analysis to measure managerial efficiency in English football, using T1 (Premier League) data. An innovative feature is that managerial spells are the unit of observation, enabling the effects of within-season managerial changes to be incorporated. Player talent indices, based on weighted sums of player characteristics and career statistics (age, career appearances, career goals, number of previous clubs, and so on), are used to measure the playing input, based on data from before the season in question. Establishing an ex ante measure of playing quality is important in order to measure the indirect impact of the manager on team output, measured by win percent. Dawson, Dobson and Gerrard (2000a) estimate the temporal variation in managerial efficiency, using a time-varying stochastic production function.5 Both timeinvariant and time-varying managerial efficiency scores are reported. However, the time-invariant specification is found to provide an inadequate representation of the data. Using a similar approach, Dawson, Dobson and Gerrard (2000b) investigate the robustness of estimates of managerial efficiency over a range of estimation methods, model specifications and definitions of input and output variables.

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Dawson and Dobson (2002) investigate the sources of variation in managerial efficiency. First, managers have varying levels of accumulated human capital and inherent managerial ability. Second, clubs differ in terms of their compensation packages and incentive structures for players and managers, and according to the frequency with which they change their managers. Manager human capital is found to be significant in explaining variations in managerial efficiency, as are club-specific factors. Barros and Leach (2006, 2007) use stochastic frontier analysis to measure efficiency scores for twelve English T1 clubs for seasons 1999 to 2003. The cost function has three factor input prices (for labour, and two capital inputs) and three outputs (league points, attendance and turnover). An average (time-invariant) efficiency score of 88 per cent is reported, which suggests that by operating at maximum efficiency the average club could reduce its costs by around 12 percent without affecting its outputs. Kern and Suessmuth (2005) use stochastic frontier analysis to estimate team production functions for the German Bundesliga. Ex ante inputs (fixed wages of the players and the coach) are transformed into ex post sporting success. The output measure takes into account performance in four competitions (domestic league and cup, UEFA Cup and UEFA Champions League). There is wide variation in the reported team efficiency scores. Several recent efficiency studies employ a variant of stochastic frontier analysis, known as the random frontier model (Greene, 2005). In a standard stochastic frontier analysis, the teams are assumed to have the same technological possibilities. If these differ between teams, however, measured technical inefficiency may be overstated. The random frontier model takes heterogeneity into account, by separating technical inefficiency from technological differences between teams. Using data on twelve teams that competed in T1 in England throughout seasons 1999 to 2004, Barros and Garcia-del-Barrio (2008) compare the efficiency scores obtained from several cost function specifications, including a homogenous (standard) stochastic frontier analysis and a random frontier model. The random frontier provides a better representation of the data than the homogeneous frontier. Barros, del Corral and Garcia-del-Barrio (2008) and Barros, Garcia-del-Barrio and Leach (2009) estimate efficiency scores for the Spanish La Liga, by estimating a random frontier model using data from seasons 1996 to 2005. As before, the random frontier model provides the best representation of the data. Frick and Lee (2010) estimate time-varying efficiency scores for German clubs using data from seasons 1982 to 2003. As noted above, deterministic frontiers have also been used to estimate production and cost frontiers based on team sports data, fitted using the DEA linear programming technique. North American examples include Anderson and Sharp (1997), Mazur (1994) and Volz (2009) for MLB; and Einolf (2004) for the NFL and MLB. Haas (2003) uses DEA to measure the productive efficiency of English T1 teams during the 2001 season. Input measures are team payroll as a proxy for playing talent, and the manager’s salary as a proxy for the managerial

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contribution; however, there is no ex ante measure of team quality or manager capability. Outputs are league points and revenues. DEA frontiers are fitted based on both constant returns to scale (CRS) and variable returns to scale (VRS) assumptions concerning the production technology. Barros and Leach (2006) combine sporting and financial variables to estimate a DEA cost frontier, using English T1 data for seasons 1999 to 2003. Inputs are number of players, payroll, net assets and expenditure on stadium facilities. Outputs are league points, attendances and turnover. Efficiency scores are estimated using both CRS and VRS specifications. Teams that are found to be technically efficient using the CRS specification are also technically efficient using the VRS specification, signifying that the dominant source of efficiency is scale. Guzmán and Morrow (2007) estimate a DEA frontier and calculate a Malmquist total factor productivity index to measure changes in productivity over seasons 1998 to 2003 for English T1 teams. Input measures are based on staff payroll (excluding costs relating to non-football activities), directors’ remuneration and other operating costs (lease and rental charges, fixed asset depreciation, training ground costs and professional fees). Outputs are league points and revenues. A CRS specification is adopted. An average efficiency score of around 85 per cent is reported, which suggests that by operating at maximum efficiency the average club could reduce its costs by around 15 per cent. The factor productivity analysis fails to uncover any evidence of improvements in productivity over time. Haas, Kocher and Sutter (2004) estimate a DEA frontier using German Bundesliga data for the 2000 season. Input measures are based on staff payroll (separately for players and managers); and outputs are league points, total revenues and average stadium utilisation (ratio attendance to stadium capacity). Both CRS and VRS specifications are adopted. The measured efficiency scores are not correlated with league position, indicating that athletic performance and efficiency are not synonymous. Haas (2004) estimates a DEA frontier using North American Major League Soccer (MLS) data for the 2000 season. Input measures are again based on players’ and coaches’ payroll; and outputs are league points, numbers of spectators and revenues. In this case the efficiency scores are highly correlated with league performance, and scale is the principal determinant of the level of efficiency. Espita-Escuer and García-Cebrián (2004) use DEA to measure the efficiency of teams in converting attacking moves during the match into sporting success, by applying CRS and VRS specifications to Spanish La Liga data from seasons 1999 to 2001. The input variables are the number of players used, the number of attacking moves, the number of minutes during which the teams had possession of the ball, and the number of shots and headers, all of them throughout the length of the season. Outputs are the number of league points achieved throughout the season. Efficient teams do not always correspond with those that finished highest in the league at the end of the season, implying that highly placed but inefficient teams could have achieved the same results with fewer resources or could have

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improved their results with the same resources. Scale effects are found to be significant, suggesting that a VRS specification is preferred. Garcia-Sanchez (2007) analyses the operating efficiency of the attack and defence of Spanish La Liga teams during the 2005 season. The inputs used are goals scored and goals conceded, and output is measured by total points obtained at the end of the season. Boscá et al. (2009) present a comparative analysis of attacking and defensive efficiency for three seasons (2001 to 2003) in Italian and Spanish football. In a DEA model, the attacking inputs are shots on goal, attacking plays made by the team, balls kicked into the opposing team’s centre area and minutes of possession. The inverse of the attacking inputs are used for the defence. The output for attacking and defensive production is the number of goals scored by a team and the inverse of the number of goals conceded, respectively. The difference between the best and worst teams is wider in Italy than in Spain. In the Italian league the bestranked teams score more goals, concede fewer goals and obtain more points, on average. In Spain, by contrast, the correlations between these indicators are generally smaller. In Italy, league rankings are more highly correlated with measures of efficiency in defence, rather than attack; but in Spain the opposite applies. Although DEA has been used widely in football efficiency studies, the linear programming methodology has two important limitations. First, DEA is reliant upon an assumption that there is no ‘noise’ (or error) in the data being studied. Second, although the fact that there is no requirement to specify a particular functional form for the production technology might be considered a strength, the inability to evaluate the results of a DEA study using the conventional criteria of statistical inference is a weakness. In an attempt to overcome this problem, Simar and Wilson (1999, 2007) use a bootstrap methodology to carry out hypothesis tests on DEA efficiency scores. In a recent application of this approach to sport, Barros, Assaf and Earp (2010) measure the technical efficiency of twenty football clubs in Brazil between 2006–7. Outputs are attendance, total receipts and points in a league. Input measures are based on operational cost (excluding labour costs), total assets and team payroll. Efficiency scores are estimated using a VRS specification. The results reveal that none of the clubs are operating close to full technical efficiency, a finding that contrasts markedly with the results from standard DEA estimation. The authors also find that technical efficiency is correlated positively (negatively) with positive (negative) results on the pitch. Another variant of production function analysis shifts the focus away from quantification of the relationship between inputs used and outputs achieved over an entire football season, towards an analysis of the performance of teams at match level. In the case of English football, this type of analysis draws on the Opta Index, first published in 1996, which provides detailed performance statistics based on records of every touch of the ball in every T1 match, compiled by a team of analysts using videotapes. The ‘play’ records include shots on goal (on-target, off-target and blocked); passes (successful and unsuccessful); dribbles/runs (possession retained and lost); clearances, blocks and interceptions; interventions by

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the goalkeeper (catches and spillages); tackles; free kicks conceded for foul tackles and handballs; and yellow and red cards incurred. Using data from the 1998 season, Carmichael, Thomas and Ward (2000) estimate regressions in which the dependent variable is the difference in scores, and the explanatory variables are the differences between the teams in various ‘play’ variables. Most of the estimated coefficients are correctly signed and many are significant, confirming the importance for match outcomes of accurate shooting, and effective defensive skills including tackles, clearances and blocks. In a follow-up study, Carmichael, Thomas and Ward (2001) use the Opta data in a more aggregated format to estimate season-based production functions for each T1 team. Carmichael and Thomas (2005) examine the empirical relationship between a number of team play measures, interpreted as inputs to a team production function, and the numbers of shots and goals scored by each team in each match, interpreted as outputs. The team play measures include the numbers of passes, dribbles, runs, tackles, fouls, clearances, blocks and goalkeeper saves. To investigate the origins of home-field advantage in differences in play, the empirical analysis is carried out separately for home and away teams. The statistical significance of attack-related team play measures is stronger in regressions for home-team performance; and conversely, the significance of defence-related measures is stronger in regressions for away-team performance. 9.3  Patterns of managerial change in English football

The analysis of managerial change and team performance draws on data for 1,572 managerial spells with English league clubs recorded between the 1973 and 2009 seasons (inclusive). The database includes eighty-five left-censored spells that commenced before the end of the 1972 season. The number of spells that started either at the start of the 1973 season or subsequently, and terminated before the start of the 2010 season, is 1,411. There were seventy-six right-censored spells that started before the end of the 2009 season and continued subsequently into the 2010 season. For the 1,572 managerial spells, Table 9.1 shows the top 50 ranked in descending order of duration, measured in league matches completed. Win ratios are ­calculated (as in previous chapters) by awarding 1 point for a win, 0.5 points for a draw and 0 points for a loss, and dividing the total by the number of league matches played. Of course, in view of the notorious insecurity of the English football manager’s job tenure, the longevity of a spell is itself often a meaningful measure of success. In some cases longevity may reflect attributes or attitudes of the club’s owners, which influence their willingness either to stick with or dismiss a manager during a lean spell. A highly atypical example from the modern era, featuring at the very top of the list, is the extraordinary 1,092-match spell recorded by Dario Gradi of Crewe Alexandra between 1983 and 2007:  a spell that included four promotions and three relegations as Crewe’s divisional status fluctuated between T2, T3 and T4.

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Table 9.1 Managerial spells ranked by duration (matches), English League, 1973–2009 seasons Rank

Manager

Team

Start year

End year Matches Win ratio

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

Dario Gradi Alex Ferguson Ted Bates Brian Clough Tony Waddington John Rudge Bill Nicholson Alan Curbishley John Lyall Bill Shankly Bobby Robson Don Revie Ron Greenwood Joe Harvey Jimmy Frizell Alan Dicks Bryan Flynn Joe Royle Harry Catterick Arsène Wenger Lawrie McMenemy Brian Laws Graham Taylor Tommy McAnearney John King Barry Fry Bertie Mee John Neal Harry Redknapp Arthur Cox Jimmy Scoular Gordon Milne Ken Roberts Bob Paisley Steve Coppell Mike Buxton Frank Clark George Graham Lennie Lawrence Johnny Newman Ronnie Moore Graham Turner David Pleat Benny Fenton Neil Warnock

Crewe Manchester Utd Southampton Nottm Forest Stoke Port Vale Tottenham Charlton West Ham Liverpool Ipswich Leeds West Ham Newcastle Oldham Bristol City Wrexham Oldham Everton Arsenal Southampton Scunthorpe Watford Aldershot Tranmere Peterborough Arsenal Wrexham Bournemouth Derby Cardiff Coventry Chester Liverpool Crystal Palace Huddersfield Leyton Orient Arsenal Charlton Exeter Rotherham Wolverhampton Luton Millwall Sheffield Utd

1983 1986 1955 1975 1960 1984 1958 1991 1974 1959 1969 1961 1961 1962 1970 1967 1989 1982 1961 1996 1973 1997 1977 1972 1987 1996 1966 1968 1983 1984 1964 1972 1986 1974 1984 1978 1983 1986 1982 1969 1997 1986 1978 1966 1999

2007 — 1973 1993 1977 1999 1974 2006 1989 1974 1982 1974 1974 1975 1982 1980 2001 1994 1973 — 1985 2006 1987 1981 1996 2005 1976 1977 1992 1993 1973 1981 1976 1983 1993 1986 1991 1995 1991 1976 2005 1994 1986 1974 2007

1092 883 792 758 701 701 666 634 621 610 572 555 549 546 545 542 540 534 499 494 488 447 434 427 415 414 413 409 401 397 391 390 388 378 376 374 368 363 358 358 355 355 352 347 341

0.492 0.708 0.516 0.574 0.484 0.514 0.582 0.513 0.507 0.650 0.547 0.660 0.468 0.508 0.516 0.476 0.496 0.504 0.584 0.715 0.550 0.519 0.568 0.516 0.564 0.467 0.574 0.550 0.510 0.524 0.474 0.464 0.509 0.692 0.535 0.537 0.507 0.609 0.443 0.510 0.524 0.569 0.523 0.535 0.544

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Table 9.1 (cont.) Rank

Manager

Team

Start year

End year Matches Win ratio

46 47 48 49 50

George Burley Dave Bassett Keith Burkinshaw Howard Wilkinson Harry McNally

Ipswich Sheffield Utd Tottenham Leeds Chester

1994 1988 1976 1988 1985

2002 1995 1984 1996 1992

341 339 336 335 333

0.557 0.506 0.531 0.584 0.482

Source: Rothmans/Sky Sports Football Yearbook, www.soccerbase.com

Others from the modern era featuring prominently in the upper echelons of the top 50 include Alex Ferguson and Arsène Wenger (see Section 9.1). Several managers achieved longevity by steering their clubs through one or more promotion campaigns, before consolidating and achieving further success at a higher level. Brian Clough (Nottingham Forest), John Rudge (Port Vale), Joe Royle (Oldham Athletic) and Graham Taylor (Watford) all fall into this category. Another striking feature of Table 9.1 is the preponderance towards the top end of the list of a number of long-serving managers of T1 clubs at the start of the period. No fewer than eight of the twenty-two T1 managers at the start of the 1973 season had been in post for more than ten years. Pride of place among this group belongs to Ted Bates, whose eighteen years at the helm saw Southampton’s divisional status raised from the old Third Division (South) in 1955, to T1 status in the early 1970s, through two promotions achieved in 1960 and 1966. The list of long-servers at the start of the 1973 season also includes legendary names such as Don Revie (Leeds), Bill Shankly (Liverpool), Ron Greenwood (West Ham) and Bill Nicholson (Tottenham). By contrast, some distance behind Ferguson and Wenger (and failing to make the top 50), the third-, fourth- and fifth-longest serving T1 managers in post at the start of the 2010 season were David Moyes (Everton, appointed in 2002), Rafa Benitez (Liverpool, 2004) and Tony Pulis (Stoke, 2006). At the opposite end of the scale, Leroy Rosenior (Torquay) lays claim to the record for the shortest managerial spell of all time, timed at ten minutes according to football folklore. In May 2007 it was reported that Rosenior, a former Torquay manager, was reappointed by club chairman Mike Bateson, who also sold his majority shareholding in the club on the same day. The purchasers decided immediately to relieve the newly appointed manager of his duties. This spell does not contain a league match, and therefore does not register in the database that is used to compile the tabulations that are reported in this section. The shortest managerial spell that does register belongs to Micky Adams, who oversaw three consecutive defeats by Swansea during the 1998 season before resigning, reportedly over a disagreement about money for signing new players. Using a measure of success that would perhaps be of greater interest to many spectators than longevity, Table 9.2 shows the rankings of the managerial spells by win ratio. For the purposes of constructing Table 9.2, spells of less than twenty matches’ duration (to the end of the 2009 season) are excluded.

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Table 9.2 Managerial spells ranked by win ratio, English League, 1973–2009 seasons Rank Manager

Team

Start year End year Matches

Win ratio

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

Chelsea Chelsea Fulham Leicester Milton Keynes Liverpool Brighton Leeds Arsenal Manchester Utd Chelsea Liverpool Liverpool Liverpool Hull Milton Keynes Wigan Blackburn Oxford Peterborough Leeds Newcastle Gillingham West Bromwich Southend Liverpool Bradford City Chelsea Sheffield Utd Brentford Milton Keynes Hartlepool Preston Everton Leeds Chelsea Plymouth Sheffield Utd Wigan Barnet Swansea Wycombe Manchester Utd Bournemouth Southend Liverpool

2004 2007 1998 2008 2007 1985 2001 2008 1996 1986 2008 1974 2004 1983 1982 2008 1999 1991 1982 2007 1961 1992 1999 1992 1986 1959 1981 2000 2008 2001 2006 2002 2004 1981 1998 1998 2000 1997 2000 1986 2007 2008 1981 1970 1993 1998

0.813 0.813 0.761 0.750 0.739 0.732 0.721 0.720 0.715 0.708 0.700 0.692 0.689 0.673 0.671 0.663 0.663 0.663 0.663 0.662 0.660 0.656 0.652 0.652 0.652 0.650 0.643 0.643 0.642 0.641 0.641 0.638 0.638 0.637 0.634 0.633 0.633 0.632 0.632 0.631 0.631 0.630 0.629 0.628 0.625 0.625

Jose Mourinho Avram Grant Kevin Keegan Nigel Pearson Paul Ince Kenny Dalglish Peter Taylor Simon Grayson Arsène Wenger Alex Ferguson Phil Scolari Bob Paisley Rafael Benitez Joe Fagan Colin Appleton Roberto Di Matteo John Benson Kenny Dalglish Jim Smith Darren Ferguson Don Revie Kevin Keegan Peter Taylor Osvaldo Ardiles David Webb Bill Shankly Roy McFarland Claudio Ranieri Kevin Blackwell Steve Coppell Martin Allen Mike Newell Billy Davies Howard Kendall David O’Leary Gianluca Vialli Paul Sturrock Nigel Spackman Bruce Rioch Barry Fry Roberto Martinez Peter Taylor Ron Atkinson John Bond Barry Fry Gerard Houllier

2007 2008 1999 — 2008 1991 2002 — — — 2009 1983 — 1985 1984 2009 2000 1995 1985 — 1974 1997 2000 1993 1987 1974 1982 2004 — 2002 2007 2003 2006 1987 2002 2000 2004 1998 2001 1993 2009 — 1986 1973 1993 2004

120 32 46 46 46 224 34 25 494 883 25 378 190 84 111 46 46 169 160 111 555 205 46 46 33 610 70 147 60 46 46 29 87 252 145 94 162 34 34 80 107 46 225 156 28 216

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Table 9.2 (cont.) Rank Manager

Team

Start year End year Matches

Win ratio

47 48 49 50

Wigan Stoke Shrewsbury Peterborough

1985 1999 1978 1991

0.625 0.624 0.621 0.621

Bryan Hamilton Gudjohn Thordarson Richie Barker Chris Turner

1986 2002 1978 1992

60 121 33 87

Source: Rothmans/Sky Sports Football Yearbook, www.soccerbase.com

Two Chelsea managers who presided over the club’s exceptional run of success during the mid to late 2000s, Jose Mourinho and Avram Grant, top the list with identical win ratios achieved over spells of differing durations. Ironically, Grant’s brief tenure is viewed in some quarters as unsuccessful, with Chelsea forced to settle for the runners-up position to Manchester United in both the Premier League and the European Champions League at the end of the 2008 season. A third recent Chelsea manager, Guus Hiddink (February–May 2009) achieved a win ratio even higher than those of Mourinho and Grant, but does not feature in Table 9.2 because his spell contained fewer than twenty matches. Even Phil Scolari, abruptly ejected from the Chelsea manager’s post in February 2009 a few months after his appointment at the start of the same season, achieves a creditable eleventh position. Others featuring prominently in Table 9.2 include Peter Taylor (Brighton, Gillingham and Wycombe), the only manager to appear three times in the top 50; and Kevin Keegan (Fulham and Newcastle), Kenny Dalglish (Liverpool and Blackburn) and Barry Fry (Barnet and Southend), each of whom appears twice. Closely wedged together in ninth and tenth positions respectively are the ubiquitous Wenger and Ferguson; from their respective dates of appointment to the end of the 2009 season, the former held a hair’s-breadth advantage over the latter on the win ratio measure. Rafa Benitez (Liverpool) follows a short distance behind. Table 9.2 also includes several recent appointees who achieved early success during spells that were incomplete at the end of the 2009 season, such as Nigel Pearson (Leicester) and Simon Grayson (Leeds). Audas, Dobson and Goddard (1999) discuss a number of factors contributing to the chronic insecurity of the English football manager’s position. On the one hand, match results (the manager’s most important performance measure) are completely transparent, easily interpreted and instantly in the public domain.6 On the other hand, the manager’s ability to influence results is constrained by uncertainty concerning the fitness, performance and motivation of players. Whether or not a group of players will combine to form a successful team has always depended on a mixture of luck and judgement, in proportions that are ultimately impossible to fathom. In any event, each match and each season’s league programme are by their very nature zero-sum affairs, in that are failure for some participants is inevitable. As characteristics of the manager’s position, the combination of direct

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accountability for outcomes that are transparent and public, and imperfect control over the processes that determine the same outcomes, could not be better designed to minimise job security. Whereas inadequate performance in business tends to lead to the loss of customers followed by events such as internal restructuring, acquisition by new owners or liquidation, football clubs are highly resilient, even in the face of catastrophic failure on the field of play or on the balance sheet. This is due mainly to the highly loyal or fanatical nature of their customer base. Relegation to a lower division, or even to non-league status, usually requires some restructuring of finances and personnel, but is invariably accepted by regular spectators in sufficient numbers to ensure that clubs remain viable as going concerns. In accounting terms, all clubs benefit from significant (but intangible) goodwill. But such fierce customer loyalty can generate extreme pressure for the scapegoating of an unsuccessful manager. Finally, the specialised nature of the football manager’s contribution usually makes it difficult for an unsuccessful manager to be accommodated elsewhere within the club by means of an upward, sideways or downward move (as often happens elsewhere in business). The uniformity of football’s ‘production technology’, however, makes the team manager’s function highly transferable between clubs, since the relevant skills tend to be job-specific and not firm-specific. There are perhaps a few rigidities within the managerial labour market that should be considered. At times, many club owners have shown a preference for appointing individuals with a current or past association with the club to the manager’s position. This may be because lower transaction costs are associated with the appointment of an individual who is already known to the owner; or it may be because an ex-player often brings advantages of credibility or popularity with supporters. Either way, however, it seems unlikely that the occasional propensity for clubs to show preference towards insiders (of one kind or another) seriously undermines the conclusion that the managerial labour market is highly flexible and competitive. For the purposes of the empirical analysis that is reported below in Section 9.5, each of the 1,495 managerial departures recorded in the data set is classified as either ‘involuntary’ or ‘voluntary’. This distinction is important for identification of the empirical relationship between team performance and the manager’s job security. While it seems reasonable to expect that poor team performance would lead to involuntary departure, voluntary departure is often a consequence of good performance resulting in the manager receiving a more attractive job offer from another club. In making the distinction between involuntary and voluntary departures, it seems unwise to rely too heavily on the club’s original explanation of the reason for the change as either a ‘dismissal’ or a ‘resignation’. To do so would probably lead to overcounting of the number of voluntary departures, since many ‘resignations’ actually occur in response to behind-the-scenes pressure from the chairman or directors. In extremis, this can take the form of an ultimatum to resign or be sacked (Audas, Dobson and Goddard, 1999).

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In classifying managerial departures as either involuntary or voluntary, any information available on the circumstances at the time of the departure was assessed. Particularly relevant criteria were the team’s performance prior to termination; the nature of any new appointment accepted by the manager immediately after his departure; and the reasons given by the club or the manager for the latter’s departure. Involuntary departures (the majority) include those that were at the club’s instigation, as well as resignations for which there was no obvious explanation other than disappointing results or other pressures emanating from the manager’s current appointment. Voluntary departures include those for which there is clear and tangible evidence that the manager instigated the move. Such evidence is usually in the form of an immediate or imminent move to another job at a club (at home or overseas) of comparable or higher status, or a move to a national team manager’s position. A few recent examples will illustrate the method of classification. Despite some inconsistent results, and press reports of dressing-room discontent, the abrupt termination of Phil Scolari’s short reign as Chelsea manager (summer 2008–­ February 2009) took most observers by surprise. The mode of departure was clearly involuntary. In contrast, Scolari’s successor Guus Hiddink stated consistently that his appointment was only temporary, to the end of the 2009 season. Hiddink’s departure, which took place according to schedule, is therefore classed as voluntary. In summer 2008 Paul Ince left the T3 club Milton Keynes (MK) Dons voluntarily to take charge of Blackburn Rovers in T1. But with Blackburn positioned near the foot of the table throughout the first half of the 2009 season, Ince was ejected from his post, involuntarily, in December 2008. Meanwhile Ince’s successor at MK Dons, Roberto Di Matteo, was enjoying a successful first season in charge. When Tony Mobray left the relegated T1 club West Bromwich Albion voluntarily (to take charge of the Scottish club Celtic) at the end of the 2009 season, Di Matteo was invited to take charge at West Bromwich. His departure from MK Dons is therefore classed as voluntary. Ironically, Paul Ince was subsequently reinstated to his original position as manager of MK Dons. Table 9.3 reports the numbers of involuntary and voluntary managerial departures by season; and Table 9.4 reports the same data reported as yearly averages for bands of four seasons’ duration. Clearly, the level of job insecurity of football managers has increased over time. While there is considerable year-on-year variation in the total numbers of departures, the long-term trend is relentlessly upward. Significantly, the increase in the total is driven almost entirely by increases in the numbers of involuntary departures, while there is no clear upward trend in the numbers of voluntary departures. An increasing tendency for senior clubs to appoint current or recently retired players directly into managerial posts, or to recruit managers from overseas, may account for this pattern. With sixty-one managerial departures, the 1995 season established a new record for managerial turnover, which has never been surpassed. At the end of the 1995 season, the league structure was changed from 22–24 –24 –22 to 20 –24 –24 –24

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Table 9.3 Managerial departures, by season, English League, 1973–2009 seasons Number of departures Season 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 Total

Involuntary

Voluntary

All

26 18 23 22 29 35 23 20 32 32 31 32 29 32 30 26 23 33 34 29 32 29 48 30 35 41 31 37 39 49 31 43 37 42 39 39 43 1204

6 15 9 5 7 10 9 1 15 5 5 6 6 8 8 2 8 4 14 3 8 7 13 9 12 7 7 8 7 11 4 7 3 11 10 10 12 292

32 33 32 27 36 45 32 21 47 37 36 38 35 40 38 28 31 37 48 32 40 36 61 39 47 48 38 45 46 60 35 50 40 53 49 49 55 1496

Source: Rothmans/Sky Sports Football Yearbook, www.soccerbase.com

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Table 9.4 Average number of managerial departures per season, four-season bands, English League, 1974–2009 seasons

1974–1977 1978–1981 1982–1985 1986–1989 1990–1993 1994–1997 1998–2001 2002–2005 2006–2009

Involuntary

Voluntary

All

23.0 27.5 31.0 27.8 32.0 35.5 37.0 40.0 40.8

9.0 8.8 5.5 6.5 7.3 10.3 7.3 6.3 10.8

32.0 36.3 36.5 34.3 39.3 45.8 44.3 46.3 51.5

Source: Rothmans/Sky Sports Football Yearbook, www.soccerbase.com

teams in the four tiers. The transition was made by creating one fewer promotion berth and one additional relegation berth in each tier for one season only: a measure that appears to have created sufficient panic at boardroom level to cost many managers their jobs. Financial pressures on many T2, T3 and T4 clubs created by the collapse of ITV Digital (see Chapter 6, Section 6.5) may have been a contributory factor to a near-repeat of this record number of departures during the 2002 season. It appears that team managers may have faced even greater pressure than usual to deliver a winning team that would generate gate revenues to compensate for the disappeared broadcast revenue. Similarly, financial pressures on many football clubs, exacerbated by the economic recession of 2008–9, may have contributed to a further outbreak of boardroom panic, and the third-highest all-time total of fifty-five departures recorded in the 2009 season. Table 9.5 reveals a high level of monthly variation in the incidence of managerial departure. 1,036 of the 1,464 departures recorded between the 1974 and 2009 seasons (70.8 per cent) took place during the course of the season, and 428 (29.2 per cent) during the close season. Of the 1,036 within-season departures, 152 (14.7 per cent) were voluntary; and of the 428 close season departures, 134 (31.3 per cent) were voluntary. Departure within the season is therefore relatively more likely to be at the club’s behest, while departure during the close season (when most managerial contracts tend to expire) is more likely to be at the manager’s behest. October and November, when failure to realise overoptimistic pre-season aspirations first becomes inevitable for many clubs, are the peak months for within-season departures. December and January, perhaps the latest time at which a new appointment might reasonably be expected to bring about a change of fortune within the current season, is another period of high turnover; so too are March, April and May, when many clubs begin planning for the next season. There appears to be a (slight) lull in the rate of turnover during the month of February.

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Table 9.5 Managerial departures by month, English League, 1974–2009 seasons Involuntary August September October November December January February March April/May Close season

Voluntary

32 92 123 122 99 105 100 108 103 294

All

8 13 25 24 25 17 9 16 15 134

40 105 148 146 124 122 109 124 118 428

Source: Rothmans/Sky Sports Football Yearbook, www.soccerbase.com

Table 9.6 Managerial departures by tier, four-season bands, English League, 1974–2009 seasons

1974–1977 1978–1981 1982–1985 1986–1989 1990–1993 1994–1997 1998–2001 2002–2005 2006–2009 Involuntary Voluntary Total

T1

T2

T3

T4

All

31 28 30 28 27 34 31 29 40 203 75 278

21 31 37 34 43 50 49 44 52 288 70 361

36 46 39 35 37 47 52 46 59 306 79 397

40 40 40 40 50 52 45 65 54 356 53 426

128 145 146 137 157 183 177 185 206 1155 277 1464

Source: Rothmans/Sky Sports Football Yearbook, www.soccerbase.com

Table 9.6 suggests that managerial insecurity is greater in the lower tiers than in the higher tiers. Both the number of involuntary departures and the total number of departures vary inversely with divisional status. If, as seems likely, recent relegation often triggers managerial departure, the pattern might be explained by the fact that while no team can be relegated to T1, most teams, with the exception of those promoted (or in earlier times elected) from non-league, enter T4 as a result of relegation. In contrast, the incidence of voluntary departure is highest in T3, which appears to be the most effective launch pad for a successful manager seeking another post at a higher level.

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Table 9.7 Average duration (matches completed) of terminating managerial spells, four-season bands, English League, 1974–2009 seasons

1974–1977 1978–1981 1982–1985 1986–1989 1990–1993 1994–1997 1998–2001 2002–2005 2006–2009

Involuntary

Voluntary

All

146.5 109.1 98.7 102.1 101.4 86.3 80.3 83.1 77.8

193.9 117.7 182.5 149.9 129.7 127.0 101.4 102.3 135.0

159.8 111.2 111.4 111.2 106.6 95.4 83.8 85.7 89.7

Source: Rothmans/Sky Sports Football Yearbook, www.soccerbase.com

Table 9.7 reports the average durations (in matches completed) of terminating managerial spells in four-season bands for the period 1974–2009. As expected in view of the upward trend in the numbers of departures, the trend in the average duration of managerial spells is relentlessly downward. By the end of the period, the duration of the average managerial spell was around two seasons. The average duration figure for seasons 1974–1977 is magnified by the closure of several longduration spells with top-level clubs that were noted previously (see Table 9.1). The era when even a moderately successful manager could expect to remain in post for a period as long as fifteen or twenty years, a common occurrence before the Second World War and during the 1950s and 1960s, was drawing rapidly to a close; and several star performers from the latter part of this era (Shankly, Nicholson, Catterick, Revie) were, by the mid-1970s, among a handful of survivors of a dying breed. Table 9.8 reports the average durations of terminating spells by tier and mode of departure (involuntary or voluntary), and the average win ratio of terminating spells. The latter is invariably higher for voluntary departures than it is for involuntary departures. 9.4  Determinants of managerial change

Grusky’s (1963) investigation of managerial succession in North American baseball appears to have been the first academic study to consider the possibility of a bi-directional link between managerial change and team performance. For sixteen professional baseball teams, Grusky obtains a negative correlation between the number of managerial changes and the average standing of each team, for both of the periods 1921–41 and 1951–8. In other words, teams that made more managerial changes tended to underperform. Grusky also obtains a negative correlation between the change in the average duration of managerial tenure between these two periods, and the change in average standing. The teams that increased their

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Table 9.8 Average duration (matches completed) and average win ratio, in terminating managerial spells by tier, English League, 1974–2009 seasons Involuntary

Voluntary

All

Average duration (matches completed) of terminating managerial spells T1 115.9 183.5 T2 99.9 135.8 T3 97.8 133.2 T4 78.1 82.7 All tiers 95.2 137.3

134.1 106.9 105.4 78.7 103.4

Average win ratio of terminating managerial spells T1 0.471 T2 0.457 T3 0.455 T4 0.420 All tiers 0.447

0.485 0.471 0.475 0.432 0.463

0.525 0.529 0.546 0.510 0.529

Source: Rothmans/Sky Sports Football Yearbook, www.soccerbase.com

rate of managerial turnover the fastest tended to experience a decline in average standing. Grusky (1963) and Gamson and Scotch (1964), in a comment on the Grusky paper, go on to identify three possible theories of managerial turnover: • The common sense theory. When a team is underperforming, the manager is held accountable and is likely to be replaced. If a more effective replacement is hired, or if the incoming manager can learn from the mistakes of his predecessor, team performance should improve post-succession. This would be sufficient to explain Grusky’s finding of negative correlation between managerial turnover and team performance. • The vicious circle theory. Again, poor performance tends to trigger managerial change. But the disruptive effect of a change of leadership, particularly if it occurs within-season, tends to make matters worse rather than better. Faltering teams become trapped in a vicious circle of high managerial turnover and declining performance. Grusky’s empirical results therefore reflect a bi-directional relationship between turnover and performance. • The ritual scapegoating theory. On average, the appointment of a new manager makes no difference to team performance. The latter depends primarily on the supply of playing talent and not on the managerial input. A change of manager is not and cannot be expected to improve matters overnight. The supply of playing talent is determined primarily by the effectiveness of scouting and player development programmes, for which club owners are ultimately responsible. Grusky’s inverse relationship between turnover and performance is an effect of scapegoating:  during a poor spell, owners can appease disgruntled spectators

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and perhaps deflect attention from any shortcomings in their own contribution, by offering the manager’s head in ritual sacrifice. Grusky himself argues in favour of the vicious circle, bi-directional causality theory, on the grounds that it captures a wider range of possible interactions between performance and succession than the common sense theory, in which causality is unidirectional. Gamson and Scotch are more hesitant to discard the latter, but in the absence of any clear evidence as to whether a change of manager actually does affect team performance, argue that the ritual scapegoating explanation should be adopted as a working hypothesis. This debate provided sufficient motivation for a number of other researchers to seek to determine whether or not a change of manager affected team performance after the change took place. These studies are reviewed in Section 9.6. Scully (1992, 1994, 1995) and Fizel and D’Itri (1997) investigate the common sense theory for several North American professional team sports, using more sophisticated empirical techniques than were available to the first-generation researchers whose findings are outlined above. In developing a model of managerial departure in MLB, the NBA and NFL, Scully views the role of the manager as twofold. First, he seeks to maximise points scored subject to the quality of his team’s offensive skills relative to his opponents’ defensive skills, and to minimise points conceded subject to the quality of his team’s defensive skills relative to his opponents’ offensive skills. Second, he seeks to convert the realised points scored and conceded into the maximum attainable win ratio. Scully assumes that all managers perform the first of these tasks with equal efficiency. But there are differences between managers in terms of the efficiency of the conversion of points into win ratios. Each manager achieves an efficiency score based on the residuals, ε, from a regression of the form: ln( W ) = β0 + β1ln(S / OS) + ε 

[9.1]

where W is the win ratio and S and OS are points scored and conceded, respectively. Scully (1995) obtains ε from OLS estimation of [9.1]. It is shown that career efficiency is positively related to career length, demonstrating (indirectly) that efficiency does influence the decision to terminate the manager’s appointment. Evidence is also found that in baseball and basketball, player-managers are less efficient than their non-playing counterparts, and that average efficiency increased over time in all three sports. Scully (1995) models the decision to terminate the manager’s appointment directly. In principle the decision to terminate or retain should be based on a comparison between the actual and the maximum attainable win ratio, given the quality of playing resources at the manager’s disposal. In practice, however, many other factors also come into play: owners’ subjective judgements about the quality of their own and their opponents’ players; the manager’s relationships with both

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the owner and the players; the manager’s past experience; the possibility that the owner may wish to sacrifice the manager primarily in order to send signals to players, supporters or the media; and last but not least, the influence of luck on team performance. In Scully’s empirical estimations, the dependent variable is a 0–1 dummy that indicates either continuation or termination of the manager’s position within or at the end of each season. The independent variable is the team’s league standing at the end of the season (or at the time of departure for within-season departures). Although this measure is crude because it takes no account of either playing strengths or managerial efficiency (as defined above), it is justified on the grounds that ‘[f]or both owner and manager, [the club’s standing] is the bottom line’ (Scully, 1995, p161). No distinction is made between involuntary and voluntary managerial departures. The linear probability model and logit and probit are used for estimation. The main finding, that in both sports the decision to terminate is highly sensitive to league standing, is robust across all estimation methods. Scully (1994) suggests several technical improvements and refinements in the estimation of managerial efficiency, and the modelling of the decision to terminate the manager’s appointment. Equation [9.1] is estimated as a stochastic frontier in order to obtain the managerial efficiency scores. The latter (rather than league standings) are the main explanatory variable in regressions that model the decision to terminate the manager’s appointment, making this decision dependent directly on the manager’s own performance, rather than on player quality. Regressions are estimated in the form of survivor functions. The main finding is that efficiency exerts a strong positive influence on average managerial survival time. Fizel and D’Itri (1997) investigate the decision to terminate the coach’s appointment in US college basketball. Efficiency scores are generated by comparing win ratios with standardised measures of own-team playing talent and opponent strength. Playing talent is measured ex ante and independently of team performance, using a ‘talent index’ compiled from expert assessments of each player’s talent when he first entered college. Ex ante measurement of inputs avoids most of the simultaneity problems inherent in the usual ex post measures based on observed performance. Simultaneity problems normally arise because player performance depends partly on the coach’s contribution, which the model seeks to capture in the error term and not in the input measures. In probit regressions indicating either continuation or termination of the coach’s position, and estimated separately for involuntary and voluntary departures, Fizel and D’Itri find that efficiency and playing talent both affect the probability of involuntary departure in the expected direction. The number of years’ service is positively related to the probability of departure. The significance of the efficiency and playing talent variables disappears, however, if the win ratio is also included among the covariates. This might suggest that a lack of adequate playing resources is an ineffective mitigating plea for a coach failing to achieve a sufficient proportion of wins.

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In the recent North American literature, attention has focused on the extent to which managerial survival is influenced by the race of the coach (manager). For example, Volz (2009) shows that after controlling for team performance and personal characteristics, baseball managers from ethnic minorities are on average 9.6 percentage points more likely to survive to the following season. Accordingly, the relatively small number of ethnic minority managers in MLB is not due to a lower probability of survival. A similar result is obtained by Mixon and Trevino (2004), in a study of US college football coaches. Other things being equal, black coaches face a significantly lower dismissal probability than their non-black counterparts. However, Kahn (2006) and Fort, Lee and Berri (2008) identify no significant differences in the firing and retention of NBA coaches by race. For football, Audas, Dobson and Goddard (1999) examine the causes of manager departure (both voluntary and involuntary) in the English league by estimating competing-risks hazard functions specified in accordance with the Cox proportional hazards model. The job departure hazard is found to be dependent on both recent match results, and the win ratio achieved over the entire managerial spell. The probability of being fired is positively and significantly correlated with age, but not with previous managerial experience. Section 9.5 presents results from the estimation of a similar empirical model, based on an updated version of the data set that was used in the 1999 study. Bachan, Reilly and Witt (2008) focus on the determinants of (involuntary) managerial departure using English match-level data for ninety-one clubs covering seasons 2003 to 2005. A discrete-time logit regression is used, on the grounds that it is less restrictive in dealing with time-varying covariates than the competing-risks specification. The fact that each manager is observed on several occasions permits the inclusion of controls for unobservable manager heterogeneity (ability), in the form of random- or fixed-effects. The teams are separated into two groups: those positioned in or near the relegation zone at the start of each month, and those that were not. The probability that the manager of a relegation-threatened team will be dismissed is estimated to be 3.6 percentage points higher than the probability in the case of a more successful team. Salomo and Teichmann (2000) estimate logit regressions to model managerial departure, using German Bundesliga data for the period 1979–98. As in other studies, poor performance in the most recent few matches increases the probability of departure. The appointment of a new board president increases the likelihood that the manager will be dismissed; and managers of teams exposed to high levels of media coverage (especially when performing badly) are more likely to be dismissed. Hautsch et al. (2001) estimate probit regressions, Weibull regressions and Cox proportional hazard functions, using German Bundesliga data for the period 1963–98. The managers of top teams have significantly longer survival times than the managers of middle- and lower-ranked teams. The probability of dismissal is higher for older managers, while the survival probability increases with the number of previous jobs. More recently, Frick, Barros and Passos (2009) apply four

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specifications to German Bundesliga data from seasons 1982 to 2003. In all specifications, higher-paid managers have the same prospects of survival as low-paid managers; but the managers of large-market teams are at higher risk of dismissal than managers of small-market teams. De Dios Tena and Forrest (2007) examine twenty within-season (involuntary) managerial departures in the top division of the Spanish La Liga during the 2003, 2004 and 2005 seasons, by estimating probit regressions. The prospect of possible relegation is a major cause of involuntary managerial departure. Other explanatory variables include the time of season (represented by match round), and a measure of ‘managerial efficiency’ (number of places by which a club’s current league position is superior to its ranking in terms of its (wage) budget). Dummy variables identify teams having already dismissed a manager in the current season, and a defeat in the team’s most recent match. The coefficient on the latter is significant, suggesting that the timing of the decision to remove a manager is heavily influenced by the most recent match result. Most of the studies reviewed above use either logit or probit regression, or parametric or semi-parametric hazard function models. In constrast, Frick, Barros and Prince (2010) estimate a mixed logit model, in which there is variation in the coefficients of the model between different managerial spells. The idea is to allow for heterogeneity into the manner in which the characteristics of the manager or club determine the probability of dismissal. German Bundesliga data are used, covering 398 team-season observations featuring 39 clubs over seasons 1982 to 2003. The probability of managerial departure (both involuntary and voluntary) is positively related to the manager’s salary and the team payroll, and negatively related to the win ratio. Previous managerial experience reduces the probability of departure. A novel and interesting perspective on the topic of managerial tenure is provided by Aidt et al. (2006), who fit power-law distributions to data on the durations of 7,183 managerial spells recorded in several sports and countries over the period 1874–2005:  football (England, Switzerland, France, Spain and Germany), baseball (US and Japan), and American football (the NFL). According to a power-law distribution, the probability than any individual managerial spell in sport i achieves duration t (in years) and terminates before t+1 takes the form p(t) = b(i)t a(i) 

[9.2]

where a(i) is the key parameter that describes the shape of the power-law distribution, and b(i) is a normalising constant. It has been shown elsewhere that power-law distributions characterise a wide variety of both natural and social phenomena. Furthermore, the emergence of distributions of this kind can be replicated by means of stochastic simulation, in which the underlying processes that generate the data are entirely random. As explained by Aidt et al. (2006, p698), ‘a surprising implication is that factors, such as talent, effort choices, and selection

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and matching processes that normally play a role in tenure, are not essential for understanding the dynamic evolution of hiring and firing in competitive sports’. Aidt et al. develop a theoretical model that is capable of generating a power-law distribution for job tenure, in which the processes that determine success or failure are completely random. The core model is based upon a round-robin tournament that links the managers (and teams) in a simple network. For example, twenty managers (teams) play against each other twice, once at home and once away, and in each game the win-draw-lose probabilities correspond to those observed in English football over the long term. The probabilities are independent of the identities of the two managers. Managerial turnover is governed by a number of rules that relate job tenure to performance. The model is initialised with twenty randomly selected managers, each with two attributes, reputation and tenure. Each manager’s reputation when the season starts is a random positive integer with a constant probability distribution between 0 and the poaching threshold (see below), and each manager starts with a random tenure duration distributed uniformly between one and forty years. Each manager’s reputation is enhanced by a win and diminished by a loss. Job tenure depends upon the evolution of the reputation variable. The manager remains in post while reputation remains within a lower bound (the ‘firing’ threshold) and an upper bound (the ‘poaching’ threshold). Tenure also terminates due to relegation, or retirement (when the age variable exceeds an ‘ossification’ threshold). With appropriate choices for the threshold parameters, the model generates a power-law distribution for tenure duration, with exponents in the range 21). (ix) Home-team double result (25 points for a win, 10 points for a draw, based on half-time and full-time scores added together). (x) Sum of minutes in which all goals are scored. (xi) Sum of minutes in which home-team goals are scored. (xii) Number of minutes during the match in which home team was leading. (xiii) Time (minutes) when k’th goal is scored (defined for various k, 90 for 0–0 draw). (xiv) Time (minutes) when k’th home-team goal is scored (defined for various k, 90 if home team fails to score k goals). (xv) Time (minutes) when last goal is scored (0 for 0–0 draw). (xvi) Time (minutes) when winning goal is scored (0 for any draw). Indices equivalent to (iv), (v), (vi), (vii), (ix), (xi), (xii), (xiv) are also defined for the away team. Other football spread betting markets, based on corners, include total corners, difference between the two teams’ corners, multicorners (the product of the numbers of corners taken in each half of the match), and four flags (the time in minutes that elapses before at least one corner has been taken from each of the four corner positions). Fitt (2009) derives formulae for the fair values of each of the match results and goals-based spread bets listed above, based on an assumption that the total numbers of goals scored by each team during each match follows a Poisson

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distribution. In order to apply these formulae, the bettor needs to supply numerical values for the Poisson means or expected goals scored by each team. These values might be inferred from the centre spreads for bets (i) and (ii); or the bettor might decide to take an independent view of the correct expected values for any particular match. In formulating a spread-betting strategy in a situation where multiple betting opportunities are available, Fitt (2009) suggests the bettor faces a choice analagous to the choice faced by the risk-averse investor in Markowitz’s (1952) portfolio theory. The investor (bettor) seeks to create a portfolio of assets (bets) that either maximises the expected return for any given target level of risk, or minimises the risk for any given target expected return. Risk is measured by the variance of the return on the portfolio of assets (bets). In fact, the analogy between spread betting on football and Markowitz’s portfolio theory is imperfect. In the latter the solution to the risk-averse investor’s problem is to invest some proportion of his or her total fund in a unique selection of risky assets known as the ‘optimum portfolio’, and invest the remainder of the fund in a risk-free asset. The definition of the optimum portfolio is the same for every investor, regardless of their individual preferences concerning target expected return and acceptable levels of risk. In the case of spread betting, all of the risk is concentrated into 90 minutes’ play, and no alternative risk-free asset exists that would offer a meaningful return over such a short period. Therefore the bettor’s sole decision is the selection of the unique optimum portfolio of risky bets. For any array of bets for which the expected returns and variances have been evaluated, the computation of the optimal portfolio is a routine, mechanical task. Accordingly, Fitt (2009) concludes that there is only one unique combination out of any available selection of spread bets that any bettor need ever consider. The optimum portfolio approach to the problem of selecting a portfolio of bets offering different combinations of expected return and risk offers an alternative betting strategy to the strategy based on the well-known ‘Kelly criterion’. Kelly (1956) examines how a bettor with a fixed initial fund and an edge over the bookmaker, which gives a positive expected return for each bet placed, should place bets over a sequence of betting opportunities in order to maximise his overall expected return, in the case where no further bets are placed if the fund is wiped out.1 Although the expected return for each bet is maximised by staking the entire fund, this strategy would not maximise the bettor’s overall expected return, since it would offer a low probability of a large win on the first bet and a high probability of being wiped out by the first bet, and being unable to exploit the edge in any future bets. Kelly shows that the bettor’s optimal strategy is to stake a fraction of the remaining fund on each bet, with the fraction chosen so as to maximise the expectation of the natural logarithm of the fund’s value after the bet is settled. The optimal fraction for each bet is a function of the odds, the edge, and any taxes or commission payable on the bet, but it does not depend on the size of the fund. The optimal

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stake for each bet, however, is a function of the size of the fund, and decreases pro rata if the fund is depleted by a run of losing bets. In its original form, the Kelly criterion is applicable for bets with a discrete (typically binary) distribution of possible outcomes. Haigh (2000) and Chapman (2007) examine the adaptation of the Kelly criterion for spread bets, for which the outcomes may be considered as following a continuous distribution. The optimal fraction is shown to be a function of the distribution of payoffs. Fitt, Howls and Kabelka (2006) examine the valuation of in-play spread betting markets, which operate dynamically while matches are underway. Arrivals of goals and corners are modelled as Poisson processes, with arrival rates that are assumed, for simplicity but (as we have seen in Chapter 5) probably counterfactually, not to change over the course of the match. As before, the bets are valued conditional upon numerical values supplied by the user for the Poisson means or expected goals scored by each team. Using simple probability theory, a fair value can be calculated for each spread bet at any stage in the match, conditional on the state of the match at that time (defined, for example, by the number of goals already scored or corners already taken, their timings, and any other information that is relevant to the bet in question). A variance can also be computed, to measure the riskiness of the bet. Fitt, Howls and Kabelka explore the variation of the fair value and the variance over the duration of the match, and the variation as relevant events occur (for example, when a goal is scored or a corner is taken), for various spread bets. For matches played during the 2004 European Championships (Euro 2004), the spreads quoted by online bookmakers appear to be highly consistent with the theoretical valuations. Sentiment bias in betting markets

Sentiment bias in team sports betting markets is the subject of several recent studies. Betting firms might offer more favourable odds for bets on wins by popular teams, in an attempt to attract larger volumes of business by shading margins. Alternatively, bettors might tend to form upwardly biased assessments of the win probabilities for the teams they support, and betting firms might attempt to exploit this tendency by offering downwardly biased odds to those bettors. Forrest and Simmons (2008) test for sentiment bias using online betting odds data for top-tier football matches in Spain’s La Liga and the Scottish Premier League. In both cases, there is a large disparity between the popularity of the two largest-market teams (Barcelona and Real Madrid in Spain; Celtic and Rangers in Scotland) and the rest, suggesting that these leagues should provide promising opportunities for the investigation of sentiment bias. Consistent with a model of profit-maximising behaviour by bookmakers operating in a competitive market, the odds offered for wins by the most popular teams are found to be relatively favourable. Similarly, in an analysis of betting odds for club football matches played in the English Premier League and Football League between seasons 2001 and 2008,

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Franck, Verbeek and Nuesch (2008) estimate probit regressions in which the dependent variable is coded 1 for a winning bet and 0 for a losing bet, and the explanatory variables are the betting odds, and proxies for the relative popularity of the two teams based on attendance data and an indicator of the volume of press coverage received by each team, both from the previous season. In the latter part of the sample period, the odds for a win are found to be positively related to the popularity of the team concerned. This suggests that betting firms may offer more favourable prices in order to attract betting volume evoked by sentiment. In an empirical analysis of betting odds data for international and European club football matches, the prior of Page (2009) is that an ‘optimistic bias’ on the part of supporters is exploited by bookmakers who offer less favourable odds. Page examines whether betting firms located in various countries offer downwardbiased odds for wins by teams from their own country, and whether the odds offered by all betting firms for wins by British teams are downward biased. If there is an optimistic bias, the latter pattern might be explained by the fact that the betting market in the UK (relative to population) is substantially larger than betting markets in other European countries. The empirical analysis, based on regressions of the returns for individual bets against the odds and dummy variables for bets on British teams and for bets on teams from the same country as the betting firm, reveals no evidence of optimistic bias; on the contrary, there is some evidence that British betting firms offer upwardly biased odds for wins by Wales, Scotland and Northern Ireland in international matches. Sentiment bias is investigated from a different angle by Palomino, Renneboog and Zhang (2009), who use share price data on listed football clubs in the UK to examine the stock market reaction to the publication of the betting odds for forthcoming matches of the teams concerned, and to the results of the same matches. The market does not react to the publication of betting odds, but share prices tend to increase rapidly following match wins, and to decrease rather more slowly following defeats. The finding that football club share prices are sensitive to individual match results replicates results reported previously by Dobson and Goddard (2001) and Gannon, Evans and Goddard (2006). The stock market response to victories seems to contain an element of overreaction: the positive share price effect is apparent even for victories which, according to the betting odds, were strongly anticipated. This feature is attributed to a form of optimistic bias, being driven by investor sentiment rather than by rational expectations. However, the negative share price reaction to defeats is weaker for defeats that were strongly anticipated, in accordance with the rational expectations hypothesis. Overall, there is an element of asymmetry between the stock market’s reactions to victories and defeats. Similarly, Bernile and Lyandres (2008) analyse share price data on twenty stock market-listed football clubs from eight European countries which participated in European club competition between the 2000 and 2006 seasons. The ex ante probabilities of match outcomes implied by prices of contracts traded on betting

A forecasting model for half-time/full-time outcomes

365

exchanges are biased, on average, both relative to the actual distribution of match results and relative to the probabilities implied by bookmakers’ odds. It is argued that betting exchange odds data provide a superior representation of bettor or investor sentiment than betting firms’ odds data. The stock market reaction to match results is asymmetric: on average, losses result in negative returns that are larger in absolute terms than positive returns following victories. This pattern is attributed to the presence of an optimistic bias in investors’ ex ante assessments of the relevant win probabilities. 12.2  A forecasting model for half-time/full-time match outcomes

The next three sections of Chapter 12 present a retrospective analysis of the informational efficiency of the fixed-odds betting market on half-time/full-time match outcomes in English League football. Section 12.2 begins by specifying a model to generate probabilistic forecasts for permutations of half-time and fulltime match outcomes. Section 12.3 presents some comparisons of the forecasts obtained from the model with the odds posted for fixed-odds betting by five UK high-street bookmakers. Finally, Section 12.4 tests for the informational efficiency of the half-time/full-time fixed-odds betting market, by examining the prospects for the formulation of a profitable betting strategy based on the forecasts of the model. In the half-time/full-time match outcomes betting market, bettors choose between nine bets on any match, corresponding to the nine possible permutations of outcomes (states of the match) at half-time and at full-time. In order to model a match outcomes dependent variable with this structure, two ordered probit regressions are required: a ‘first-half’ model to generate unconditional probabilities for the three possible outcomes (states of the match) at half-time; and a ‘second-half’ model to generate probabilities for the three possible outcomes at full-time, conditioned on the half-time outcome. The model that is developed in this chapter allows for a non-zero covariance between the first-half and second-half disturbance terms for the same match. Probabilistic forecasts for the nine possible permutations of half-time/fulltime outcomes can be generated from an extended version of the results-based forecasting model (see Section 4.4). In the extended version of this model, it is assumed that the half-time outcome of the match between teams i and j, denoted y0,i,j, depends on the unobserved variable y*0,i,j, and a ‘first-half’ disturbance term ε(F) i,j, as follows: Home team leading: R0,i,j = 1 if µ 0,2 < y*0,i,j + ε (F) i,j Teams level: R0,i,j = 2 if µ 0,1 < y*0,i,j + ε (F) i,j < µ 0,2 (F) * Away team leading: R0,i,j = 3 if y 0,i,j + ε i,j < µ 0,1

[12.1]

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Similarly, the full-time outcome of the match between teams i and j, conditional on the half-time outcome y0,i,j = k for k = 1,2,3, depends on the unobserved variable y*k,i,j, and a ‘second-half’ disturbance term ε(s)i,j , as follows: Home win: Rk,i,j = 1 if µ k,2 < y*k,i,j + ε (s) i,j (s) * Draw: Rk,i,j = 2 if µ k,1 < y k,i,j + ε i,j < µ k,2 Away win: Rk,i,j = 3 if y*k,i,j + ε (s) i,j < µ k,1

[12.2]

In [12.1] and [12.2], it is assumed that the latent variables y*k,i,j for k = 0,1,2,3 are linear functions of a set of covariates, which are defined using data that are available before the match is played. The covariates are the same as those used in the results-based forecasting model reported in Section 4.4. The magnitudes and statistical significance of the estimated coefficients in the half-time/fulltime outcomes model are broadly similar to those in the full-time results-based model (see Section 4.4 and Table 4.5). To conserve space the estimation results for the half-time/full-time outcomes model are not reported. In the estimations of [12.1] and [12.2], allowance is made for a separate pair of values for the cut-off parameters μk,1 and μk,2 for each football season within the estimation period. This allows for variation over time in the overall proportions of matches producing each of the nine possible half-time/full-time outcomes. It is assumed that the joint distribution of the first-half and second-half (S) (F) (S) ­disturbance terms ε(F) i,j and ε i,j is bivariate normal, with E[ε i,j ] = E[ε i,j ] = 0, (F) (S) (F) (S) (F) (S) var[ε i,j] = var[ε i,j] = 1, and cov[ε i,j, ε i,j] = corr[ε i,j, ε i,j] = σ, where σ is an ancil(S) lary parameter to be estimated. The prior is σ>0. ε(F) i,j and ε i,j allow for all factors other than those included among the defined model covariates that may influence the match result. Some such factors, including good or bad luck with refereeing decisions or the ‘run of the ball’, may operate quite randomly, with no statistical association between the size and direction of the effects in the first and second halves of the same match. Other factors, such as player absences due to injury or suspension, or factors relating to playing conditions or the crowd that tend to favour one team over the other, may well tend to operate in the same direction during both halves of the same match, producing a positive (S) 2 association between ε(F) i,j and ε i,j. Let Φ1 and Φ2 denote the univariate and bivariate standard normal distribution functions. The nine possible permutations of half-time and full-time outcomes are m = {HH, HD, HA, DH, DD, DA, AH, AD, AA}, where HH denotes home team leading at half time and home-team win, DH denotes match level at half time and home-team win, AH denotes away team leading at half time and home-team win, and so on. The nine (unconditional) probabilities for the match between team i and team j, are defined as follows:

Comparing the model with betting odds



367

* * ˆ ˆ *0,i,j ) − Φ1 (µˆ 1,2 − yˆ 1,i,j pHH ) + Φ 2 (µˆ 0,2 − yˆ *0,i,j ,µˆ 1,2 − yˆ 1,i,j ,σˆ ) i,j = 1 − Φ1 (µ 0,2 − y DH * * p i,j = Φ1 (µˆ 0,2 − yˆ 0,i,j ) − Φ1 (µˆ 0,1 − yˆ 0,i,j ) − Φ 2 (µˆ 0,2 − yˆ *0,i,j ,µˆ 2,2 − yˆ *2,i,j ,σˆ ) + Φ 2 (µˆ 0,1 − yˆ *0,i,j ,µˆ 2,2 − yˆ *2,i,j ,σˆ ) AH * p i,j = Φ1 (µˆ 0,1 − yˆ 0,i,j ) − Φ 2 (µˆ 0,1 − yˆ *0,i,j ,µˆ 3,2 − yˆ *3,i,j ,σˆ ) * * * ˆ ˆ 1,i,j ) − Φ 2 (µˆ 0,2 − yˆ *0,i,j ,µˆ 1,2 − yˆ 1,i,j ,σˆ ) − Φ1 (µˆ 1,1 − yˆ 1,i,j ) pHD i,j = Φ1 (µ1,2 − y * * ˆ ˆ ˆ ˆ ˆ + Φ 2 (µ 0,2 − y 0,i,j ,µ1,1 − y1,i,j ,σ ) * ˆ ˆ ˆ ˆ *2,i,j ,σˆ ) − Φ 2 (µˆ 0,2 − yˆ *0,i,j ,µˆ 2,1 − yˆ *2,i,j ,σˆ ) = Φ µ − y , pDD ( 2 0,2 0,i,j µ 2,2 − y i,j − Φ 2 (µˆ 0,1 − yˆ *0,i,j ,µˆ 2,2 − yˆ *2,i,j ,σˆ ) + Φ 2 (µˆ 0,1 − yˆ *0,i,j ,µˆ 2,1 − yˆ *2,i,j ,σˆ ) ˆ ˆ *0,i,j ,µˆ 3,2 − yˆ *3,i,j ,σˆ ) − Φ 2 (µˆ 0,1 − yˆ *0,i,j ,µˆ 3,1 − yˆ *3,i,j ,σˆ ) p AD i,j = Φ 2 (µ 0,1 − y HA * * ) − Φ 2 (µˆ 0,2 − yˆ *0,i,j ,µˆ 1,1 − yˆ 1,i,j ,σˆ ) p i,j = Φ1 (µˆ 1,1 − yˆ 1,i,j DA * * ˆ ˆ ˆ ˆ pi,j = Φ 2 (µ 0,2 − yˆ 0,i,j ,µ 2,1 − yˆ 2,i,j ,σ ) − Φ 2 (µ 0,1 − yˆ *0,i,j ,µˆ 2,1 − yˆ *2,i,j ,σˆ ) ˆ ˆ *0,i,j ,µˆ 3,1 − yˆ *3,i,j ,σˆ ) p AA i,j = Φ 2 (µ 0,1 − y [12.3]

In order to generate probabilistic half-time/full-time forecasts for the 1999 season (for example), maximum likelihood estimation is used to obtain estimates of the coefficients on the covariates in the linear equations for ŷ*k,i,j for k = 0,1,2,3, and estimates of the additional parameters μk,1, μk,2 and σ, using data from the previous fifteen seasons (1984 to 1998 inclusive). The probabilities pmi,j are obtained by substituting these coefficient and parameter estimates, together with the values of the covariates for each match played in the 1999 season, into [12.3]. In order to generate forecasts for subsequent seasons, the model is re-estimated using data for successive (overlapping) fifteen-season windows. For example, forecasts for the 2000 season are generated using the version of the model estimated with data for seasons 1985 to 1999 inclusive; forecasts for the 2001 season are generated using the version of the model estimated with data for seasons 1986 to 2000 inclusive; and so on. There are five estimated versions of the model in total. The five estimated values of the parameter σ vary between 0.806 and 0.911. Each of these five estimates is significantly different from zero at the 0.01 level, indicating that there (S) is (as expected) a strong positive association between ε(F) i,j and εi,j . 12.3  Comparing the model’s probabilistic forecasts with betting odds

Section 12.3 presents some comparisons between the probabilistic half-time/fulltime forecasts generated by the model described in Section 12.2, and five sets of odds posted by high-street bookmakers in the UK for bets on half-time/full-time outcomes. The odds are those compiled by four major high-street bookmakers that were trading throughout the period covered by this study:  Coral, William Hill, Ladbrokes and StanleyBet; and those of Super Soccer, a specialist agency that supplies odds to independent bookmakers. The fixed-odds betting data cover the five seasons from 1999 to 2003 inclusive. The data source is the electronic betting odds archive www.mabels-tables.com.

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Bookmakers’ fixed odds for betting on the outcomes of English football matches are published several days before the match is played, and are not adjusted as bets are placed, even if new information is received. The odds are quoted in either fractional form or decimal form. With fractional odds, a quoted price of a-to-b on the outcome HH means that if b is staked on this outcome, the net payoffs to the bettor are +a (the bookmaker pays the winnings and returns the stake) if the bet wins; and –b (the bookmaker keeps the stake) if the bet loses. With decimal odds, the quoted price for the same bet is (a+b)/b. If the bet were ‘fair’, in the sense of producing an expected return of zero to both the bookmaker and the bettor, the implicit probability for the outcome HH would be θi,jHH = b/(a+b). A necessary condition for all nine possible bets on a single match to be ‘fair’ is ∑ θmi,j =1 (where Θ is the set of nine possible outcomes, as m∈Θ

before). However, in practice ∑ θmi,j > 1 , because the bookmakers’ odds contain m ∈Θ

margins for costs and profit. The bookmaker’s overround is λ i,j = ∑ θmi,j − 1. An m ∈Θ

implicit probability for the outcome HH (for example) is obtained by rescaling HH HH m m θHH i,j as follows:  φi,j = θ i,j / ∑ θ i,j . There are analogous definitions for φ i,j for the m ∈Θ

other eight outcomes. By construction ∑ φi,jm = 1 . φmi,j can be interpreted as probm∈Θ

abilities on the assumption that the bookmakers set their odds to achieve the same expected return from every bet.3 Different UK high-street bookmakers usually quote similar but not always identical odds for the same bet. There may therefore exist arbitrage opportunities for a bettor who is willing to search for the bookmaker offering the most favourable (longest) odds for each bet. In this study, the efficiency tests are based on two sets of odds that are constructed from the five sets of bookmaker odds in the original data set. The first constructed set, ‘best odds’, contains the longest odds available from any of the five sets of bookmaker odds for each possible bet. The second constructed set, ‘median odds’, contains the third-longest (or median) odds from the five sets of bookmaker odds. ‘Best odds’ are the odds actually available to the bettor who searches for the most favourable odds; and ‘median odds’ are representative of the odds typically available to the bettor who does not search. Table 12.1 reports summary data on the mean values of various unconditional and conditional probabilities for the 9,727 matches for which bookmaker odds and probabilistic half-time/full-time forecasts are available.4 Panel 1 reports the proportions of matches that produced each of the three possible half-time outcomes for (i) the initial fifteen-year estimation period (seasons 1984 to 1998), and (ii) the five-year holdout sample period over which the bookmakers’ odds are also observed (seasons 1999 to 2003). Panel 1 also reports (iii) the average values of the bookmakers’ implicit probabilities based on ‘best odds’ for the holdout sample period, and (iv) the average values of the forecasting model probabilities for the holdout sample period. For example, the bookmakers’ implicit probability for the home team to be HD HA leading at half-time is φHH i,j + φi,j + φi,j ; similarly, the forecasting model probability

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Table 12.1 Probabilities for half-time/full-time outcomes 1. Probabilities for half-time outcomes (unconditional) Home team leading Level 1984–1998: observed .3557 .4326 proportions 1999–2003: observed .3464 .4223 proportions 1999–2003: bookmakers’ .3449 .4282 implicit probabilities 1999–2003: forecasting .3466 .4280 model probabilities

Away team leading .2117 .2313 .2269 .2254

2. Probabilities for full-time outcomes (unconditional) Home win Draw 1984–1998: observed .4750 .2716 proportions 1999–2003: observed .4552 .2723 proportions 1999–2003: bookmakers’ .4601 .2586 implicit probabilities 1999–2003: forecasting .4624 .2745 model probabilities 3. Half-time/full-time probabilities (unconditional) HH DH AH HD .2845 .1650 .0255 .0542 1984–1998: observed proportions 1999–2003: observed .2753 .1540 .0259 .0562 proportions 1999–2003: bookmakers’ .2685 .1619 .0297 .0513 implicit probabilities 1999–2003: forecasting .2779 .1583 .0261 .0550 model probabilities

Away win .2534 .2724 .2813 .2631

DD AD HA DA AA .1685 .0488 .0169 .0990 .1374 .1627 .0534 .0148 .1056 .1521 .1545 .0528 .0252 .1118 .1444 .1683 .0512 .0137 .1013 .1482

4. Full-time probabilities (conditional on half-time outcome) HH DH AH HD DD 1984–1998: observed .8000 .3815 .1202 .1524 .3896 proportions .7949 .3647 .1120 .1624 .3853 1999–2003: observed proportions 1999–2003: bookmakers’ .7783 .3781 .1311 .1487 .3609 implicit probabilities 1999–2003: forecasting .7885 .3725 .1282 .1678 .3924 model probabilities

AD HA DA AA .2307 .0476 .2289 .6491 .2307 .0427 .2500 .6573 .2327 .0730 .2611 .6362 .2359 .0437 .2359 .6358

Source: Rothmans/Sky Sports Football Yearbook

is pi,jHH + pi,jHD + pi,jHA. The drop in the observed proportion of matches in which the home team was leading between periods (i) and (ii), and the corresponding rise in the proportion in which the away team was leading, reflects a weakening of the home-field advantage effect (see Chapter 3, Section 3.2), which is also apparent in

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Table 12.2 Mean returns based on bookmakers’ ‘best odds’ 2. Bets on each half-time/ full-time outcome

1. All bets ranked in order of decimal odds Decimal odds

Number of bets

Mean odds

Mean return

Bet

Mean odds

Mean return

All 1.4 – 4.33 4.5 – 5 5.5 6 – 6.5 7 – 16 17 19 – 29 34 – 101

87543 8347 9636 9571 8140 14224 15794 12461 9370

14.74 3.13 4.87 5.50 6.17 10.47 17.00 27.27 38.11

−.1529 −.0953 −.1023 −.0978 −.1283 −.1000 −.0765 −.1944 −.4885

HH DH AH HD DD AD HA DA AA

3.76 5.65 30.04 17.42 5.80 16.86 36.46 9.14 7.50

−.0758 −.1613 −.2346 −.0232 −.0691 −.1047 −.4976 −.1470 −.0634

Source: Sky Sports Football Yearbook; www.football-data.co.uk

the corresponding data for full-time outcomes shown in Panel 2. Here, the bookmakers’ probability for the home team to win the match is φi,jHH + φi,jDH + φAH i,j ; and AH the forecasting model probability is pi,jHH + pDH + p . i,j i,j Panel 3 reports the proportions of matches that produced each of the nine possible half-time/full-time outcomes, and the sample mean values of the corresponding bookmakers’ implicit probabilities and the forecasting model probabilities. In this case, the model generally comes closer than the bookmakers to replicating the observed proportions. In particular, the bookmakers overstate the probabilities for the two outcomes that are least likely on average, AH and HA (both of which involve victory for the team that is trailing at half-time). Similar patterns are also apparent in the full-time probabilities conditional on the half-time outcome, shown in Panel 4. Table 12.2 presents some further descriptive analysis of the bookmakers’ ‘best odds’ data set. In Panel 1, the 87,543 available bets (= nine possible bets × 9,727 matches) are placed into eight bands based on a ranking in ascending order of the decimal odds. The mean return is evaluated for the bets in each band. The overall mean return of –15.29 per cent is slightly worse than the return suggested by the mean overround based on the ‘best odds’ of 0.1290.5 The calculation of mean returns when the ‘best odds’ are classified by their length reveals clear evidence of a favourite-longshot bias, in the form of mean returns for bets in the two longest odds bands (decimal odds in the ranges 19 –29 and 34 –101) that are substantially lower than the mean returns in any of the other six bands. Panel 2 presents a similar analysis for bets on each of the nine half-time/full-time outcomes individually. From the bettor’s perspective, bets on the outcomes AH and HA, with mean returns of –23.5 per cent and – 49.8 per cent respectively, represent poor value on average (as is also suggested by Table 12.1). Bets on AH and HA account for the

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majority of long-odds bets that are subject to the favourite-longshot bias. From the bettor’s perspective, bets on the outcome HD, with a mean return of –2.32 per cent, provide the best value on average. 12.4 Testing the informational efficiency of the half-time/full-time fixed-odds betting market

Section 12.4 reports an empirical test for the informational efficiency of the halftime/full-time fixed-odds betting market, in the form of an investigation of the profitability of a simple betting strategy that selects the bet offering the highest expected return according to the probabilistic forecasts generated from the model, from the choice of nine bets that are available on each match. First, the mechanics of the betting strategy are described, using as an example the ten Premier League matches that were played on 11 May 2003, the final day of the 2003 season. Then the results of applying the ‘highest expected return’ strategy across the entire holdout sample are presented. The application of the ‘highest expected return’ strategy on 11 May 2003 is illustrated in Table 12.3. Panel 1 shows the forecasting model probabilities, pi,jm, for the nine possible half-time/full-time outcomes (m = HH, DH, …) for each of the ten matches. pi,jm are calculated from [12.3] using ŷ*k,i,j     for k = 0,1,2,3,  μˆ k,1 and  μˆ k,2 calculated by applying the forecasting model estimated with data from seasons 1988 to 2002 to the covariates for each of the ten matches. Panel 2 shows the ‘best odds’ for each of the nine outcomes. Panel 3 shows the forecasting model’s expected return for each bet placed at ‘best odds’. For example, a £1 bet on a HH outcome in Birmingham versus West Ham at ‘best odds’ of 6.5 would provide a net return of +5.5 if the bet wins, and –1 if the bet loses. The expected return is +5.5×.2862 + –1×(1 – .2862) = 0.860. For each fixture, the highest of the nine expected returns is shown in italics. On this basis, HH is the model’s recommended bet for three of the ten matches (including Birmingham versus West Ham); HD is recommended for four matches; and AA is recommended for three matches. Panel 3 shows the actual half-time/full-time match outcomes, in the standard format of ‘(half-time score) full-time score’ for each team. For two of the ten matches highlighted in bold, Chelsea versus Liverpool (HH) and Manchester City versus Southampton (AA), the half-time/full-time outcome corresponds to the recommended bet. The bettor achieves positive net returns of +3.5 and +8 on these two bets respectively (shown in the final column of Panel 3). The other eight bets are unsuccessful. Across all ten bets, the bettor’s overall net return is +3.5. These ten bets turn out to be more profitable for the bettor than the average for the entire holdout sample. As is shown below, however, the return obtained by applying the same strategy across the entire holdout sample is also positive. Table 12.4 presents summary results for the application of the ‘highest expected return’ strategy across the entire holdout sample. Panel 1 reports the outcome from

West Ham Middlesbrough Fulham Liverpool Man Utd Aston Villa Southampton Arsenal Blackburn Newcastle

Birmingham Bolton Charlton Chelsea Everton Leeds Man City Sunderland Tottenham WBA

West Ham Middlesbrough Fulham Liverpool Man Utd Aston Villa Southampton Arsenal Blackburn Newcastle

2. Fixtures, best available bookmaker odds

Birmingham Bolton Charlton Chelsea Everton Leeds Man City Sunderland Tottenham WBA

1. Fixtures, forecasting model probabilities

6.5 2.4 3.5 4.5 5 3.2 2.75 9 5 7

.2862 .3029 .2743 .2717 .1377 .2791 .3046 .1002 .2772 .1326

HH

8 4.5 4.5 5.5 6 4.5 4.5 10 7.5 8.5

.1401 .1412 .1277 .1626 .0753 .1536 .1639 .0510 .1476 .0744

DH

34 29 29 29 34 29 29 41 34 34

.0229 .0273 .0191 .0332 .0123 .0330 .0260 .0057 .0262 .0187

AH

17 19 17 17 17 17 17 17 17 17

.0457 .0622 .0683 .0592 .0632 .0774 .0608 .0758 .0630 .0634

HD

6 6.5 5.5 5 6 5.5 6 6 6 6

.1693 .1660 .1689 .1651 .1581 .1641 .1615 .1409 .1673 .1573

DD

19 17 17 17 17 17 17 17 17 17

.0525 .0526 .0469 .0606 .0449 .0566 .0516 .0285 .0542 .0568

AD

29 41 34 34 29 34 41 29 29 29

.0069 .0114 .0143 .0111 .0200 .0177 .0109 .0383 .0122 .0208

HA

4.5 11 8 6.5 5.5 8.5 10 4.5 5.5 4.5

.1080 .1031 .1177 .0893 .1791 .0930 .0850 .2186 .1004 .1796

DA

Table 12.3 Illustration of ‘highest expected return’ betting strategy: English Premier League, 11 May 2003

3.4 10 6 5 5 7 9 2.63 3.6 3.2

.1684 .1333 .1627 .1473 .3093 .1254 .1358 .3410 .1520 .2964

AA

West Ham (0) 2 Middlesbrough (0) 1 Fulham (1) 1 Liverpool (1) 1 Man Utd (1) 2 Aston Villa (1) 1 Southampton (1) 1 Arsenal (2) 4 Blackburn (2) 4 Newcastle (1) 2

.860 −.273 −.040 .223 −.312 −.107 −.162 −.098 .386 −.072

.121 −.364 −.425 −.106 −.548 −.309 −.263 −.490 .107 −.368

−.221 −.208 −.445 −.039 −.582 −.044 −.247 −.766 −.110 −.365

−.222 .181 .161 .007 .075 .315 .034 .289 .071 .078

.016 .079 −.071 −.175 −.051 −.098 −.031 −.155 .004 −.056

−.003 −.105 −.203 .031 −.236 −.038 −.122 −.516 −.078 −.034

−.801 −.534 −.515 −.623 −.419 −.397 −.553 .110 −.645 −.398

−.514 .134 −.058 −.420 −.015 −.209 −.150 −.016 −.448 −.192

−.427 .333 −.024 −.264 .547 −.122 .222 −.103 −.453 −.052

−1 −1 −1 +3.5 −1 −1 +8 −1 −1 −1

Note: Birmingham (0) 2 West Ham (0) 2 means half-time score of 0-0, full-time score of 2-2. Matches for which winning bets were selected, and actual returns for winning bets, are shown in bold. Source: Sky Sports Football Yearbook; www.football-data.co.uk

Birmingham (0) 2 Bolton (2) 2 Charlton (0) 0 Chelsea (2) 2 Everton (1) 1 Leeds (1) 3 Man City (0) 0 Sunderland (0) 0 Tottenham (0) 0 WBA (0) 2

3. Match results, expected returns on each bet, selected bets (italics), winning bets (bold italics), actual returns

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Table 12.4 Returns from ‘highest expected return’ and indiscriminate betting strategies Betting strategy: ‘Highest expected return’ Odds:

Indiscriminate

Best

Median

Median

No. of winning bets

Average winning odds

Average rate of return

Average rate of return

Average rate of return

1342

7.53

.0390

−.0223

−.2154

2. Results classified by selected bet HH 2158 524 DH 732 142 AH 867 29 HD 1674 99 DD 1082 190 AD 698 50 HA 16 2 DA 350 36 AA 2150 270

3.37 4.29 29.10 16.26 4.77 16.00 28.00 9.46 6.78

.0621 .0260 .0069 .0209 .0139 .2178 2.6250 .0757 −.0232

−.0180 −.0558 .0798 −.0377 −.0772 .1759 2.7143 .0076 −.1024

−.1401 −.2158 −.2948 −.0937 −.1274 −.1633 −.5420 −.2171 −.1442

3. Results classified by season 1999 1944 2000 1946 2001 1946 2002 1945 2003 1946

328 290 226 200 298

5.98 6.85 9.00 10.24 6.96

.0095 .0210 .0458 .0527 .0662

−.0417 −.0234 .0470 −.0320 −.0614

−.2265 −.2256 −.1806 −.2381 −.2062

4. Results classified by stage of season Aug. to Oct. 3148 450 Nov. to Dec. 1991 282 Jan. to Feb. 1800 227 Mar. to May 2788 401

7.72 7.81 7.48 7.20

.1037 .1060 −.0570 .0349

−.0001 .0169 −.0612 −.0502

−.2113 −.2267 −.2252 −.1900

5. Results classified by tier (division) T1 1900 251 T2 2760 406 T3 2714 379 T4 2353 324

7.80 7.40 7.18 7.95

.0303 .0887 .0022 .0951

.0047 −.0926 −.0113 .0257

−.2325 −.2142 −.2063 −.2134

No. of bets 1. Results across all matches 9727

Source: Rothmans/Sky Sports Football Yearbook; www.football-data.co.uk

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375

placing one bet on each of the 9,727 matches at ‘best odds’, on the half-time/fulltime outcome with the highest expected return according to the model. There are 1,342 winning bets (13.8 per cent of the total). The average decimal odds for the winning bets are 7.53. If £1 is staked in each bet, the overall net return is £379.35 on a total stake of £9,727. Therefore the average rate of return is 379.35/9727 = 0.0390, or +3.9 per cent. For purposes of comparison, the final two columns of Table 12.4 show the average rates of return under two alternative scenarios. In the first alternative, the same betting strategy is applied using ‘median odds’ instead of ‘best odds’. This produces an average return of –2.2 per cent. In the second alternative, nine bets are placed on each of the 9,727 matches indiscriminately: one bet on each of the nine possible outcomes. This produces an average return of –21.5 per cent (roughly equivalent to the average of the overrounds implicit in the five sets of bookmaker odds). Overall, a bettor who adopts the ‘highest expected return’ strategy using ‘best odds’ achieves a rate of return 25.4 per cent higher than a bettor who places bets indiscriminately. Of this gain, 19.3 per cent can be attributed to the use of the forecasting model to select bets with favourable expected returns, and 6.1 per cent can be attributed to arbitrage between the five sets of bookmaker odds, using the ‘best odds’ rather than the ‘median odds’ for each bet. The remaining panels of Table 12.4 show the equivalent results when the holdout sample of 9,727 matches is disaggregated in various ways: in Panel 2 by the half-time/full-time outcome that was the selected bet according to the ‘highest expected return’ criterion; in Panel 3 by the five football seasons within the holdout sample period chronologically; in Panel 4 by the stage of the season (identified by calendar month) when the match was played; and in Panel 5 by the tier (or division) in which the match was played. The classification by the half-time/full-time outcome that was the selected bet indicates that the proportions in which the nine possible bets are selected do not correspond closely either to the proportions in which the nine outcomes occur, or to the average differences between the bookmakers’ implicit probabilities and the forecasting model probabilities (see Table 12.1, Panel 3). For example, the rates of occurrence of the two least common outcomes, AH and HA, are 2.6 per cent and 1.5 per cent; but AH and HA are the selected bets for 8.9 per cent and 0.2 per cent of all matches. The bookmakers’ implicit probabilities for AH bets tend to overstate the actual proportions, so AH bets offer poor value on average. However, while AH bets would perform poorly if placed on all matches indiscriminately, it is not unusual to find particular matches for which the forecasting model indicates that an AH bet represents good value, in the form of a higher expected return than for any of the other eight bets. Therefore the relatively high proportion of AH bets chosen is due to the forecasting model’s selectivity capability. The classification by season is of practical importance for bettors who might realistically hope to achieve a positive return over a period perhaps considerably shorter than five years. Although the average return is positive for all five seasons

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Table 12.5 Average rate of return by tier (division): chronological analysis

08/98 to 10/98 11/98 to 12/98 01/99 to 02/99 03/99 to 05/99 08/99 to 10/99 11/99 to 12/99 01/00 to 02/00 03/00 to 05/00 08/00 to 10/00 11/00 to 12/00 01/01 to 02/01 03/01 to 05/01 08/01 to 10/01 11/01 to 12/01 01/02 to 02/02 03/02 to 05/02 08/02 to 10/02 11/02 to 12/02 01/03 to 02/03 03/03 to 05/03

T1

T2

T3

T4

.3623 −.3069 −.0522 −.2260 .1655 .0988 −.3333 −.0858 .3739 .5313 .1957 −.0090 .1505 .6000 −.2887 −.0054 −.1780 .0216 .3577 −.6420

.1151 .1387 .4427 −.1420 .2457 −.2132 −.1563 .1329 −.0821 .1073 .0733 .2211 .4622 −.1852 .0564 −.1000 −.1024 −.1788 −.0301 .1136

.1854 −.2584 −.1861 −.1640 −.4823 .5461 −.0009 .0521 −.2534 .2283 −.4252 −.1108 −.0559 .3220 .1420 .1793 .1528 .1701 −.3261 .2041

−.1141 .1222 .1170 .1036 .0712 −.0819 −.2505 .7831 .5367 −.1107 −.2451 −.1496 −.3024 −.2922 .1115 −.1079 .3914 .4153 .6249 .1430

All matches .1143 −.0596 .0831 −.0999 −.0067 −.0560 −.1641 .2154 .1038 .2030 −.1336 −.0104 .0735 .1036 .0371 −.0061 .0832 .0719 .1166 .0120

Source: Rothmans/Sky Sports Football Yearbook; www.football-data.co.uk

individually, this result is borderline for the 1999 season. There appears to be sufficient year-to-year variation in the results to suggest the probability of achieving a negative average return in any individual season may be non-negligible. It is interesting to note that there is no evidence of any improvement in the informational efficiency of the half-time/full-time betting market within the five-year holdout sample period. In fact, the ‘highest expected return’ betting strategy becomes progressively more profitable over time. The classification by stage of the season and by tier (division) suggests the ‘highest expected return’ betting strategy was more effective over the earlier months of the football season than over the later months; and more effective for bets on T2 and T4 matches than for bets on T1 and T3 matches. In an effort to investigate the stability of these patterns, Table 12.5 reports a more detailed analysis of the average returns, disaggregated chronologically and by tier (division). The variations in average returns by stage of the season and by tier do not appear to be at all stable at the levels of aggregation that are used to construct Table 12.5. Accordingly, the patterns in the average returns suggested by Panels 4 and 5 of Table 12.4 appear more likely to be due to sampling error than to any factors that operate systematically. In fact, the results in Table 12.5 demonstrate that there is considerable smallsample variation in the returns. This suggests that with the benefit of hindsight it

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377

Table 12.6 Mean expected and actual returns: all possible bets ranked by expected return Band (ordered by expected return)

Mean odds

Mean expected return

Mean actual return

Best 9,727 bets 2nd-best 9,727 3rd-best 9,727 4th-best 9,727 5th-best 9,727 6th-best 9,727 7th-best 9,727 8th-best 9,727 Worst 9,727 bets

13.29 10.91 10.58 10.23 10.88 11.60 13.18 18.50 33.48

+.2223 +.0487 −.0222 −.0789 −.1329 −.1922 −.2649 −.3692 −.5906

+.0564 −.0763 −.0707 −.1207 −.1193 −.1656 −.2134 −.2208 −.4463

Source: Rothmans/Sky Sports Football Yearbook; www.football-data.co.uk

is not at all difficult to identify betting strategies that would have been locally profitable, over limited numbers of bets placed over specific periods that are also selected with the benefit of hindsight. An implication for future research is that it is important for any claims concerning the out-of-sample or universal profitability of particular betting strategies to be validated using large-sample evidence. Finally, Table 12.6 reports the mean returns earned by ranking all 87,543 available bets (= nine possible bets × 9,727 matches) in descending order of their expected return evaluated using the forecasting model probabilities. For convenience, the 87,543 bets are placed into nine equal-sized bands, each containing 9,727 bets. (It is possible, indeed common, for more than one bet on the same match to appear in the same band.) While there is a clear association between the expected and actual returns, the gradient (based on the change in values between successive bands in Table 12.6) for expected returns is generally steeper than that for actual returns. Bets in the top band by expected return produce a positive actual return of +5.64 per cent, slightly higher than the mean return of +3.90 per cent produced by the ‘highest expected return’ strategy that is analysed in Tables 12.4 and 12.5. Although Table 12.6 could not have been compiled by a bettor operating in real time (since knowledge of the outcomes over the entire five-season holdout sample period is required), a rule-of-thumb involving the selection of bets with an expected return exceeding about +9 per cent or +10 per cent would have produced a portfolio of bets approximating closely to the top band of Table 12.6. Conclusion

The theoretical and empirical economics literature contains numerous studies of the informational efficiency of betting markets. Stylised facts that emerge from this

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literature include the following. The market prices or odds for racetrack betting, and for some team sports betting, are subject to a consistent and longstanding favourite-longshot bias, such that bets placed on favourites yield a higher average return than bets placed on longshots or underdogs. There is some evidence of a reverse favourite-longshot bias in the betting markets for North American major league sports; but this pattern is not replicated for fixed-odds betting on football match outcomes. Reasons for the existence of favourite-longshot bias, or its reversal, have proven surprisingly difficult to pin down. Explanations popular in the academic literature include risk-preference theories and information asymmetry theories. There is evidence that a contrarian strategy of betting against teams currently undergoing a winning streak may be profitable in some cases, in defiance of belief in the ‘hot-hand’ phenomenon. There is also some evidence that pricing anomalies in betting markets have a tendency to correct themselves over time, as bettors and bookmakers learn from past experience. The growth of internet betting during the 1990s and 2000s has presented tremendous new betting opportunities, based on the rapid information processing and transmission capabilities of the new technology. It has also presented major challenges to the traditional betting firms, which have experienced fierce new competition and a squeeze on margins. Person-to-person betting, transacted through an online betting exchange, has been the most successful new business model to have emerged during the internet era. The increasing popularity of sophisticated new spread betting markets for football (and other sports) has also been fuelled by the development of internet technology. For all of the improvement in information and communication technology, however, recent literature on sentiment bias in sports betting suggests that bettors are not immune to a tendency for their judgement to be sometimes coloured by their emotions. This chapter has reported tests for the informational efficiency of the fixedodds betting market on the half-time/full-time match outcomes of English league football matches. In this market, bettors choose between nine alternative bets on any match, corresponding to nine possible permutations for the half-time and fulltime match outcome. With nine (rather than three) bets available on each match, this betting market appears to provide more scope for detecting anomalies in the bookmakers’ odds and for formulating profitable betting strategies than the fixedodds market for full-time match results, which has been the subject of previous English football betting market efficiency studies. Probabilistic forecasts for the nine possible half-time/full-time match outcomes are obtained from a forecasting model that is estimated using data from the fifteen football seasons prior to the current season in which the match in question takes place. The estimated model is updated at the start of each season. The model combines ordered probit regressions for the half-time outcome, and the full-time outcome conditional on each of the three possible half-time outcomes, using covariates based on information that would have been publicly available at the time bets were being accepted immediately prior to the match being played.

Informational efficiency of fixed-odds betting

379

The profitability of a relatively simple betting strategy is investigated. The strategy involves placing a bet on every match on the half-time/full-time outcome for which the best odds available from any of the five sets of bookmaker odds produce the highest expected return according to the probabilities generated from the forecasting model. This strategy would have been profitable over a five-season holdout sample period covering football seasons 1999 to 2003, inclusive, and for each of these five seasons individually. It is claimed that these results constitute stronger evidence than has been available previously that it is possible to use historical data to formulate a betting strategy that is universally (rather than just locally) profitable. Notes 1 This type of constraint does not arise in portfolio theory, because an assumption of perfect capital markets allows investors to either borrow or lend without any limits at an interest rate equivalent to the risk-free rate of return. 2 The parameter σ plays a role in the model analogous to that of Heckman’s (1979) correction for sample selection bias, exploiting the information from the estimation of the (unconditional) half-time outcome probabilities in order to correct for selection bias in the estimations of the full-time probabilities conditional on the half-time outcome. For example, the estimated probabilities for the full-time outcome conditional on the away team leading at half-time are based on a non-random subsample of matches in which the away team was leading at half-time. If in one particular match, the home team was expected to dominate, but the away team was actually leading at half-time, ε(F) i,j must have been large and negative. If σ>0, ε(S) is also expected to be large and negative. This information should be taken into i,j account in the estimation of the probability for the full-time outcome conditional on the away team having been leading at half-time. Since σ is constrained to lie between  –1 and +1, it is convenient to estimate δ = atanh(σ), which is unconstrained. The estimated value ˆ = {exp( δ)−exp(− ˆ ˆ of the parameter σ is obtained using the transformation σˆ = tanh( δ) δ)}/ ˆ ˆ {exp ( δ)+exp (−   δ)}. 3 This assumption need not necessarily be true. For example, bookmakers might set their odds to exploit patterns of demand among bettors that are influenced by factors other than expected return. If so, the probabilities used to set the odds might diverge from φmi,j; and based on these probabilities some bets might yield higher expected returns than others. Nevertheless, below we refer to φmi,j as the bookmakers’ implicit probabilities, invoking the assumption of equal expected returns implicitly whenever we do so. 4 From 10,180 league matches played in total, the model is capable of generating predictions for 9,728. The model does not generate predictions for matches involving teams that entered the league up to two calendar years before the match is played, for which the full set of halftime/full-time outcomes data over a two-year period prior to the match in question were not available. In the 2002 season, one T4 fixture was rescheduled with insufficient notice for the bookmakers to quote odds; this match is discarded from the sample. 5 The overround based on ‘median odds’, which corresponds closely to the margins built into each individual set of bookmaker odds, is 0.2135.

13 Football around the world: France, Germany, Brazil, Japan and China

Introduction

Previous chapters of this volume have presented an extensive descriptive and empirical analysis of English club football. Chapter 13 widens the perspective, by providing a brief description of the historical development and present-day competitive and commercial structure of football in five other countries from around the world. Sections 13.1 and 13.2 examine two further major Western European footballing powers:  France and Germany. Section 13.3 examines Brazil, whose national team’s highly skilled attacking style of play in several successive World Cup tournaments, especially during the 1950s, 1960s and 1970s, gained plaudits and admirers throughout the world. Finally, Sections 13.4 and 13.5 examine Japan and China, two east Asian countries in which attempts were made during the 1990s and 2000s to establish professional football as a popular spectator sport in territories with none of the longstanding traditions of participation and fanaticism that have characterised football in many other countries. 13.1  France

Football was first introduced into France, as in a number of other countries, by travelling British businessmen during the late nineteenth century. The first club was founded in the port city of Le Havre in 1872 by members of shipping and transit companies who wished to play both football and rugby. A number of other multi-sports clubs were formed in the 1870s and 1880s, before clubs devoted exclusively to football began to appear during the 1890s. The first national cup tournament was won by Standard AC in 1894, and an embryonic league competition was won by Club Français in 1896. By the turn of the century, football was played extensively throughout northern France, including Paris (Pickup, 1999). At the start of the twentieth century, football spread rapidly to the east and south of France. France’s first international was played against Belgium in 1904, but the administration of the sport during the pre-war period was chaotic, due to rivalries between a number of alternative governing bodies. This situation was resolved in 380

France

381

1919 by unification of the competing bodies under the Federation Française de Football (FFF). A French official, Jules Rimet, was the first president of the newly created international football federation FIFA when it was formed in 1920. Rimet played a key part in the creation of the first international World Cup tournament, played in Uruguay in 1930. The legal framework for the organisation of professional football clubs in France was established by the 1901 freedom of association law, which permitted the formation of associations of citizens on a non-profit basis for any purpose. Clubs such as Sochaux and RC Paris, dominated by local business personalities seeking influence and prestige (rather than financial reward), became the norm from the 1930s onwards. From the outset, there was also a strong tradition of local government involvement in the financing and administration of football (including municipal ownership of most major football stadia), deriving from a statutory duty for municipalities to promote and develop sport. In domestic football, a major advance came with the acceptance of professionalism in 1932, followed by the introduction of a national league competition (currently named Ligue 1), won by Sête in its inaugural 1934 season. The 1935 winners were Sochaux, a club which had been formed in 1929 on a professional basis with the backing of the Peugeot car manufacturer. This development had been instrumental in prompting the authorities to adopt professionalism. Racing Club (RC) Paris, formed by a Parisian estate agent in 1932, were champions in 1936. The 1930s also saw a trend towards the recruitment of foreign players. The enforced transfer of players against their will encouraged the formation of a players’ mutual association in 1934, and a players’ union in 1936. Before the introduction of fixed-term contracts in 1968, professional players were tied contractually to a single club up to the age of 35. This draconian contractual position may explain football’s relatively unattractive status as a working-class occupation following the introduction of professionalism: most players were middle class and semi-professional. The proportion of imported players was relatively high: 329 foreigners played in the top tier of French football before 1939. The pattern was similar after the Second World War (Lanfranchi, 1994). Indigenous working-class involvement increased gradually, however, during the post-war period (Eastham, 1999; Pickup, 1999; Mignon, 2000). Since 1945 Ligue 1 has switched several times between an eighteen- and twentyteam format. The current twenty-team Ligue 1 format has operated since the 2003 season. Promotion and relegation between Ligue 1 and Ligue 2 and between Ligue 2 and Ligue 3 is three-up three-down. Before automatic promotion and relegation between Ligue 2 and Ligue 3 was introduced in 1970, membership of Ligue 3 included the reserve teams of Ligue 1 clubs. Four-up four-down promotion and relegation operates between Ligue 3 and the Championnat de France Amateurs. Between 1973 and 1976 a bonus league point was awarded if a team scored three goals or more, regardless of the match result. Three points for a win was introduced in the 1995 season.1

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Football around the world

Table 13.1 Historical performance of top French teams in league and cup competition 1946–1959 Championships Stade Reims 4 Nice 4 Lille 2 St Etienne 1 Roubaix 1 Bordeaux 1 Marseille 1

1960–1969

1970–1979

1980–1989

1990–1999

2000–2009

St Etienne 4 Stade Reims 2 Monaco 2 Nantes 2

St Etienne 4 Marseille 2 Nantes 2 Strasbourg 1 Monaco 1

Bordeaux 3 Monaco 2 Nantes 2 St Etienne 1 Marseille 1 Paris SG 1

Marseille 4 Bordeaux 1 Lens 1 Monaco 1 Nantes 1 Paris SG 1 Auxerre 1

Lyon 7 Bordeaux 1 Monaco 1 Nantes 1

Bordeaux 13 Nantes 12 Monaco 10 St Etienne 6 Paris SG 6 Marseille 5 Sochaux 3 Roubaix 2 Auxerre 1 Montpellier 1 Toulouse 1

Marseille 16 Monaco 11 Paris SG 11 Bordeaux 5 Auxerre 5 Nantes 4 Lens 3 Lyon 3 Metz 2

Lyon 25 Bordeaux 7 Monaco 7 Marseille 6 Paris SG 4 Lille 4 Lens 2 Toulouse 1 Auxerre 1

Monaco 2 Paris SG 2 Metz 2 Bordeaux 2 Marseille 1 Bastia 1

Paris SG 3 Auxerre 2 Nice 1 Nantes 1 Montpellier 1 Monaco 1

Auxerre 2 Paris SG 2 Sochaux 1 Lyon 1 Guingamp 1 Nantes 1 Strasbourg 1 Lorient 1

Paris SG 2 Metz 1 Strasbourg 1 Lens 1

Bordeaux 3 Lyon 1 Monaco 1 Sochaux 1 Strasbourg 1 Nancy 1 Paris SG 1 Gueugnon 1

Championship – points for a top three finish Stade Reims 19 St Etienne 12 St Etienne 15 Lille 15 Stade Reims 9 Nantes 13 Nice 12 Monaco 8 Marseille 11 Bordeaux 7 Nantes 8 Strasbourg 4 St Etienne 5 Bordeaux 6 Nice 4 Lens 5 RC Paris 5 Monaco 3 Roubaix 4 Nimes 3 Sochaux 2 Marseille 4 Nice 2 Lens 2 Nimes 4 Valenciennes 2 Nimes 2 Sochaux 2 Sochaux 1 Lyon 2 Toulouse 2 Lens 1 Sedan 1 Strasbourg 1 Angers 1 Bastia 1 Le Havre 1 Sedan 1 Monaco 1 Metz 1 Angers 1 RC Paris 1 French Cup wins Lille 5 Stade Reims 2 Nice 2 Strasbourg 1 RC Paris 1 CS Sedan 1 Toulouse 1 Le Havre 1

Monaco 2 St Etienne 2 Lyon 2 CS Sedan 1 Stade Rennais 1 Strasbourg 1 Marseille 1

St Etienne 4 Marseille 2 St Rennais 1 Lyon 1 Nantes 1 Nancy Lorr. 1

League Cup wins (from 1995)

France

383

Table 13.1 (cont.) 1946–1959

1960–1969

1970–1979

1980–1989

1990–1999

2000–2009

Eurpean Competition wins (from 1956) Marseille 1 Paris SG 1 Note: Marseille’s 1993 domestic championship and European Cup victories were subsequently rescinded, but are included here. The French Cup was cancelled at the semi-final stage in 1992, following the collapse of a stand at the Armand Césari Stadium in Bastia (Corsica), during a match between Bastia and Marseille. Eighteen people were killed in the incident. Source: French Professional League, www.ligue1.com/indexSite.asp

Table 13.1 presents data on the performance of French clubs in domestic and European competition. In comparison with many other European countries, success in French domestic football has not been highly concentrated. Stade Reims, the most successful team of the 1950s and early 1960s, were eventually relegated in 1967 and have never returned to the top tier. The dominance of St Etienne, champions ten times between 1957 and 1981 and a major force in European competition during the 1970s, had run its course by the early 1980s. The club was relegated in 1996, but returned to Ligue 1 in 2004. Spells of success for Bordeaux and Marseilles in the 1980s and 1990s ended abruptly in scandal and enforced relegation in both cases. Since 2000 Lyon have been the dominant force and the wealthiest club in French football. French officials were highly influential in the development of the first European club tournaments during the 1950s, as they had been in establishing the World Cup thirty years earlier. Stade Reims were runners up to Real Madrid in the first European (Champions) Cup tournament in 1956, and again in 1959. In domestic football, however, the 1960s and 1970s were a period of retrenchment. The successes of St Etienne in domestic competition took place against a background of declining spectator interest and financial crisis on the domestic scene. Population decline in many smaller industrial towns led to reductions in municipal funding, and several clubs reverted to amateur status (Pickup, 1999; Mignon, 2000). The French tradition of state involvement in the organisation of sport takes some of the credit for steps taken during the 1970s that have subsequently contributed to a renaissance in the fortunes of French football, both at club and (especially) at international level. In 1974 the National Football Institute was established to provide training to forty of the most promising young players. At the same time, all professional clubs were required to set up their own training centres with links to local schools and other community organisations (Eastham, 1999). At international level, many of the products of this system went on to

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achieve unprecedented success. France were World Cup semi-finalists in 1982 and 1986, World Cup winners in 1998, World Cup finalists in 2006 and European Champions in 1984 and 2000. Domestically the benefits were more ambiguous, with many of the leading players choosing to enhance their earnings by playing for Italian, Spanish, German or British clubs, rather than remaining with their (relatively impoverished) French counterparts. Naturally, the Bosman ruling has made this ambition easier to achieve. Weaknesses in the administrative and financial control of French club football were apparent following the implication of officials of St Etienne, Paris Saint Germaine and Bordeaux in a series of financial scandals during the 1970s and 1980s. In 1984, a change to the legal constitution of the larger professional clubs permitted greater involvement of private investors, while still preventing profits from being paid to chairmen and directors. Several early experiences of the involvement of the 1980s breed of entrepreneur were far from happy, however. Most notorious was Bernard Tapie’s flamboyant reign as chairman of Olympique Marseilles, which won five successive domestic championships between 1989 and 1993 (the last of which was subsequently rescinded). Marseille were also stripped of their victory in the 1993 European Cup. This phase ended in enforced relegation for the club in 1994, and in Tapie (and several other club officials) being jailed in 1995 for a variety of bribery and corruption offences including match-fixing during the 1993 season. In 1991 the National Directorate for the Control of Management of Sporting Bodies (DNCG) was set up, comprising independent members nominated by the clubs and other organisations with interests in football, and with representatives from the accountancy profession. The DNCG has powers to intervene in cases of alleged illegal payments, accounting fraud or tax evasion (Amara et al., 2005). As part of its supervisory role, it also has powers to block any spending that may cause a financial imbalance. The DNCG is authorised to place a club under temporary suspension, and ban all transfer activity, if it is dissatisfied with a club’s finances. If DNCG directives are ignored, a club can be relegated to a lower tier (Eastham, 1999). The commercial development of French football has lagged behind several other major Western European countries. Mignon (2000) suggests there is an underlying difference between the football culture in France (based on Jacobin, republican values) and the more financially driven ethos that exists elsewhere. Nevertheless, the 1990s witnessed a strong revival in the fortunes of French football at club level, which has been sustained during the 2000s. Table 13.2 reports the trend in Ligue 1 average attendances for seasons 1981 to 2009 (inclusive). Ligue 2 recorded an increase in average attendances during the 2000s, from 5,000 in 2001 to 8,600 in 2009. Table 13.3 reports data on the principal categories of revenue and expenditure of Ligue 1 clubs since the late 1990s. Between 1999 and 2008 total revenue increased by 151 per cent. In 1999 matchday income and revenue from sponsorship and advertising accounted for 41.8 per cent of total revenue; in 2008 the corresponding

Germany

385

Table 13.2 Average league attendances, France Ligue 1 and German Bundesliga 1, 1981–2010 (’000) Season

Ligue 1

Bundesliga 1

Season

Ligue 1

Bundesliga 1

1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995

11.4 10.8 11.5 11.2 10.9 10.9 12.6 13.5 11.8 14.3 12.2 12.4 15.1 13.1 14.6

24.5 22.1 21.8 20.7 19.9 19.2 21.4 20.0 19.0 21.8 21.8 24.7 26.8 27.1 29.6

1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

16.0 16.4 17.9 19.3 22.3 22.9 21.8 19.6 20.1 21.3 21.5 21.8 21.8 21.1 20.1

30.1 30.5 30.4 31.9 31.2 30.8 32.7 33.8 37.5 37.8 40.7 40.0 39.4 42.6 42.5

Source: http://rernes.free.fr./; www.european-football-statistics.co.uk/attn.htm

figure was 33.3 per cent. The share of broadcast revenue in total revenue increased from 41.8 per cent to 56.3 per cent over the same period. In 2009 the average revenue per Ligue 1 club was €52.4 million. Lyon and Marseille are regularly listed among Europe’s twenty wealthiest clubs, with revenues in 2009 of €139.6 million and €133.2 million, respectively (Deloitte, 2010). Between 1999 and 2008, total costs increased by 123 per cent. The share of wages and salary expenditure in total costs increased from 45.0 per cent in 1999 to 54.5 per cent in 2008. Taking transfer expenditure and receipts into account, Ligue 1 clubs recorded aggregate losses in most of the seasons between 1998 and 2008. The deficit would have been larger without a healthy positive contribution from net transfer expenditure. Ligue 1 clubs carry a significant debt burden, although the ratio of assets to debts improved markedly towards the end of the 2000s. 13.2  Germany

The official history of football in Germany began with the formation of the German Football Association (DFB) in Leipzig on 28 January 1900, with eighty-six member clubs. Prior to the formation of the Bundesliga in the 1960s, German football was played at an amateur level in a large number of subregional leagues (Oberliga). Regional champions and, from 1925 onwards, runners-up played a series of play-off matches for the right to compete in a final game for the national championship.

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Table 13.3 Revenue, costs and profitability, aggregates and breakdown, France, all Ligue 1 clubs, selected years, € thousands

Matchday income Sponsorship and advertising Broadcast rights Other Total revenue Wages and salaries Social security Other Total costs Transfer fee balance Pre-tax accounting balance

1999

2002

2005

2008

84,877 79,583 164,173 64,549 393,183 208,203 65,298 189,220 462,721 65,885 −7,081

97,552 126,541 332,810 86,186 643,089 340,505 101,038 299,830 741,373 −68,080 −46,324

131,264 142,735 343,874 78,522 696,394 339,978 98,811 274,316 713,105 3,018 −32,470

136,971 191,832 556,737 103,048 988,588 562,346 140,901 328,211 1,031,458 133,231 24,944

Note: Eighteen clubs in 1999 and 2002, twenty clubs in 2005 and 2008. Source: French Professional League, www.lfp.fr/dncg/index.asp

After the Second World War, Oberliga play resumed in 1946 on a regional basis in the south and south-west of West Germany. Berlin and the other regions followed. FC Nuremberg defeated FC Kaiserslautern to become the first post-war national champions in 1948. There were two fundamental problems with the Oberliga system. Over time, each regional Oberliga became increasingly dominated by a small number of teams. A lack of real competition caused German clubs to lag behind their European counterparts, with teams from countries with professional national leagues, such as Italy and Spain, dominating the early years of European club competition. Germany’s disappointing quarter-final exit at the 1962 World Cup in Chile strengthened the case for a national league; and in July 1962 an agreement was reached to launch a league of sixteen clubs in the 1964 season. The original Bundesliga membership included five clubs each from the Oberliga South and Oberliga West, three from the Oberliga North, two from the Oberliga Southwest, and one from the Stadtliga Berlin. As well as sporting merit, each club’s economic situation was taken into account; and initially no city was to be represented by more than one club.2 Presently, eighteen teams compete in each of the top two tiers of the Bundesliga. Automatic promotion and relegation between tiers 1 and 2 is two-up twodown, with a possible third promotion and relegation place decided in a playoff between the third-bottom team in Bundesliga 1 and the third-placed team from Bundesliga 2. In 2009 a new third tier, Liga 3, was launched, to sit between Bundesliga 2 and the Regionalliga in the league pyramid. Unlike Bundesliga 1 and 2, Liga 3 is run directly by the DFB. The rules governing promotion and relegation between Bundesliga 2 and Liga 3 are the same as those for Bundesliga 1 and 2. Three-points-for-a-win was adopted in 1996.

Germany

387

In 2001, control of the Bundesliga was removed from the DFB and awarded to the newly formed German Football League (DFL). The DFL, while subordinate to the DFB, manages Germany’s professional leagues, and is responsible for issuing licences to clubs, fiscal oversight of the Bundesliga and selling the marketing rights for the two top tiers. In 2005, German football was overshadowed by a match-fixing scandal involving referee Robert Hoyzer, who confessed to fixing and betting on matches in Bundeliga 2, the German Cup and the Regionalliga. Hoyzer was banned for life and received a 29-month prison sentence. Other officials, players and a group of Croatian-based gamblers were implicated. Despite the scandal, Bundesliga 1 has remained popular with fans. A new attendance record was set in 2009, with a total attendance of 12.8 million and a per-game average of 42,600 (see Table 13.2). Bundesliga 1 is the world’s most popular national football league by average attendance.3 Table 13.4 presents data on the performance of German clubs in domestic and European competition. Although seven different teams won the first seven championships following the establishment of Bundesliga 1 as a national competition in the 1964 season, one of these seven teams, Bayern München, subsequently emerged as the dominant force in German club football. Borussia Moenchengladbach were also a powerful force during the 1970s, winning five championships (in 1970, 1971, 1975, 1976 and 1977) to Bayern’s three (1972, 1973 and 1974). During the 1980s, 1990s and 2000s, however, Bayern’s ascendancy has been challenged only briefly, by Hamburg during the 1980s, by Borussia Dortmund, Kaiserslauten and Werder Bremen during the 1990s and 2000s, and by Stuttgart who have won the championship on three occasions, one in each decade. Former German winners of the European Cup or Champions League are Bayern München (1973, 1974, 1975, 2001), Hamburg (1983) and Borussia Dortmund (1997). German clubs were traditionally constituted as registered associations (eingetragener Verein). The eingetragener Verein is a non-profit member organisation, managed by representatives democratically elected by the members. Liability is limited to the assets of the Verein, and individual members are not personally liable. Assets may not be distributed to members. Neither the Verein nor individual membership rights can be sold. Dietl and Franck (2007) argue that this legal structure creates problems. There is no profit incentive, because the proceeds of the Verein cannot be distributed. Club members have a strong incentive to reinvest any surpluses, and borrow against the club’s future, because competitive success is the only personal reward. Decision-making authority rests with the members; but because supporters are numerous and heterogeneous, there is no simple and reliable mechanism for the aggregation of preferences. The outcome is a governance vacuum. Elected representatives tend to seize control, and derive utility from competitive success without bearing any financial responsibility. This creates a tendency to discount future liabilities heavily, in an attempt to maximise current performance. Since 1998 professional clubs have been able to operate as incorporated businesses. So far only a minority of the thirty-six Bundesliga clubs (first and second

Bor Moench’ng’bach 5 Bayern München 3 Köln 1 Hamburg 1

1970–1979

Championship – points for a top three finish Köln 5 Bor Moench’ng’bach 20 Werder Bremen 5 Bayern München 14 1860 München 5 Köln 5 Borussia Dortmund 4 Hertha Berlin 5 Bayern München 4 Hamburg 5 Eintr Braunschweig 3 Schalke 04 4 Nurnberg 3 Fortuna Düsseldorf 2 Duisberg 2 Stuttgart 2 Bor Moench’ng’bach 2 Eintracht Frankfurt 1 Alemannia Aachen 2 Eintr Braunschweig 1 Eintracht Frankfurt 1 Kaiserslauten 1

Championships Köln 1 Werder Bremen 1 Bayern München 1 1860 München1 Eintr Braunschweig 1 Nurnberg 1

1964–1969

Bayern München 21 Hamburg 14 Werder Bremen 10 Stuttgart 6 Köln 6 Bor Moench’ng’bach 2 Bayer Uerdingen 1

Bayern München 6 Hamburg 2 Werder Bremen 1 Stuttgart 1

1980–1989

Bayern München 20 Borussia Dortmund 9 Kaiserslauten 8 Werder Bremen 6 Bayer Leverkusen 6 Eintracht Frankfurt 3 Stuttgart 2 Köln 2 Hertha Berlin 1 Schalke 04 1 Freiburg 1

Bayern München 4 Borussia Dortmund 2 Kaiserslauten 2 Werder Bremen 1 Stuttgart 1

1990–1999

Table 13.4 Historical performance of top German teams in league and cup competition

Bayern München 22 Werder Bremen 9 Schalke 04 7 Stuttgart 5 Bayer Leverkusen 5 Borussia Dortmund 5 Wolfsburg 3 Hamburg 2

Bayern München 6 Borussia Dortmund 1 Werder Bremen 1 Stuttgart 1 Wolfsburg 1

2000–2009

Bayern München 3 Bor Moench’ng’bach 2 Hamburg 1

Eintracht Frankfurt 2 Köln 2 Schalke 04 1 Bor Moench’ng’bach 1 Kickers Offenbach 1 Bayern München 1 Fortuna Düsseldorf 1 Hamburg 1 Eintracht Frankfurt 1 Hamburg 1 Bayer Leverkusen 1

Bayern München 3 Eintracht Frankfurt 2 Bayer Uerdingen 1 Borussia Dortmund 1 Köln 1 Fortuna Düsseldorf 1 Hamburg 1

Note: Data from 1964 to 1991 are for West Germany. Source: www.rsssf.com/histdom.html; www.rsssf.com/ec/ecomp.html

European Competition wins Borussia Dortmund 1 Bayern München 1

German Cup wins Bayern München 3 Borussia Dortmund 1 1860 München 1 Köln 1

Borussia Dortmund 1 Bayern München 1 Schalke 04 1 Werder Bremen 1

Werder Bremen 3 Kaiserslauten 2 Bayer Leverkusen 1 Hannover 96 1 Bor Moench’ng’bach 1 Stuttgart 1 Bayern München 1

Bayern München 1

Bayern München 5 Schalke 04 2 Werder Bremen 2 FC Nuremburg 1

390

Football around the world

tiers) have become incorporated; and for those that have, the governance mechanisms of regular corporations do not apply. German football regulations require that in floated clubs the Verein must hold 50 per cent plus one vote of the corporation (the ‘50+1 rule’). This restriction means that even if one individual acquired all of the share capital, a majority of the votes would remain under control of the Verein. Borussia Dortmund provides a prominent example of this governance model. In April 2000 Borussia Dortmund hived off its football team by creating Borussia Dortmund GmbH & Co. KGaA, a hybrid corporate form combining elements of a German stock corporation and a limited partnership.4 The general partner, Borussia Dortmund GmbH, is completely owned by Borussia Dortmund’s Verein and manages the company’s business as a permanently functioning executive. The shareholders are not allowed to exercise control through the supervisory board of the hybrid with respect to personnel or substantive management decisions (Dietl and Franck, 2007). German football operates a licensing system, operated by the national football association, but without any form of external control and with the football association not permitted to challenge the data provided by the clubs. In 2002 the national association refused to issue a licence to Eintracht Frankfurt, because of doubts over a bank guarantee to cover a €4 million shortfall. An internal court of arbitration subsequently ruled in the club’s favour, and concluded that licensing decisions must be based only on the data provided by the clubs. External scrutiny of the financial reporting of German football clubs is weak. Pure member clubs are not required to publish accounts. Some incorporated clubs have not been punished for failing to report, even though they are required to do so (Brase and Reichart, 2005). German society tolerates weak law enforcement because football is perceived to be other than a business. FC Kaiserslautern, for example, received a licence between 1997 and 2002 because it succeeded in hiding large salary payments (over €20 million) to star players. The national association fined the club €125,000 and deducted three points for the 2004 season. The club later received financial support from its home state, even though the hidden payments constituted tax fraud (Dietl and Franck, 2007). Table 13.5 indicates that strong growth in revenues for Bundesliga 1 clubs since the late 1990s has been accompanied by relative restraint in total expenditure on wages and salaries. Total revenue increased by 149 per cent between seasons 1999 and 2008. Average revenue per club in 2008 was €79.9 million. According to figures reported by Deloitte (2010), Bayern Munchen’s revenue of €295 million in 2008 was around twice that of Schalke 04 (€148 million), its nearest rival, with Hamburg (€128 million) in third place. Matchday income accounts for around one-quarter of total revenue of the leading German clubs; broadcast revenue contributes around one-quarter; and other commercial activities contribute around one-half. Expenditure on wages and salaries increased by 129 per cent between

Brazil

391

Table 13.5 Revenue, costs and profitability, aggregates, Germany, all Bundesliga 1 clubs, selected years, €m

Total revenue Wages and salaries Operating profit

1999

2002

2005

2008

577 317 47

1043 553 100

1236 576 183

1438 725 136

Source: Deloitte

1999 and 2008, less than the rate of growth in revenue. Consequently profitability has improved, and throughout the 2000s the financial condition of German club football has been relatively healthy. 13.3  Brazil

According to FIFA, there are over 2 million registered footballers in Brazil, and over 29,000 football clubs. Tradition has it that football first came to Brazil in 1894 when Charles Miller, a Brazilian-born Englishman, returned to Sao Paulo from England carrying a ball and rulebook. The game was initially taken up by the British community in Sao Paulo and the cosmopolitan upper classes. Soon the game spread across the city’s social landscape. Clubs were founded and neighbourhood and city-wide leagues were organised. Apart from Miller’s club (Sao Paulo Athletic Club), many other clubs were organised on the basis of ethnic and national identity (Bellos, 2002). For example, the first city league in 1901 consisted of two Brazilian clubs, one club of European immigrants and one club from the German population, as well as the British Sao Paulo Athletic. In the years that followed, other ethnic/national clubs emerged. Rio de Janeiro, the other major centre of early Brazilian football, was home to British clubs, such as the Payssandu Cricket Club, and a Portuguese club, Club de Regattas Vasco de Gama. Clubs based upon ethnicity and nationality could also be found in Salvador, Belo Horizonte and elsewhere, as football proliferated throughout Brazil (Bocketti, 2008). Not all football during this early period was dominated by ethnic clubs. Clubs such as Corinthians and Paulistano in Sao Paulo, and Fluminense and Flamengo in Rio de Janeiro, originated in neighbourhoods, schools or workplaces. In the early days of Brazilian club football, explicit barriers were constructed to deny participation to non-whites and working-class players. In Sao Paulo and elsewhere, the amateur status of clubs and leagues was a major barrier, ensuring that the vast majority of players were of European ethnicity and could draw on personal financial resources. By the 1920s, however, working-class representation had increased, and the practice of paying players under the table was widespread

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Football around the world

(Bocketti, 2008). Many clubs embraced professionalism from 1933 onwards, and professional and amateur leagues emerged in Rio de Janeiro and Sao Paulo. The Brazilian Confederation (CBF) recognised professionalism in 1937. Brazilian club football is organised in a series of interconnected leagues, comprising a national pyramid and state pyramids. The leading teams compete in the national and state pyramids simultaneously. The best-placed teams in the state championships, and the highest-ranked teams in CBF’s rankings, compete in the Copa do Brasil. National competition is organised by CBF, and the state championships are organised by the football federations in each state. The national pyramid competitions start in April and end in December. The state pyramid has a different duration and schedule in each state, but in states with teams competing in the national first and second divisions, the main state championships run from January/February to April/May. Most states have at least one secondary tournament, which runs from July to December, involving teams that do not participate in the top two leagues of the national championship. Competition in states whose teams do not participate in the national competitions usually runs from April to October.5 The national pyramid has four tiers, named Serie A to Serie D. Serie A, B and C have twenty teams each, and Serie D has forty teams. Before 2009 there were three tiers (A, B and C), with sixty-four teams in Serie C. Promotion and relegation between each tier is four-up four-down. The membership of Serie D consists of the highest-placed state championship clubs that do not participate in Serie A, B and C. Teams that are successful in their state leagues can be promoted to Serie D. State championships sometimes operate experimental formats. For example, in the 2008 state championship in Rio de Janeiro, the four most popular teams, Botafogo, Flamengo, Fluminense and Vasco da Gama, played all of their matches at home.6 National competition in Brazil at club level has a relatively short tradition, due partly to the large geographical size of the country. The modern national championship began in 1971. Previously, the most prestigious competitions were the state championships of Sao Paulo and Rio de Janeiro. Prior to 2003, the national championship was decided in a play-off format, most commonly with the top eight regular-season teams competing in a single elimination tournament.7 Since 2003, Serie A has been contested in a double round-robin format, with no play-offs. In 2006 the number of teams in Serie A was reduced to twenty and the number of foreign players fielded as players or substitutes in any match was limited to three. Table 13.6 presents data on the performance of Brazilian clubs in the national championship and in cup competition (domestic and South American). The concentration of success in the national championship is relatively low, with no club winning the championship more than three times within any decade. Seven different Brazilian clubs have been successful in the Copa Libertadores, which is contested by the leading clubs from South American countries.

Brazil

393

Table 13.6 Historical performance of top Brazilian teams in league and cup competition 1971–1979 Championships Internacional 3 Palmeiras 2 Atletico – MG 1 Guarani 1 Sao Paulo 1 Vasco de Gama 1

1980–1989

1990–1999

2000–2009

Flamengo 3 Bahia 1 Coritibia 1 Fluminese 1 Gremio 1 Sao Paulo 1 Sport 1 Vasco de Gama 1

Corinthians 3 Palmeiras 2 Botafogo 1 Flamengo 1 Gremio 1 Sao Paulo 1 Vasca de Gama 1

Sao Paulo 3 Santos 2 Atletico – PR 1 Flamengo 1 Corinthians 1 Cruzeiro 1 Vasca de Gama 1

Corinthians 12 Palmeiras 8 Botafogo 5 Sao Paulo 5 Gremio 4 Vasca de Gama 4 Flamengo 3 Vitória 3 Santos 3 Cruzeiro 3 Atlético Mineiro 3 Bragantino 2 Portuguesa 2 Atlético – MG 1 Guarani 1 Internacional 1

Sao Paulo 12 Santos 10 Internacional 6 Atletico – PR 5 Corinthians 5 Gremio 5 Flamengo 4 Sao Caetano 4 Cruzeiro 3 Vasca de Gama 3 Goias 1 Fluminese 1

Cruzeiro 2 Gremio 2 Internacional 1 Flamengo 1 Criciúma 1 Corinthians 1 Palmeiras 1 Juventude 1

Cruzeiro 2 Gremio 1 Corinthians 1 Santo Andre 1 Paulista 1 Flamengo 1 Fluminese 1 Sport 1 Corinthians 1

Sao Paulo 1 Gremio 1 Vasco de Gama 1

Atletico – PR 1 Sao Paulo 1

Championship – points for a top three finish Internacional 11 Flamengo 9 Palmeiras 8 Gremio 6 Sao Paulo 7 Sao Paulo 5 Atletico – MG 6 Vasco de Gama 5 Vasco de Gama 5 Guarani 5 Cruzeiro 5 Atletico – MG 4 Botafogo 3 Fluminese 4 Guarani 3 Sport 3 Santos 1 Bahia 3 Fluminese 1 Internacional 3 Coritiba 1 Coritibia 3 Operario 1 Bangu 3 Corinthians 1 Santos 2 Ponte Preta 1 Cruzeiro 1 Brasil (Pel.) 1 Brazilian Cup wins (from 1989) Gremio 1

Copa Libertadores wins Sao Paulo 1 Cruzeiro 1

Internacional 1 Flamengo 1 Gremio 1

Source: www.rsssf.com/histdom.html; www.rsssf.com/intclub.html#sam

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Table 13.7 Percentage breakdown of total revenue, twenty-one Brazilian clubs, 2004–2007

Gate revenue Broadcast revenue Transfer proceeds Sponsorship and advertising Other

2004

2005

2006

2007

7 29 30 11 23

6 26 31 15 22

8 29 23 16 24

8 22 34 11 25

Source: Casual Auditores Independentes Annual Surveys, 2006–8.

Brazil’s national team has enjoyed more success than any other. Brazil has won the World Cup more than any other nation and won more World Cup games. They have also been ever-present at the Finals, never once failing to negotiate their region’s qualifying tournament. Brazil’s success at the World Cup began in 1958 in Sweden when a 17-year-old Pele guided Brazil to victory. His skills, along with those of Garrincha and others enabled Brazil to add further titles in Chile 1962 and, perhaps most spectacularly of all, at Mexico 1970. Following Pele’s retirement, there was a downturn in Brazil’s fortunes and it was not until 1994 that Brazil lifted the World Cup trophy again, beating Italy on penalties after the first goalless Final. Though tipped to win again in 1998 the team lost to France in the Final. Although Luiz Felipe Scolari’s unheralded team arrived at Korea/Japan 2002 without the tag of favourites, they played some dazzling football to claim a fifth FIFA World Cup. In 2006, Brazil lost at the quarter-final stage to a Zidane-inspired France; and in 2010 Brazil lost at the same stage to Holland.8 The availability of published financial data on Brazil’s football clubs is limited, but the accounting firm Casual Auditores Independentes publishes a financial survey (in English) of Brazil’s top twenty-one clubs. The figures quoted below are drawn from this source. The 2007 survey (published in 2008) was the most recent available at the time of writing. The picture that emerges of the financial structure of Brazilian club football in the mid-2000s is one of rapid growth in revenue, but even faster growth in expenditure and a rapidly deteriorating financial position. The clubs covered by the 2004 survey reported total revenue of $311.6 million. The 2007 figure was $703 million. Increased proceeds from player transfers, an increase in gate revenues and a favourable movement in the Brazilian currency against the US dollar all contributed to the growth in total revenue measured in dollars. Sao Paulo, with reported revenue of $100 million, had the largest turnover of any Brazilian club in 2007. Ticket prices in Brazil are relatively low, and gate revenue makes a relatively small contribution to the clubs’ total revenue. Table 13.7 reports a percentage breakdown of total revenue for the period 2004–7.

Japan

395

Total reported costs in 2007 were $861 million. Six of the twenty-one clubs recorded profits in 2007, and the other fifteen clubs reported losses. The aggregate loss was $158 million, up from $107 million in 2006 and $5 million in 2005. The largest single loss-makers in 2007 were Fluminese ($73.4 million) and Flamengo ($31.2 million). Combined assets totalled $822.7 million in 2004, and $1.67 billion in 2007. Total liabilities grew from $682 million in 2004 to $1.36 billion in 2007. For many decades, one of Brazilian football’s defining features has been its capacity for exporting its most talented players overseas. As long ago as 1930, Italian recruiting agents travelled to Brazil and within a year had recruited thirty-nine players to play in Italy (Bocketti, 2008). In 2008 1,776 players left Brazil (an 8.3 per cent increase on 2007). Europe was the destination for more than 40 per cent of these players, with 209 bound for Portugal alone.9 Brazilian footballers can be found in many countries throughout the world: Vietnam, Azerbaijan, Japan, the United Arab Emirates, South Africa and Australia, to mention only a few. The trend has accelerated in more recent times, however. Every player in Brazil’s squad for the 1970 World Cup played in the Brazilian league; but in 1994 less than half the squad (ten players) were based in Brazil. The numbers of home-based players in the 1998, 2002 and 2006 World Cup squads were nine, ten and two, respectively.10 The drain of footballing talent assists the clubs in balancing the books or servicing their debts. Often, however, the Brazilian clubs are not the main financial beneficiaries. Kaka, elected FIFA’s best player in the world in 2007, was sold by Sao Paulo to AC Milan in 2003 for $8.25 million. Six years later Kaka was sold by Milan to Real Madrid for $100 million. In recent times, there has been an increase in the number of players returning to Brazil later in their careers. Highprofile examples include Roberto Carlos joining Corinthians, Vagner Love joining Flamengo, and Robinho rejoining former club Santos on loan. Returning stars tend to be highly marketable. Adriano’s goal-scoring achievements for Flamengo in 2009 assisted the club in selling more than one million replica shirts, a record figure.11 13.4  Japan

The first football match to be played in Japan is reported to have taken place just one year after the sport first appeared in France. In 1873, Lieutenant Commander Archibald Douglas of the British navy organised a game at the Naval Academy in Tokyo Bay. Trade links with Britain ensured that Japan received continued exposure to football during the rest of the nineteenth century, and by the turn of the century football featured on the curricula of a number of teacher training schools. A schools championship was introduced in 1918, and the Japanese Football Association (JFA) was formed in 1921 to administer the first national

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Football around the world

football tournament. The JFA joined FIFA in 1929 (Horne, 1996, 2000; Sugden and Tomlinson, 1998). Despite these early developments, the growth in football’s popularity was severely constrained by the pre-eminence of baseball as Japan’s leading national sport. The initial introduction and subsequent development of baseball was due to the strong American influence, which extended throughout the Pacific Rim and was paramount in Japan between the late nineteenth century and the 1930s, and again after 1945. Academics following Whiting (1977) have attempted to explain baseball’s popularity in terms of its compatability with certain attributes of the Japanese national character, most clearly identified (in the west at least) with the samurai warrior class. According to this interpretation, the distinctive Japanese variant of baseball shares many characteristics with the martial arts, including a rigorous training and disciplinary regime, an emphasis on the repetition of set moves, a focus on the psychological duel between pitcher and hitter, and the suppression of individuality for the benefit of the team (Horne, 1996, 2000). Whether such insights are helpful, or whether they merely reflect the stereotypical cultural prejudices of outsiders, has become a matter for debate among sociologists. There is no doubt, however, that baseball remained Japan’s most popular national sport throughout the twentieth century. Professional baseball was introduced in 1936, and the present-day competitive structure comprising the Central League and the Pacific League was introduced, along US lines, in 1950. Baseball rather than football is played at the elite universities, which are the main recruiting grounds for the top positions in industry and commerce, the media and the professions. Ownership of the leading professional baseball teams rests with large corporations. Japan’s most popular team, Tokyo’s Giants (of the Central League) regularly attract crowds of 50,000, and in general the level of television exposure is high. Despite its tendency to celebrate rather than suppress individuality, football maintained its subsidiary position within the schools curricula throughout the twentieth century. The Japan Football League (JFL), a national league competition comprising non-professional company teams (whose players typically worked in the mornings and trained in the afternoons) was first launched in 1965. Foreign players were admitted from 1967, but had to become employees of the sponsoring company. The principle of professionalism was not accepted by the JSL until 1985 (Nogawa and Maeda, 1999). At international level Japan entered the World Cup qualifying tournament for the first time in 1954, but prior to the 1990s success for the national team was confined mainly to the Olympics. As host nation Japan were quarter-finalists in 1964 and then semi-finalists in Mexico four years later. Japan hosted the FIFA World Youth Championships in 1979, and staged a challenge match between the top European and South American club teams a number of times during the 1980s. Eventually, however, repeated failure by the national team to achieve World Cup qualification

Japan

397

Table 13.8 J. League winners and runners-up, Japan, 1993–2009 1st stage 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002

2nd stage

Kashima Antlers Verdy Kawasaki* Sanfreece Hiroshima Verdy Kawasaki* Yokohama Marinos* Verdy Kawasaki Kashima Antlersx Kashima Antlers Jubilo Iwata* Jubilo Iwata Kashima Antlers* Jubilo Iwata* Shimizu S-Pulse Yokohama F Marinos Kashima Antlers* Jubilo Iwata Kashima Antlers* Jubilo Iwata+

1st stage

2nd stage

2003 Yokohama F Marinos+ 2004 Yokohama F Marinos* Urawa Red Diamonds

2005 2006 2007 2008 2009

Champion Gamba Osaka Urawa Red Diamonds Kashima Antlers Kashima Antlers Kashima Antlers

Runner-up Kashima Antlers Gamba Osaka Gamba Osaka Nagoya Grampus Gamba Osaka

Notes: * Play-off winners; x J. League was played in a single-season format in 1996, before reverting to the split-season format in 1997; + Winners of both stages in the split-season format. Source: http://en.wikipedia.org/wiki/J._League#An_era_after_the_boom_.281996–1999.29

convinced officials of the need to introduce professionalism. In 1986 a committee was set up to investigate the issue, and in 1990 plans were announced for the launch of the professional J. League in May 1993 (Sugden and Tomlinson, 1998; Horne, 2000). Part of the launch strategy was for the J. League to assume a role in urban redevelopment, so no team was allowed to locate in central Tokyo. A stadium capacity of at least 15,000 and a youth policy linked to local schools were among the criteria for league membership. All teams were required to employ qualified coaches. Broadcast rights and sponsorship were to be sold collectively by the J. League. The clubs were registered corporations, with football as their main business concern, ensuring that the management of clubs would be professional and the clubs would not be subsidiaries dominated by other interests. The initial J. League membership of ten was increased progressively to eighteen teams by 1998. The addition of a second tier in 1999 increased the total to twenty-six (sixteen in J1, ten in J2). By 2010 the number of teams had increased to thirty-seven (eighteen in J1, nineteen in J2). In most seasons between 1993 and 2004, the competition in the top tier of the J. League was divided into two stages, with a play-off between the first-stage and second-stage winners held at the end of the season to determine the overall champions. From 2005 the competition was reorganised so as to operate on a round-robin basis along European lines, with the championship winner determined by league points and no ­play-off.12 Table 13.8 reports the winners and runners-up in each season from 1993 to 2009. Initially, automatic promotion and relegation between J1 and J2 was two-up two-down. Between 2004 to 2008, the third-placed J2 club entered a play-off

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series against the sixteenth-placed J1 club. From 2009, automatic promotion and relegation is three-up three-down. The Japan Football League (JFL) is a ­semi-professional league, from which promotion to the J. League is possible but not automatic. In 2000, 2001 and 2006 the JFL champion was promoted to J2; in 2005 two teams were promoted. Since 2007 J. League Associate Membership and at least a fourth-place finish in JFL are requirements for promotion to J2. Currently, there is no relegation from J2 to JFL.13 An important part of football’s ‘rebranding’ was the creation of team identities associated with places of residence rather than employment, and with parts of team names borrowed from Europe and North America; for example, Furukawa Electric from the JSL became JEF United Ichihara, Mitsubuishi Motors became Urawa Red Diamonds, Sumitomo Metals became Kashima Antlers and Yomiuro FC became Verdy Kawasaki (the first J. League champions). Several foreign coaches, including Arsène Wenger and Osvaldo Ardiles, were employed in the early years of the J League, and a number of high-profile foreign players were recruited, including England’s Gary Lineker, Germany’s Pierre Litbarski and Brazil’s Zico and Dunga. Links with Brazil are especially strong due to Brazil’s large ethnic Japanese community (Nogawa and Maeda, 1999; Birchall, 2000; Horne, 2000). It would be hard to argue, as in the case of England in the 1880s or France in the 1930s, that the introduction of professionalism in Japanese football in the 1990s was a natural and inevitable stage in the sport’s organic development. Instead Birchall (2000) has described the creation of the J. League as ‘perhaps one of the greatest mass-marketing events even Japan, and probably the world, has ever seen’. All aspects of the launch were subject to detailed and carefully coordinated planning. While the commercialisation of football has evolved gradually elsewhere, in Japan commercial concerns were paramount from the outset. For example, Japan’s second-largest advertising company, Hakuhodo, were given responsibility for marketing and publicity, while Sony Creative Products took charge of all aspects of product design, including the design of team shirts and other items of merchandise (Birchall, 2000). Initial three-year J. League sponsorship deals were arranged with drinks manufacturer Suntory and consumer credit firm Nippon Shinpan (Nicos) for ¥400 million ($4.4 million at 2010 exchange rates) each, while the sale of broadcast rights raised more than ¥1,000 million ($11.0 million) in 1993, and twice as much in 1994 (Horne, 1996, 2000). Table 13.9 indicates that the average revenue of the J. League J1 clubs increased from ¥2,349 million ($25.8 million) in 1999 to ¥3,328 million ($36.6 million) in 2008. Average attendances increased from 11,658 to 19,278 over the same period, but in 2008 ticket sales accounted for only around 22 per cent of revenues. Advertising made the largest single contribution, of around 45 per cent. Expenditure on the wages and salaries of players and coaches increased at a similar rate from an average of ¥1,144 million ($12.6 million) in 1999 to ¥1,593 million ($17.5 million) in

China

399

Table 13.9 Average attendance, revenue and salary expenditure, Japan, J1 clubs, 1999–2008, ¥m Wages and salaries expenditure

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

Attendance

Operating revenue

Coaches

Home players

Foreign players

Total

11658 11065 16547 16368 17351 18965 18765 18292 19081 19278

2349 2370 2727 2724 2756 2956 3084 3019 3267 3328

241 258 267 285 285 288 303 323 345 347

555 555 559 586 576 661 710 698 753 808

349 333 410 399 349 421 506 424 436 438

1144 1146 1236 1269 1210 1370 1518 1445 1533 1593

Source: J. League, www.j-league.or.jp/eng/data/index_03.html

2008. The share of home-based players in total wages and salaries expenditure has increased gradually over this period. 13.5  China

When modern football was introduced to China in the late nineteenth century it was played mainly by university and high school students. The development of the game was slow until the formation of the Peoples’ Republic of China on 1 October 1949. On that day the Shengyan football team was invited to Beijing to play as part of the celebration of the establishment of the new communist regime. ‘Football was seen as a symbol of modernity; a talisman of topicality; a statement of intent. The intention was clear: modern sport would characterize modern China’ (Jinxia and Mangan, 2001, p79). The first National Football Championships took place in Tianjin in December 1951, contested by teams from the six administrative areas, the Army and the Railway Association. Shortly afterwards, thirty-one players were selected to form the national football squad. This marked the beginning of state-organised football in China. Subsequently, ‘specialised’ (professional) teams were established in virtually every province, municipality and autonomous region, as Chinese football became institutionalised, professionalised and politicised (Jinxia and Mangan, 2001). In the early 1950s China established close football contacts with other socialist countries. The most influential contact was with Hungary, whose national team at the time was world-class. Hungarian experts were invited to China to give lectures, and the Hungarian national team travelled to China to demonstrate its

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Table 13.10 Football League and Super League winners and runners-up, China, 1994–2009

1994 1995 1996 1997 1998 1999 2000 2001 2002

Champion

Runner-up

Dalian Wanda Shanghai Shenhua Dalian Wanda Dalian Wanda Dalian Wanda Shandong Luneng Taishan Dalian Shide Dalian Shide Dalian Shide

Guangzhou Apollo Beijing Guoan Shanghai Shenhua Shanghai Shenhua Shanghai Shenhua Liaoning Shanghai Shenhua Shanghai Shenhua Shenzhen Ping An

Champion

Runner-up

2003 2004

Shanghai Shenhua Shenzhen Jianlibao

2005 2006

Dalian Shide Shandong Luneng Taishan Chanchung Yatai Shandong Luneng Taishan Beijing Guoan

Inter Shanghai Shandong Luneng Taishan Shanghai Shenhua Shanghai Shenhua

2007 2008 2009

Beijing Guoan Shanghai Shenhua Changchun Yatai

Source: http://en.wikipedia.org/wiki/Chinese_football_champions

skills. China also sent a squad of twenty-five players to Hungary for eighteen months’ training. As a means of improving playing quality, a national league system was set up in 1956 comprising two divisions. This seemed to have the desired result:  playing standards improved, and by the end of the 1950s China was a footballing power in Asia. As the Chinese economy entered a more turbulent phase in the early 1960s, followed by the Cultural Revolution which began in 1966, organised football in China was hard hit. The number of ‘centralised’ footballers and teams was reduced, and the national football championship was not staged for several years. Following Chairman Mao Tse Tung’s death in 1976, the ruling party embarked on a period of economic and social reform. The promotion of football throughout the country was given higher priority, and football was permitted to become more ‘commercial’. In 1988, ‘professional’ clubs were formed and, as a consequence, players were rewarded financially and became more professional in their attitude (Jinxia and Mangan, 2001). The Chinese Football League was established in 1994 with two tiers: Division 1A (Jia A) and Division 1B (Jia B). Initially there were twelve clubs in each tier, until 1998 when two more clubs were added to Division 1A. Table 13.10 reports the winners and runners-up of the Football League (1994–2003) and its successor the Super League (2004–9). In 1998, the annual income of each player in Jia A was at least 100,000 yuan ($14,700 at 2010 exchange rates), twenty times the average personal income. A star player could earn more than one or two million yuan per year. Most ‘professional’ clubs were run by national enterprises, and were underwritten financially by the state. Consequently, rising debt was not seen as a problem (Jinxia and

China

401

Mangan, 2001). While footballers were being highly paid, the national team was underachieving. This prompted calls for wages to be reduced. In January 2001 the Chinese Football Association introduced maximum salaries and transfer fees. The monthly salary for a Jia A player was capped at 12,000 yuan ($1,765), and each team’s win bonus was capped at 400,000 yuan ($58,800) (Jinxia and Mangan, 2001). Transfer fees were set by the Chinese Football Association, and the transfer market was largely controlled. A player seeking a transfer requires the approval of his club, even if his contract has already expired, for up to thirty months from when he last represented the club. This rule appears to contravene a FIFA regulation that any professional footballer is free to conclude a contract with another club, if his contract with his present club has expired or is due to expire within six months. Clubs are allowed to set their own ticket prices, subject to state agreement under the auspices of the local Price Management Department. Jia A clubs were required to pay 5 per cent of their ticket income to the Chinese Football Association and Jia B clubs 2.5 per cent (Amara et al., 2005). The Chinese Football Association is responsible for negotiating and controlling the sale of broadcast rights at national level, though local broadcast rights are owned by clubs and may be negotiated locally. The income for Jia A clubs was, on average, 3.08 million yuan ($450,000) in 2000, of which approximately 1.2 million yuan ($175,000) came from naming rights and sponsorship (Amara et al., 2005). To promote greater professionalism, enterprises were encouraged to provide sponsorship and other forms of financial support, and major investors are identified in the names of most clubs. The number of investors in each Jia A club varies from one to more than twenty. In practice the majority of the investing enterprises are state-owned, and company sponsorship is simply another form of public subsidy by a different name. Even so, there has been pressure for football clubs to operate on a more commercial footing. The Chinese Football Association, for example, established a set of eighteen benchmarks for professional clubs wishing to join the Chinese Super League (CSL), formed in 2004 when Jia A was replaced by the CSL and Jia B was renamed the China League (CL). Requirements include a stadium with a seating capacity of 30,000, an income in excess of 3.3m yuan (excluding transfers), a financial record that does not show losses for three consecutive years, and a healthy balance sheet in the year of entry into the Premier League. The clubs argued that these requirements were too stringent, but the Chinese Football Association felt it would rather have fewer clubs participating than lower the standards for entry (Amara et al., 2005). Soon after the CSL started, play was suspended temporarily over issues of match-fixing and corruption, and the financial instability of several clubs became apparent. In its inaugural year the CSL had twelve member teams. Initially it was planned to increase the number of teams to sixteen by 2006, with no teams relegated at the

402

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end of the first two campaigns. A membership of sixteen was not achieved until 2008, however, due to the withdrawal of Sichuan Guancheng in 2006, and the merger between Shanghai United and Shanghai Shenhua in 2007. The CSL starts in February–March and ends in November–December. From 2008, two-up twodown promotion and relegation operated between the CSL and the CL. The first sponsor of the CSL was Siemens. Following a controversial first season, Siemens did not renew its sponsorship. The start of the second season in 2005 was delayed for a month while new sponsors were sought, unsuccessfully. At the time of writing, Pirelli are the sponsors for the period 2009–11.14 Before the start of the 2010 season, the Chinese Football Association relegated two teams from the CSL to the CL following a corruption scandal involving accusations of match-fixing and illicit gambling. The two lowest-placed teams at the end of the 2009 season retained their places in the CSL. One of the relegated teams, Chengdu Blades, was owned by the English Football League club Sheffield United, which acquired a majority stake in 2006 with the aim of developing new playing talent. Chengdu Blades were promoted to the CSL in 2007, but were subsequently accused of bribing an opposing team to lose a crucial game in order to secure promotion. Guangzhou GPC, also promoted in 2007, were similarly accused. These actions are part of a widening crackdown on corruption. Twenty senior officials and players were implicated, including the former head of the Chinese Football Association. Conclusion

Chapter 13 has presented a brief description of the historical development and present-day competitive and commercial structure of football in France, Germany, Brazil, Japan and China. The histories of professional football in these countries provide many fascinating comparisons and contrasts, both with each other and with the story in England, the main subject of the previous chapters of this volume. In no other country does football’s top tier come close to matching the English Premier League financially, in terms of the revenue the Premier League generates and the sums its member clubs spend, primarily on players’ remuneration. Nevertheless, the existence of a somewhat less rampant commercial ethos in French professional football has not precluded the development of a national team capable of competing successfully at the very highest level, in a manner that has proven notoriously elusive for England in successive World Cups and European Championships since the national team’s sole World Cup triumph in 1966. Likewise the German national team, and (especially) its West German predecessor before unification, has been a highly successful international competitor. The commercial organisation of German club football also presents some stark contrasts with the English model. Although German clubs tend to feature

China

403

less prominently at the very highest levels of European club football than they once did, the club licensing system that operates in the Bundesliga appears to be effective in preventing some of the more reckless styles of financial management at club level that have occasionally embarrassed or disfigured the Premier League. The Brazilian national teams that triumphed in the 1994 and 2006 World Cups were more prosaic in terms of their style of play than their predecessors of 1958, 1962 and 1970, but Brazil still retains a special place in the affections of many football supporters worldwide. Rather like France, a tradition of exporting its most talented players has, over the years, acted as a drain on the competitive strength of Brazilian club football. Brazil is renowned for the fanatical enthusiasm of its population for participation in football, from the grassroots level upwards. In contrast, the east Asian economic powerhouses of Japan and China have little or no historical footballing tradition, at either the grassroots or the professional level. Recent attempts in these countries to establish a market for professional football from the top down present an interesting contrast to the bottom-up evolution of the professional sport elsewhere, from its early historical origins in England and other countries. Notes 1 See http://en.wikipedia.org/wiki/Ligue_1#Foundation 2 See www.bundesliga.de/en/liga/news/2008/index.php?f = 0000128159.php 3 See http://en.wikipedia.org/wiki/Fu%C3%9Fball-Bundesliga 4 A KgaA is a separate legal entity whose share capital is divided into shares which are held by at least one shareholder (the general partner) with unlimited liability and limited liability shareholders (Kommanditaktionäre) that are not personally liable for the debts of the company. Borussia Dortmund GmbH & Co. KgaA is different to a German stock corporation in that it has no management board. Instead, Borussia Dortmund GmbH, as the general partner, is solely responsible for its management and representation. Borussia Dortmund’s Verein is the sole shareholder of GmbH. The supervisory board of KgaA has no authority to appoint and dismiss managing directors at Borussia Dortmund GmbH or to regulate the terms of their contracts. See http://eng.borussia-aktie.de/?%9FY%1B%E4%F4%9D. 5 See http://en.wikipedia.org/wiki/Brazilian_football_league_system 6 See http://en.wikipedia.org/wiki/Brazilian_football_league_system 7 Bellos (2002) describes the format as ‘unfeasibly complicated’. For example, in 1978 there were seventy-four teams divided into six groups (A–F). Each team in each group played each other once and all teams qualified for the second round. The six top clubs in groups A–F formed four groups of nine (G–J). In these groups the six best teams moved to the third round. The other thirty-eight teams from round one formed six groups (K–P) and the winners of each qualified for the third round. Together with the best-placed loser from G–J and K–P, these thirty teams formed four groups of eight (Q–T). The top two in each of Q–T went through to the next phase of eight teams who played a knockout of quarter final, semi-final and then a final. 8 See www.fifa.com/worldcup/preliminaries/southamerica/teams/team = 43924/profile.html 9 See www.insidefutbol.com/2010/02/05/economic-crisis-changes-brazilian-game/16983/

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10 See www.planetworldcup.com/atwc/atwc_squads.html 11 See www.insidefutbol.com/2010/02/05/economic-crisis-changes-brazilian-game/16983/ 12 See www.j-league.or.jp/eng/history/ 13 See http://en.wikipedia.org/wiki/J._League 14 See http://en.wikipedia.org/wiki/Chinese_Super_League

14 The economics of the World Cup

Introduction

Countries compete fiercely for the right to host mega sporting events such as football’s World Cup, and the Olympic Games. In order to host a mega event, large volumes of public subsidy are usually required. In this respect, the 1984 Los Angeles and 1996 Atlanta Olympics were exceptional, in having been funded primarily from the private sector. Those who advocate the use of public funding to secure and stage a mega event invariably promise a wide range of benefits for host cities and the host nation, including increased employment and per capita income, as well as less tangible social and cultural benefits deriving from an enhanced local or national reputation. Since the economic benefits are the more tangible, these have tended to receive the most attention from academic and non-academic economists. Indeed, bids to host the World Cup have in recent times been ‘sold’ to the public on the basis of extravagant predictions about the large gains in employment and income that can be anticipated if the bid is successful. In recent decades, academic economists have gained some experience in evaluating the credibility of claims of this kind, due to a remarkable late twentieth-­century boom in the construction of sports stadia for major league sports franchises in North America. Crudely speaking, the public sports strategies of many cities are based on offering taxpayer-funded financial subsidies for investment in sports stadium construction or renovation projects, in an attempt to attract or retain major league franchises. Taking advantage of tight restrictions on the supply of major league sports that are imposed by the franchise system, team owners have been complicit in encouraging a competitive bidding war to emerge between municipalities. Team owners can and sometimes do make threats to move to another city offering a better deal, unless the present host city makes an acceptable counter-offer. Many local politicians have participated willingly in this process, mindful of the possible kudos to be gained by attracting a new major league franchise, or fearful of the opprobrium the departure of an established franchise might bring. Consequently, a curious market has developed in economic impact studies produced by consultancies, showing that the economic benefits of particular stadium infrastructure 405

406

The economics of the World Cup

projects justify the proposed public subsidy. Academic economists, however, tend to view such claims with extreme scepticism. Some economists believe the net economic impact of sports stadium infrastructure projects is negligible at best, or perhaps even significantly negative at worst. Noll and Zimbalist (1997) present a collection of detailed case study material, and Siegfried and Zimbalist (2000) provide a concise review. In view of the enormous expenditures involved in hosting the World Cup, Chapter 14 examines whether a successful World Cup bid is likely to yield economic benefits to the host nation that are capable of justifying the enormous financial outlays. Hosting the World Cup certainly carries heavy costs. FIFA requires the World Cup host country to provide at least eight and preferably ten modern stadia capable of seating 40,000 spectators or more. For the jointly hosted 2002 World Cup in Japan and South Korea, each country offered to provide ten separate stadia. As neither country had any large pre-existing football infrastructure, South Korea constructed ten new stadia at an estimated cost of nearly $2 billion, and Japan built seven new stadia and refurbished three others at a cost of at least $4 billion (Baade, 2006). As in the case of city-level stadium infrastructure projects for US major league sports, when the question is asked whether the massive expenditures required to host a mega event are justified by corresponding anticipated gains in employment or per capita income, the answer is typically an unequivocal ‘yes’ when given by those advocating the use of public funds in order to secure and stage the event. The answer tends to be an equally resounding ‘no’ when given by academic economists. For example, the 1994 World Cup Organizing Committee in the US  predicted that around one million international visitors would come to the US, making the event one of the most significant tourist attractions in American history (Baade and Matheson, 2004). Prior to the event, it was estimated that hosting the 2010 World Cup would boost South Africa’s national income by more than $6 billion (Grant Thornton, 2008). Academics, however, have been quick to point out the failings of prospective economic impact studies. It is claimed that many such studies are based on poor methodology, fail to distinguish between gross and net effects, fail to take account of substitution and crowding-out effects (see below), and are based on over-optimistic assumptions concerning the propensity for any additional expenditures to deliver economic benefits at the local level. Section 14.1 provides a description of the origins and competitive structure of the World Cup, and highlights several of its unique economic characteristics. Section 14.2 discusses some of the key issues and principles involved in evaluating the economic benefits derived from hosting a mega sporting event. Section 14.3 reviews a number of prospective economic impact studies, most of which use either input-output models or computable general equilibrium (CGE) models to generate predictions for the employment and income effects. While offering some improvements over the relatively simplistic input-output approach, CGE models are still based upon some strong assumptions about the structure of the economy.

The World Cup

407

For this reason, most academic economists prefer to rely upon retrospective econometric analysis of the effects of mega events on indicators such as employment or per capita income, either at city, regional or national level. Section 14.4 reviews several retrospective studies, which seek to establish whether the experience of hosting a World Cup conformed to the prospectively advertised benefits. Both the prospective and retrospective analyses focus primarily on the pecuniary costs and benefits of hosting the World Cup. There is also a smaller literature that takes a broader perspective, examining the impact of the mega event on non-pecuniary (or intangible) factors, such as happiness or the ‘feelgood’ effect. Section 14.5 considers the nature of these intangible benefits, and discusses ways in which they might be measured and assessed. 14.1  The World Cup

The World Cup has been contested by the men’s national football teams of the member associations of the Federation of International Football Associations (FIFA) once every four years since the inaugural tournament was held in Uruguay in 1930, with the exceptions of 1942 and 1946 when the tournament was not staged during and immediately after the Second World War. Table 14.1 provides summary historical details of all previous World Cup tournaments, up to and including the South Africa World Cup Finals staged in 2010. The current format of the tournament involves thirty-two teams competing for the title at venues located in the host nation(s), over a period of around a month’s duration (the Finals phase) in June and July. A qualification phase, which takes place over the course of the preceding three years, determines which teams qualify for the Finals phase, together with the host nation(s) who receive a bye. Prior to the 2006 tournament, the winning team from the previous World Cup also received a bye, but currently the previous winner is required to participate in the qualification phase. The World Cup is the most widely viewed sporting event in the world: the estimated cumulative television audience for the 2006 World Cup in Germany was 26.2 billion, an average of 409 million viewers per match. It is estimated that 715.1 million people watched the final between Italy and France (FIFA, 2008).1 The World Cup generates estimated worldwide revenue of around $4 billion for FIFA, making it the world’s most popular and probably the world’s most profitable sporting event (Szymanski, 2003; Kurscheidt, 2006). FIFA funds most of its operations from the profits it generates by staging this single event once every four years. On the cost side of the profit equation, the players’ salaries continue to be paid by their clubs as their ultimate employers, and any additional payments for appearing in the tournament are borne by the national football associations. Selection to participate in the World Cup Finals phase is considered to be the pinnacle of a player’s career, and the accolade of selection may yield huge benefits to either the player or his employing club or both, in the form of enhanced bargaining power for the player in salary negotiations, the player’s enhanced marketability

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The economics of the World Cup

Table 14.1 History of the World Cup

Year

Host nation

Teams in qualifying phase

1930 1934 1938 1950 1954 1958 1962 1966 1970 1974 1978 1982 1986 1990 1994 1998 2002 2006 2010 2014

Uruguay Italy France Brazil Switzerland Sweden Chile England Mexico West Germany Argentina Spain Mexico Italy US France South Korea/Japan Germany South Africa Brazil

— 31 36 33 38 53 56 71 71 98 106 109 121 112 144 172 193 195 204 —

Teams in Finals phase

Number of cities/stadia

Winning team

Runner-up team

13 16 15 13 16 16 16 16 16 16 16 24 24 24 24 32 32 32 32 32

1/3 8/8 9/10 6/7 6/6 12/12 4/4 7/8 5/5 9/9 5/6 14/17 9/12 12/12 9/9 9/10 20/20 12/12 9/10 —

Uruguay Italy Italy Uruguay West Germany Brazil Brazil England Brazil West Germany Argentina Italy Argentina West Germany Brazil France Brazil Italy Spain —

Argentina Czechoslovakia Hungary Brazil Hungary Sweden Czechoslovakia West Germany Italy Holland Holland West Germany West Germany Argentina Italy Brazil Germany France Holland —

Source: Kurscheidt (2006), Sky Sports Football Yearbook

in football’s player transfer market, as well as lucrative opportunities for involvement in advertising and commercial sponsorship. Many of the other costs of staging the tournament, including security, communications, and investment in the construction of stadia, other physical infrastructure and transport infrastructure, are borne by the local organising committee and are usually heavily subsidised from public funds. Despite the heavy costs it entails, competition among bidding nations to stage the event is intense, and the bidding process is highly politicised. By awarding the 1994 Finals to the US, the 2002 Finals jointly to two Asian nations, Japan and South Korea, and the 2010 Finals to South Africa, FIFA has attempted to use the tournament as a means to stimulate awareness and interest in football in countries and continents where the sport’s popularity and commercial potential was hitherto underdeveloped. Beginning with the decision to award the 2010 Finals to South Africa, which was taken in 2004, FIFA announced that it would in future operate a rotation system between continents for the award of the Finals among its member federations (Kurscheidt, 2006).

Costs and benefits of hosting a mega sporting event

409

The qualification phase comprises a set of six separate qualifying tournaments held within the six FIFA continental zones (Africa, Asia, North and Central America and Caribbean, South America, Oceania, Europe), and overseen by their respective confederations. For each tournament, FIFA decides the number of places awarded to each of the continental zones beforehand, generally based on the relative strength of the confederations’ teams, but also subject to lobbying from the confederations. The formats of the qualification tournaments differ between confederations, and in some cases the qualification process begins almost three years before the Finals, and lasts for around two years. One or two places in the Finals are awarded to winners of intercontinental play-offs. For example, the winner from the Oceania zone (considered to be the weakest of the six) and the fifth-placed team from the Asia zone competed in a play-off for a place in the 2010 World Cup. Since the 2002 World Cup, the Finals phase has featured thirty-two teams. There are two stages: a group stage followed by a knockout stage. In the group stage, the teams compete within eight groups of four teams each. Eight of the thirty-two teams are seeded (including the hosts, with the other teams selected using a formula based on both the FIFA World Rankings and performances in recent World Cups) and assigned to separate groups. The other twenty-four teams are assigned to three different ‘pots’, based on team quality and on geographical criteria; and one team from each pot is assigned randomly to each of the eight groups. Since 1998 constraints have been built into the draw to ensure that no group contains more than two European teams, and no group contains more than one team from any other confederation. Each group plays a round-robin tournament, giving every team three group matches. The two final matches in each group are scheduled simultaneously. The top two teams from each group advance to the knockout stage. Points are used to rank the teams within each group. Since 1994, three points have been awarded for a win, one point for a draw and none for a loss. If two or more teams have the same number of points after three matches, a series of tiebreakers is applied: first goal difference; then total goals scored; then head-to-head results; then finally drawing lots at random. The knockout stage is a single-elimination tournament, in which teams compete on a pairwise basis in one-off matches, with extra time and penalty shoot-outs used to decide the winner if necessary. The knockout stage begins with the ‘round of sixteen’, in which the winner of each group plays against the runner-up of another group. This is followed by the quarter-finals, the semifinals, the third-place match (contested by the losing semi-finalists) and the final. 14.2  Costs and benefits of hosting a mega sporting event

The appropriate methodology for the evaluation of the economic impact of mega events such as the World Cup or Olympic Games, and for the evaluation of the impact of smaller-scale and more localised projects such as the construction of a new stadium in a particular US city for a major league sports franchise, has

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been the subject of vigorous debate. As noted in the introduction, a chasm has emerged between the hyperbolic claims of many prospective economic impact studies carried out by consultants, and the sober assessments obtained from retrospective analysis of historical income or employment data at local level before, during and after the construction of a facility or the staging of a mega event. A typical prospective economic impact study prepared by consultants estimates the number of visitors an event is expected to draw, the number of days each spectator is expected to stay, and the average expenditure of each visitor on each day. By combining these figures, an estimate of the ‘direct economic impact’ is obtained. A multiplier is then applied to the direct economic impact, to account for the recirculation of the initial direct expenditure through the local economy. Ticket-holders for the event buy hot dogs from a vendor located outside the stadium, who spends some of the proceeds on a round of drinks in the local pub, and the publican celebrates by purchasing an additional lottery ticket from the local newsagent, and so on. The additional expenditure is known as the ‘indirect economic impact’. Multipliers close to two are commonly used, making the total economic impact approximately twice the size of the initial direct expenditure. Matheson (2006) uses a three-way classification for the possible sources of bias in this type of study, arising from incorrect treatment of substitution effects, crowding-out or displacement effects, and leakages. A focus on gross rather than net expenditure is believed to be a principal cause of the tendency for many prospective studies to present exaggerated or hyperbolic assessments of economic impact. Substitution effects are incorrectly treated if the economic impact is presented as the aggregation of all gross expenditures or receipts associated with the event. The substitution effect refers to the likelihood that money spent by local residents at an event would have been spent elsewhere in the local economy if the event had not been staged. Therefore expenditure by local residents should not count in the calculation of the economic impact of the event. Incorrect treatment of substitution effects can also arise in respect of investment expenditure. For example, the construction of new transport infrastructure might have gone ahead anyway, even if the event had not been staged. Similar issues may arise with expenditures by visitors from outside the city or region. Visitors who have travelled specifically in order to attend the mega event, and who would not have visited either at the time of the event or at some other time if the event had not been staged, bring new expenditure that should count towards the economic impact. The expenditure of visitors who just happen to be in town and decide to attend, and who would have spent their free time and money on other leisure activities in town had the event not been staged, should not count. Neither should the expenditure of visitors who rearrange a trip they would have made anyway in order to attend the event. In this case, the question as to what constitutes gross and net expenditure is heavily dependent on market definition. An event that diverts tourists from one city to another within the same country

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might generate a positive net benefit if the measurement is at city level, but no net effect if the measurement is at national level. Crowding out refers to the displacement of expenditures that would have taken place if the event had not been staged, but which are diverted elsewhere as a result of the decision to stage the event. During the preparation phase, the construction of the stadium and infrastructure might divert productive resources from alternative projects that would otherwise have gone ahead. Problems of noise, pollution or traffic congestion in the vicinity of the site might result in the relocation of some residents or the diversion of some forms of economic activity to other localities. During the mega event itself, tourists who would otherwise have visited the city might decide not to visit, in order to avoid exorbitant hotel bills or traffic congestion. If the city’s hotels were already operating close to full capacity, then the mega event might simply displace one type of visitor with another, yielding no net effect. Issues relating to crowding out also arise in respect of the opportunity costs of the public expenditures deployed to subsidise a mega event. For example, expenditure on the construction of a sports stadium might have generated larger economic benefits if the same money had been used to build new hospitals or schools. If the public investment is debt-funded, the opportunity costs in terms of higher taxes or reduced public services might produce a drain on the local economy that lasts for many years. This effect might be mitigated to some extent by longstanding benefits from ongoing local usage of the stadia and other facilities, if the danger that these infrastructures assume ‘white elephant’ status following the departure of athletes and the media circus can be averted. Leakages occur when expenditure associated with an event takes place in the local economy, but is remitted elsewhere by its immediate recipients. Leakages reduce the size of the indirect economic impact on the local economy. For example, the construction workers hired to build a stadium might be brought in from outside the city, region or country, and they might remit a large proportion of their earnings to their families who are located elsewhere. The hotel which accommodates visitors to the event might form part of a national or international chain. The revenues it generates contribute to the chain’s profits, which accrue to shareholders who could be located anywhere. In measuring the indirect economic impact, the effects of leakages should be reflected in an appropriate choice of multipliers. The multipliers used in prospective economic impact studies are often calculated using input-output models, which trace the impact of changes in expenditure by consumers, investors or governments on all sectors of an economy, by quantifying the linkages between sectors created by the use in each sector of inputs that are the outputs of other sectors. A model that has been widely used in economic impact studies for the construction of sports facilities in the US is the Bureau of Economic Analysis’ Regional Industrial Multiplier System (RIMS II). This model provides final-demand output multipliers for 473 detailed industries, including hotel accommodation, eating

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and drinking establishments, and arts, entertainment and recreation. A commonly voiced criticism of prospective studies of the economic impact of the construction of new stadia for North American major league sports franchises is that the assumed multipliers tend to be too high. With major league sports, much of the consumer additional expenditure that the franchise generates, for example through ticket sales, contributes to athletes’ salaries, but many athletes live outside the local area in which they play. Expenditure on tickets to watch major league sports is therefore less likely to be recycled through the local economy than expenditure in local restaurants, theatres or cinemas, to which the local consumer expenditure on tickets might otherwise have gone, if the stadium had not been built (Siegfried and Zimbalist, 2000). More generally, input-output models are based on highly restrictive assumptions of linearity in production technology; in other words, any increase in final expenditure always generates a pro rata increase in the production of all intermediate and final outputs. Accordingly, it is assumed that the structure of the economy is invariant to shifts in demand and supply, there is no price mechanism and there are no capacity constraints. The use of incorrect multipliers compounds errors that may already have been introduced through the incorrect treatment of substitution and crowding-out effects. Despite the use of multipliers in macroeconomics having been widely discredited for various theoretical reasons, their use in economic impact studies is commonplace and largely unquestioned by practitioners (Humphreys, 2006). The issue of inflated multipliers may become even more problematic in the case of mega events. The multipliers in RIMS II (and those from other input-output tables) are based upon inter-industry relationships within regions based upon an economic area’s normal production patterns. During a mega event, however, patterns of economic activity within a region or a city are expected to differ substantially from those that are observed normally. Therefore the inter-industry linkages on which the model is based may not be relevant. If there is no reason to believe that the usual economic multipliers apply, any economic analysis based upon these multipliers is questionable (Baade, 2006; Porter and Fletcher, 2008). Besides the methodological questions associated with assessing the economic effects of mega events, there are also serious problems in the implementation. Most prospective (ex ante) economic impact studies anticipate large gains in income and employment from hosting a mega sporting event. Many such studies are carried out by consulting agencies hired by the sport’s governing body, or by local or national government. Consultancies face obvious financial incentives to produce conclusions tailored to suit the wishes of commissioning body or organisation, and tend to produce reports that are biased towards the overstatement of benefits and understatement of costs. Ideally, the results of prospective studies should be compared with those of retrospective (ex post) studies in order to determine whether, in hindsight, they were correct. However, governments, sports governing bodies or organising committees have little or no incentive to commission

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retrospective studies for mega events that have taken place in the past (Coates and Humphreys, 2003b). Political backing for the use of tax revenues to subsidise sports events tends to gain traction from the distribution of support and opposition among electorates. Sports enthusiasts might constitute only a minority of the population, but might be highly motivated and highly vocal in their advocacy of public subsidy. The majority of the population might be either indifferent or only mildly hostile, but poorly organised in order to oppose proposals that might only translate into a small or negligible additional tax burden per person (Siegfried and Zimbalist, 2000). 14.3  Prospective economic impact studies

In the past 15–20 years many prospective impact studies of mega sporting events have been produced, although until recently such studies for the World Cup were relatively few in number.2 Rahmann et al. (1998) report a cost-benefit and scenario analysis that was conducted on behalf of the German Soccer Association ahead of the 2006 World Cup. Estimates are presented of the economic impact over the next ten years following the World Cup, based on the number of venues and the spending of World Cup tourists. The estimated expected benefit was around €1.5 billion, and the top estimate was €3.4 billion. Ahlert (2000) uses an input-output model to estimate the economic impact of the 2006 World Cup on the German economy. Under a variety of financing schemes for the construction of the necessary infrastructure, the predicted increase in employment over the period 2003–10 was more than 2,400 jobs annually, with a peak employment gain of 7,300 jobs in 2006. The predicted increase in GDP was €1.5 billion in 2006, and the cumulative gain in GDP over 2003–10 was €5.3 billion. South Africa’s (unsuccessful) bid for the 2006 World Cup was based, in part, on the premise that it would boost the economy by approximately $6 billion, and create 129,000 new jobs (Khoza, 2000). Prior to the 2002 World Cup, a study by the Dentsu Institute for Human Studies estimated a $24.8 billion economic impact for Japan, and a $8.9 billion economic impact for South Korea. These figures represent 0.6 and 2.2 per cent of the total Japanese and South Korean GDP, respectively (Finer, 2002). In a report on the benefits of the 2010 World Cup, hosted by South Africa, Grant Thornton (2003) estimate that the event would generate additional direct expenditure of $1.7 billion (R12.7 billion), producing an overall economic gain to the South African economy of $2.8 billion. This estimate was based on an assumption that 230,000 foreign tourists would visit during the tournament, staying for an average of fifteen days. The estimated total costs of construction amounted to $1.8 billion. The event would create 159,000 new employment opportunities. The overall economic impact was calculated using ‘appropriate income and employment multipliers and taxation rates’. In an update to the earlier report, Grant Thornton (2008) report a revised estimate that the 2010 World Cup would contribute at least $6.8 billion (R51.1 billion)

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to South Africa’s GDP, up from $2.8 billion in the earlier report. More optimistic estimates of the event’s capacity to attract foreign tourists account for $2.1 billion of the increase. The estimated direct economic impact is $4.1 billion, up from $1.7 billion. The revised estimates are based on assumptions of 289,000 overseas tourists watching an average of between three and four matches each, 48,000 African tourists watching an average of three matches each, and 115,000 domestic tourists watching an average of two matches each. Mabugu and Mohamed (2008) also report a prospective study for the 2010 World Cup. A specially designed fiscal Social Accounting Matrix (SAM) multiplier model is used to model the macroeconomic, sectoral and household impacts of the R17.4 billion allocated by the government for World Cup capital projects.3 At the macroeconomic level, the model predicts an increase in GDP of R163 million, equivalent to a 1.2 per cent increase relative to the base year (2004). The increase in GDP is driven largely by consumer expenditure, which can be traced back, in part, to higher real household income. The $2.3 billion increase in government expenditure is estimated to yield a 1.28 per cent increase in domestic production, while the multiplier analysis suggests domestic supply would increase by 1.23 per cent relative to 2004. At the household level, lowincome households are expected to benefit more than higher-income households from the labour market and employment effects, due to the low-skill bias in construction sector employment. Middle- and higher-income households should benefit from a savings effect, attributed to the fact that the project is wholly government-financed. With specific reference to the predictions of the Grant Thornton (2003) study for South Africa, Swinnen and Vandermoortele (2008) argue that the economic impact may be overstated, for several reasons. First, the study includes domestic residents’ expenditures at the event as direct benefits. However, this is merely a reallocation of existing expenditure, and not a net addition to GDP (Baade, 2006; Johnson and Sack, 1996). Second, according to Bohlmann (2006), the report’s use of multipliers is questionable and overly optimistic. Third, the report estimated that expenditures of $240 million and $66 million would be required for upgrades to stadia and infrastructure, respectively. The International Marketing Council of South Africa (2008) reports much higher investment costs, however: $1.1 billion for ten stadia (five to be renovated and five newly constructed). The cost estimates for the construction of new stadia in Durban and Cape Town were $350 million and $380 million, respectively. The cost of infrastructure upgrades, for example, upgrades of airports and improvements to the country’s road and rail network, was estimated at $1.2 billion. Fourth, the Local Organizing Committee (LOC) planned to recruit unpaid volunteers, shedding a different light on the interpretation of the estimated 159,000 ‘employment opportunities’. Many of the jobs would only be temporary. Due to the economic situation in neighbouring Zimbabwe, and in response to announcements of numerous job vacancies, a huge inward migration of skilled and semi-skilled construction workers to South Africa

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was anticipated and considered likely to account for a considerable share of the newly created employment. In recognition of the theoretical and methodological difficulties with inputoutput models, there has been increasing use recently of computable general equilibrium (CGE) models. CGE models offer several advantages in conducting prospective economic impact analysis in comparison with input-output models. CGE models still require several heroic assumptions, however, concerning the structure of the economy and its responsiveness to the hosting of a mega event. By modelling household expenditure as income-constrained, CGE models are capable of handling displacement effects that arise from sports-related spending. Similarly, scarcity and diversion of resources from other activities is taken into account. Furthermore, the researcher is able to run simulations, in which governments neutralise the effect the event has on their own budgetary position, and, in the case of a national government, on the country’s external debt (Giesecke and Madden, 2007). While CGE modellers have paid considerable attention to the Olympic Games, less attention has been devoted to the World Cup.4 As far as we are aware, Bohlmann and van Heerden (2008) is (at the time of writing) the only prospective CGE study of the World Cup. A 32-sector CGE model of the South African economy is used to predict the economic impact of hosting the event. The model simulates the effect of various shocks, including an increase in government expenditure on construction and increased tourism. A short-term increase in real GDP of 0.61 per cent is estimated, together with a 1.11 per cent increase in employment. The employment gains are driven mainly by unskilled unemployed resources drawn into economic activity by the demand injection. The impact of financing by the government is considered, assuming most of the expenditure is financed through higher taxes. Under a high-tax scenario, there is a negligible increase in GDP, and lower employment. In this case, the economic costs of the event outweigh the benefits. Under a low-tax scenario, with future investment, GDP growth and taxes generating the remaining required resources, both GDP and employment are increased in the short term. 14.4  Retrospective economic impact studies

A very different approach to the same question of economic impact involves retrospective analysis of whether the experience of hosting a mega event, and trends in economic indicators for the cities, regions or nations concerned before, during or after the event, correspond to the claimed or advertised prospective benefits. An obvious difficulty arises in disentangling changes in income, employment, inflation, tourism, and other possible effects caused by the mega event from changes caused by other factors (currency movements, changes in fiscal and monetary policy, and so on). Major sporting events tend to generate levels of media publicity and public awareness that are disproportionate to their economic significance

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measured in terms of contribution to gross domestic product. Consequently, any retrospective analysis of aggregated income or employment data may encounter difficulties in identifying any economic effect which, even if the claims of proponents of the event are accurate, might represent only a tiny fraction of the city or region’s total economic activity. Generally speaking, the greater is the level of spatial or temporal disaggregation of the data employed, the higher is the likelihood of identifying a significant economic impact. Retrospective studies typically employ the tools of multivariate econometric analysis, and most report that the hosting of sporting events has little or no significant impact on employment or income (Baade, 1987; Baade and Dye, 1990; Baade, 1994; Baade and Sanderson, 1997; Baade and Matheson, 2001, 2002). Some studies even arrive at negative and significant estimated effects (Coates and Humphreys, 1999, 2000a, 2000b, 2002, 2003a, 2003b; Teigland, 1999). The unanimity of these findings is startling, and seems almost unprecedented for a profession that is notorious for its capacity for disagreement among its leading practitioners. The sources of the divergence between the prospective claims and the retrospective evidence are explored by Crompton (1995) and Késenne (1999). Matheson (2006) reviews a number of retrospective impact studies.5 Baade and Matheson (2004) presented the first major econometric study of the economic impact of the World Cup. Their analysis of the 1994 World Cup, hosted by the US, suggests that the economic impact of the event did not justify the magnitude of the expenditures. The host cities experienced an aggregate loss estimated at $9.255 billion, in stark contrast to the projected windfalls of the order of $4 billion that were being touted in advance by advocates of the event. Baade and Matheson examine data on growth in real personal incomes for the seventy-three largest metropolitan statistical areas (MSAs) in the US by population, for the time period 1970–2000. A model of the determinants of growth is fitted, for which the explanatory variables include measures of relative nominal wages and local taxes for each MSA, a time trend and various dummy variables. The differences between the actual values for growth in real personal income for each MSA in 1994 are compared with the fitted values obtained from the model, in order to obtain a monetary estimate of the impact of the World Cup for each city. The city-level estimates vary rather widely, from a positive estimated impact for Chicago of $992 million to negative estimates of just over $3.5 billion for both Los Angeles and Fort Worth. Overall, nine of the thirteen host MSAs experienced actual growth in personal disposable income that was lower than the predicted growth derived from the model. Hagn and Maennig (2008) analyse the long-term employment effects of the 1974 World Cup, hosted by West Germany, on the nine German host cities (Berlin, Dortmund, Düsseldorf, Frankfurt, Gelsenkirchen, Hamburg, Hannover, Munich and Stuttgart), using multivariate analysis. The study uses data for the period 1961–88 on the seventy-five most densely populated municipalities in Germany

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in 1974, including all of the host cities. Three methodological approaches are adopted and compared. First, employment in the municipalities is modelled along the same lines as in Baade and Matheson (2004), in order to obtain estimates of the short-term impact on employment in each case. Second, a fixed-effects regression is estimated, in which employment in each municipality in each year is modelled using a set of year dummy variables to register effects acting equally on all cities, city-specific time trends to register specific developments in individual cities, and a World Cup dummy variable for the host cities. Third, a difference-in-difference estimator is used to register changes in the ‘intercept’ (employment and wage levels) and ‘slope’ (growth of these two variables) before and after the World Cup, by comparing host municipalities with others that were unaffected by the event. This approach assumes that the affected municipalities would have performed the same as the unaffected municipalities if the event had not been staged. The results suggest that the 1974 World Cup did not generate any statistically significant employment effects, in either the short term or the long term. Hagn and Maennig (2009) report an analysis of the short-term effects on unemployment of the 2006 World Cup, also hosted by Germany, using monthly data for the seventy-five largest urban districts in Germany including the twelve match venues for the period from January 1998 to March 2007. The dependent variable is the monthly numbers of the unemployed for the urban districts and the independent variables include lagged unemployment, population, dummy variables for East German districts, seasonal dummy variables, gross valueadded sector dummies and a World Cup dummy variable for the host cities. The empirical methodology is essentially the same as in Hagn and Maennig (2008). As before, the results suggest that the pattern of unemployment in the twelve match venues cities was not significantly different from its pattern in the nonvenue cities.6 14.5  Intangible benefits of mega events

Empirical evidence from retrospective studies suggests that the economic benefits of hosting mega sporting events like the World Cup are doubtful at best. However, one limitation of these studies is that they tend to overlook the possible intangible benefits (or ‘feelgood’ effects) that derive from the hosting of a mega sporting event. Adopting a broader view of the potential benefits a mega sporting event might deliver may help explain the fierce competition to host. One of the intangible benefits most widely quoted is civic pride:  mega events bring intangible psychological benefits to the communities that host them. Another key intangible benefit is that of national and international exposure. Sports fans might enjoy their visit to the city and decide to pay a return visit later on, raising future tourist revenues. Corporate visitors might decide to relocate manufacturing or administrative facilities or company headquarters to the city.

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The economics of the World Cup

Television viewers might decide to take a trip to the host city at some time in the future, based on what they see of the city during the broadcast of the mega event. Finally, hosting a major event might raise the profile or general awareness of a city, so that it becomes a ‘major league’ or ‘world class’ city and travel destination. Of course, intangible effects of this kind are extremely difficult to quantify, and there is a paucity of empirical research that can conclusively demonstrate any longrun connections between the hosting of a mega event and future tourism demand or inward investment. Using survey methods, Kim and Patrick (2005) investigate Seoul residents’ perceptions of the impact of the 2002 World Cup. A factor analysis indicates that residents’ perceptions of the factors ‘tourism resource development and urban revitalisation’, ‘image enhancement and consolidation’ and ‘interest in foreign countries or their cultures’ were positive. However, negative perceptions were identified for several factors including ‘disorder and conflict’, ‘traffic problems and congestion’ and ‘negative economic perception’. The latter may well reflect public concern over the levels of public expenditure that were required to underwrite the event, and over the utilisation of the ten brand-new soccer stadia after the World Cup was complete. In general, females, especially housewives, had a more positive perception than males. Perceptions were rather variable over time, and were less favourable three months after the event than they were at the time. A different approach to the measurement of intangible benefits is taken by Kavetsos and Szymanski (2010). Drawing upon the economics of happiness literature, the impact of hosting a major sporting event (Olympic Games, World Cup and European Football Championships) and the effect of athletic success in the same event for the host nation, on happiness among the citizens of the host nation is measured using data from the Eurobarometer Survey Series. The data cover twelve countries – Belgium, Britain, Denmark, France, Germany, Greece, Ireland, Italy, Luxembourg, Netherlands, Portugal and Spain – for the period 1974–2004. The Surveys are conducted on behalf of the European Commission, in order to collect information on the social, health and political aspects of the quality of life for the populations of EU member states. The surveys are conducted twice per year (spring and autumn) and each time around 1,000 randomly selected individuals are interviewed in each country. A key question concerns satisfaction with life, with interviewees invited to respond (on a four-point scale) to the following: ‘On the whole, are you very satisfied, fairly satisfied, not very satisfied, or not at all satisfied with the life you lead?’ In view of the ordinal structure of the survey responses, Kavetsos and Szymanski use an ordered logit model, in which the independent variables capture effects emanating from a recently staged sports tournament (host-nation dummy variables and indicators of medals or tournament rankings). For the Olympic Games, the key performance measure is the difference between actual and predicted medals; and for the two football tournaments, performance is

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measured using the difference between each country’s pre- and post-tournament FIFA rankings. Controls are included for macroeconomic conditions (GDP per capita, unemployment rate and inflation rate), personal characteristics (employment status, sex, age, marital status, household income and education), and individual country and time effects. The results contain little evidence to suggest that happiness is correlated with better-than-expected athletic performance; and for the Olympic Games, host-nation status appears to be negatively associated with reported happiness. Host-nation status for the two football events is positively associated with reported happiness, however, suggesting that hosting an international football tournament may indeed produce a tangible feelgood effect. As seen in Chapter 12, Section 12.1, financial markets present opportunities for the identification of sentiment effects. Ashton, Gerrard and Hudson (2003) track changes in the FTSE 100 index on the days following matches played by England’s national team, including World Cup matches. There is a tendency for the London stock market to react positively to wins and negatively to losses. Edmans, Garcia and Norli (2007) document the stock market reaction to match results in major sporting events, including World Cup football, and international cricket, rugby and basketball. A negative and statistically significant reaction to elimination from the World Cup on the national stock market of the country whose team has been eliminated is interpreted as evidence that sports results have a strong effect on mood. The effect is interpreted as a reflection of sentiment, rather than as a rational adjustment of stock prices to new information, for several reasons. The effect does not appear to be impounded into stock prices in advance in cases where elimination from the World Cup is strongly anticipated. The effect is strongest in the stock markets of developed Western European countries, with strong football traditions and national teams that always feature prominently among the tournament favourites. The effect is stronger in small stocks, whose prices are believed to be sensitive to investor mood, because they are held predominantly by local investors. Heyne, Maennig and Suessmuth (2007) use contingent valuation methods to evaluate the feelgood factor in Germany, following the hosting of the 2006 World Cup. A survey asked 500 respondents about their willingness to pay to stage the World Cup.7 Three months prior to the start of the tournament, the respondents were informed that FIFA was (hypothetically) leaning towards relocating the Finals to Switzerland (host of the European Football Championships in 2008) for safety reasons. There was still a chance that the tournament would take place in Germany, if a series of costly safety measures was implemented, to be financed by means of immediate voluntary contributions from the population. Each person was asked if they would be willing to contribute financially to ensure that the Finals could be hosted in Germany. Three months after the Finals were staged, the same respondents were asked to imagine being faced with the same pre-­tournament decision, and were offered the opportunity to change their original decision or the

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size of their offered financial contribution, in the light of the experience of having seen the tournament actually staged. The average prospective offered contribution of respondents whose willingness to pay was non-zero was $30.4; but less than 20 per cent of respondents reported a non-zero willingness to pay. The average prospective willingness to pay for all respondents was therefore only $5.66. Extrapolated over a total population of 82 million, the estimated total prospective willingness to pay was $467 million. After the tournament was staged, however, more than 40 per cent of respondents reported a positive willingness to pay. The average retrospective willingness to pay for all respondents was $13.38, yielding an estimated total retrospective willingness to pay of $1.1 billion. The average retrospective offered contribution of respondents whose willingness to pay was non-zero was $31.4, only marginally higher than the corresponding prospective contribution. Accordingly, the increase in total willingness to pay was driven almost entirely by an increase in the numbers who were willing to pay anything, and not by any increase in the average amount each individual was willing to contribute. Respondents from Eastern Germany, and respondents with lower levels of educational attainment, were among the groups most likely to have altered their decision as a result of having witnessed or experienced the hosting of the tournament. In the language of consumer theory, the interpretation placed on these findings is that large sports events have the characteristics of experience goods: goods for which consumers cannot assess user value in advance, but only upon consumption or from past experience (Nelson, 1970). The estimated total retrospective willingness to pay of $1.1 billion suggests the value of the feelgood effect is non-negligible, especially when compared to the doubtful or non-existent direct economic effects identified by the retrospective studies that are reviewed in Section 14.4.8 Conclusion

Advocates of the allocation of large publicly funded subsidies in order to secure host nation status for mega events like the Olympic Games or football’s World Cup routinely claim that hosting the event will deliver large economic benefits. However, the overwhelming majority of independent academic studies suggest that the economic impact of the hosting of mega events, or other sports infrastructure projects, is limited. While the gross consumption and investment expenditures that can be identified with mega events are undoubtedly large, attracting tens or hundreds of thousands of live spectators as well as massive TV audiences, most of the retrospective evidence suggests that the net impact of mega events on economic indicators such as employment and per capita income in host cities or nations is either small or negligible at best, and possibly even negative at worst.

Intangible benefits of mega events

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Academic economists have been quick to point out the failings of prospective economic impact studies that make extravagant claims of large benefits. Such studies sometimes fail to distinguish between gross and net expenditures, because they do not take account of substitution and crowding-out effects. Substitution occurs if the expenditure of spectators at the event has been diverted from other leisure activities based in the same locality that would have been patronised if the event had not been staged. Crowding out occurs when economic activities that are not associated with the event are diverted elsewhere, due to congestion or constraints on the supply capacity of the local economy. Some studies prophesying large economic gains are based on overoptimistic assumptions concerning the propensity for additional expenditures associated with the event to deliver economic gains at the local level. Unrealistic assumptions concerning the size of local multipliers may be incorporated, leading to the underestimation of leakages that limit the benefits to local businesses of expenditures accruing during the preparation and the staging phases. One way of squaring the enthusiasm with which cities or nations compete to attract mega events with the lack of tangible evidence of any discernible economic impact is to search for evidence of intangible benefits or ‘feelgood’ effects. Some recent research suggests that intangible benefits might be rather important, and perhaps even sufficient to provide a justification for the public subsidy of major sporting events. Notes 1 According to FIFA the 2006 World Cup was aired in a total of 43,600 broadcasts across 214 countries and territories, generating total coverage of 73,072 hours. 2 Matheson (2006) discusses a number of prospective (ex ante) economic impact studies for other sports, and for mega events. Kasimati (2003) reviews prospective studies for the Olympic Games. 3 The SAM, created by South Africa’s Financial and Fiscal Commission, includes forty-eight economic activities and forty-eight household types, and disaggregates government accounts according to the hierarchy of tax/spending authorities (Central, Provincial and Local/ Municipal) and in respect of the major revenue sources and major categories of expenditure. The SAM is similar in nature to the RIMS II model that has been used for impact assessments of the Olympic Games and World Cup when hosted by the USA. 4 Prospective CGE studies of the Olympic Games include Blake (2005) and New South Wales Treasury (1997). Blake estimates that the 2012 London Olympic Games would lead to an increase in GDP of £1.96 billion between 2005 and 2016, and create 8,164 permanent jobs. 5 Few retrospective studies report significant economic benefits from the hosting of mega events. Most of those that do so are for the Olympic Games (Kang and Perdue, 1994; Hotchkiss, Moore and Zobay, 2003; Jasmand and Maennig, 2008). Recent retrospective CGE studies of the 2000 Sydney Olympic Games conclude that prospective assessments overestimated the economic benefits of the event, because the assumptions relating to induced tourism and the responsiveness of the labour market were too optimistic (Madden, 2006; Giesecke and Madden, 2007).

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6 In a cost-benefit analysis of the 2006 World Cup, Maennig and du Plessis (2007) obtain similar results for the impact on employment and sales. 7 Contingent valuation methods have been used to estimate willingness to pay for a number of sports infrastructure projects in the USA. For example, Johnson and Whitehead (2000), Johnson, Groothuis and Whitehead (2001) and Owen (2006) report that total willingness to pay was insufficient to cover projected or realised costs. 8 Using contingent valuation methods, Atkinson et al. (2008) estimate that Britons would be willing to pay £2 billion for the intangible benefits associated with hosting the 2012 Olympic Games in London.

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Index

Abramovich, Roman, 192 AC Milan, 395 Adams, Micky, 262 admission price, 163, 165, 167, 180, 181, 194, 254, 322, 324, 328, 329, 337, 338, 339, 345, 349, 350 Adriano, 395 AFC Telford United, 194 AFC Wimbledon, 194 Africa, 230, 231, 232, 236, 409 Albania, 231 Alcock, Paul, 315 Alternative Investment Market, 189 American Basketball Association, 18 American Broadcasting Company (ABC), 18 American football, 2, 14, 16, 18, 256, 275, 322 American Football League, 18 American League, 4, 5, 14, 18, 49, 212 American Professional Football Association, 18 Ardiles, Osvaldo, 220, 398 Argentina, 51, 198, 231, 288 Arnold, Sir Thomas, 140 Arsenal, 47, 92, 105, 143, 146, 153, 157, 158, 162, 171, 172, 189, 190, 191, 198, 220, 251, 252, 254, 310, 326, 344 Asia, 230, 236, 400, 409 Aston Villa, 101, 142, 155, 189, 190, 344 Atkinson, Ron, 239 attendances, 3, 9, 10, 52, 79, 88, 92, 104, 139, 150, 153, 154, 155, 156, 157, 165, 169, 171, 178, 180, 195, 239, 240, 254, 258, 319, 321, 322, 323, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 338, 344, 345, 348, 349, 350, 384, 398 Australia, 395 Australian Football League, 48 Australian rules football, 333, 350 Austria, 196, 231, 232 Azerbaijan, 395 Barcelona, 198, 363 Barnet, 196, 264 Barnsley, 313 Barrow, 345

baseball, 2, 3, 4, 5, 12, 14, 16, 51, 78, 205, 212, 213, 236, 239, 255, 256, 270, 272, 274, 275, 322, 396 basketball, 2, 14, 15, 17, 18, 121, 213, 236, 256, 272, 273, 287, 294, 322, 419 Bates, Ted, 262 Bateson, Mike, 262 Bayern Munchen, 387, 390 Beckham, David, 198, 210 behavioural theory of the firm, 249 Belgium, 45, 47, 196, 220, 231, 232, 380, 418 Benitez, Rafa, 262, 264 best-response functions, 31 Betfair, 359 betting markets favourite-longshot bias, 352, 354, 356, 357, 358, 359, 360, 370, 371, 378 fixed-odds betting, 79, 81, 100, 101, 352, 357, 358, 360, 365, 367, 371, 378 informational efficiency, 101, 352, 353, 356, 358, 365, 371, 376, 377, 378 online betting exchanges, 352, 359, 360 racetrack betting, 352, 353, 354, 356, 360, 377 sentiment bias, 352, 363, 364, 378 spread betting, football, 352, 360, 361, 362, 363, 378 Birmingham City, 142, 187, 201, 371 Bjornebye, Stig Inge, 220 Black, Andrew, 359 Blackburn Olympic, 140 Blackburn Rovers, 92, 101, 140, 146, 149, 264, 266 Bolivia, 51 Bolton Wanderers, 149, 155, 157 bookmakers, see betting markets Bordeaux, 384 Borussia Dortmund, 387, 390, 403 Borussia Moenchengladbach, 387 Bosman, Jean-Marc, 182, 197 Bosman ruling, 159, 182, 183, 184, 195, 217, 220, 235, 384 Boston United, 196 Botafogo, 392 Bradford City, 157

447

448

Index

Brazil, 11, 231, 236, 259, 319, 380, 391, 394, 395, 402, 403 Brazilian Confederation, 392 Brentford United, 194 Brighton and Hove Albion, 264 British Broadcasting Corporation (BBC), 171, 172, 173, 174, 175, 204, 254, 334 British Satellite Broadcasting (BSB), 171, 172, 173 British Sky Broadcasting (BSkyB), 171, 172, 173, 174, 175, 177, 178, 179, 190, 334 broadcast revenue, 18, 139, 159, 161, 169, 175, 191, 268, 385, 390 broadcast rights, 9, 18, 159, 173, 176, 177, 195, 397, 401 Brooklyn Dodgers, 18 Buckley, Major Frank, 251, 252, 293, 294 Bundesliga, see German Bundesliga Burge, Keith, 313, 315 Burnley, 146 Busby, Matt, 252, 253, 254, 293 Cambridge United, 196 Cambridge University, 140 Cameroon, 231 Cantona, Eric, 183, 220 Carlisle United, 52 Carlos, Roberto, 395 cartel, 6, 171, 177, 179 Catterick, Harry, 270 CBS, 18 Celtic, 253, 266, 335, 363 Central League, 396 Championnat de France Amateurs, 381 Champions League, 87, 142, 146, 162, 177, 191, 196, 257, 264, 302, 334, 387 Channel 4, 171 Channel 5, 171 Chapman, Herbert, 143, 251, 293 Charlton Athletic, 149, 161 Chelsea, 47, 101, 146, 158, 161, 189, 190, 192, 193, 198, 239, 264, 266, 326, 371 Cheltenham Town, 196 Chengdu Blades, 402 Chesterfield, 194 Chile, 394 China, 11, 380, 399, 400, 402, 403 China League, 401 Chinese Football Association, 401, 402 Chinese Football League, 400 Chinese Super League, 400, 401, 401 churn index, 49 Clattenburg, Mark, 315 Clough, Brian, 253, 262, 293 Club Français, 380 cointegration, 330, 331 Colchester United, 196 collusion, 3 Colombia, 51 competitive balance, 3, 8, 12, 15, 25, 27, 29, 36, 37, 42, 43, 44, 59, 77, 143, 309, 332 competitive balance ratio, 44, 333

competitive equality, see competitive balance competitive inequality, see competitive balance computable general equilibrium (CGE) models, 406, 415 concentration ratio, 47, 48, 49, 77 Copa do Brasil, 392 Copa Libertadores, 392 Coral, 367 Corinthians, 391, 395 count data, 304 Coventry City, 157, 344 Crewe Alexandra, 260 cricket, 11, 296, 419 Croatia, 231 Crystal Palace, 149, 345 Cultural Revolution, 400 Czech Republic, 232, 235 Dagenham and Redbridge, 196 Dalglish, Kenny, 143, 264 Dean, Mike, 315 Denmark, 45, 47, 220, 418 Derby County, 146, 157, 253 Desailly, Marcel, 239 Di Matteo, Roberto, 266 diminishing returns, 3, 7 DirecTV, 18 discrimination co-worker, 237, 238 customer, 237, 238, 239, 240, 247 employer, 237, 239, 240 hiring, 10, 216, 236, 238, 241, 246, 248 price, 169, 196 racial, 10, 212, 216, 236, 237, 238, 239, 247, 248 retention, 236, 239, 241 salary, 236, 237, 238, 241 diseconomies of scale, 202, 203, 204 Doncaster Rovers, 157 Douglas, Lieutenant Commander Archibald, 395 Dowd, Phil, 315 draft, 8, 13, 16 Dunga, 398 duration analysis, see hazard function Durkin, Paul, 315 Eastern Europe, 230, 231, 232, 236, 241 Eastham, George, 181 Ebbsfleet United, 194 economies of scale, 201, 203, 237 Ecuador, 51 eingetragener Verein, 387, 390 Eintracht Frankfurt, 390 elasticity of demand income, 329 price, 323, 329, 330, 331, 345, 349 England, 1, 11, 14, 45, 47, 48, 49, 56, 59, 140, 142, 153, 155, 157, 158, 171, 177, 178, 181, 195, 198, 215, 216, 224, 231, 232, 235, 240, 248, 253, 257, 275, 288, 293, 294, 296, 297, 334, 336, 391, 398, 402, 403

Index

449

English football competitive structure, 9, 139, 141 financial structure, 159, 161, 180, 181 governance, 9, 139, 189, 195 ownership, 9, 139, 187, 188, 190, 192, 194, 195 ESPN, 18, 173, 174 Europa League, see UEFA Cup European Championship, 176, 216, 232, 235, 248, 254, 296, 363, 402, 418, 419 European Commission, 173, 177, 178, 418 European Court of Justice, 184 European Cup, 142, 157, 253, 384, 387 European Cup Winners’ Cup, 142 Everton, 100, 135, 136, 140, 155, 172, 191, 196, 262, 328, 344 exponential distribution, 122, 131 externality network, 359 positive, 176, 177

home team bias, 10, 52, 295, 296, 298, 299, 300, 301, 305, 308, 309, 315, 319 professionalism, 298, 302 social pressure, 295, 300, 301, 302 football teams strategic behaviour, 107, 111, 122, 136, 137 Fox, 18 France, 11, 14, 45, 47, 48, 49, 51, 56, 59, 196, 215, 220, 231, 232, 235, 275, 319, 336, 380, 381, 384, 394, 395, 398, 402, 403, 407, 418 franchise, 4, 8, 13, 14, 15, 18, 19, 193, 254, 405, 409, 412 Frank copula, 63, 305, 320 Frechet distribution, 82 free agency, 3, 4, 12, 16, 44, 184, 195, 200, 204, 208, 209, 212, 213, 214, 217, 238 free agent, see free agency Fry, Barry, 264 Fulham, 100, 135, 181, 264 Furukawa Electric, 398

FA Cup, 50, 79, 84, 87, 92, 104, 105, 140, 141, 143, 146, 155, 157, 170, 171, 186, 291, 294, 313 Fagan, Joe, 143 Fairs Cup, see UEFA Cup FC Kaiserslautern, 386, 387, 390 FC Nuremberg, 386 FC United of Manchester, 194 Federal League, 18 Federation Française de Football, 381 Federation of International Football Associations (FIFA), 182, 236, 296, 381, 391, 394, 396, 401, 406, 407, 408, 409, 419, 421 Ferguson, Alex, 143, 254, 262, 264, 294 fixed effects, 351 Flamengo, 391, 392, 395 Fluminese, 391, 392, 395 Football Association (FA), 140, 173, 180, 296, 297 Football League, 1, 9, 49, 46, 93, 119, 140, 141, 157, 159, 160, 161, 163, 170, 171, 172, 173, 174, 175, 179, 184, 185, 187, 193, 194, 195, 198, 201, 216, 217, 226, 239, 241, 358, 363, 402 football managers, 10, 251, 266, 293, 297, 298, 313 managerial change, 250, 260, 270, 271, 285, 286, 287, 288, 290, 291, 293, 294 managerial contribution, 10, 143, 255, 258 managerial efficiency, 250, 255, 256, 257, 273, 275, 287 managerial succession effect, 251, 270, 286, 289, 293 football match results forecasting model, 79, 80, 82, 86, 95, 96, 98, 99, 100, 104, 289, 290, 307, 353, 358, 359, 365, 366 persistence, 8, 42, 67, 71, 73, 74, 76, 77, 78, 98 statistical properties, 42, 59 football referees disciplinary sanction, 118, 124, 296, 299, 300, 301, 302, 303, 307, 308, 309, 310, 313, 315, 317, 318, 319, 320 favouritism, see home team bias

G14 payroll cap, 33, 38, 39, 192 game theory, 9, 106, 107, 137 dominant strategy, 115 mixed-strategy equilibrium, 108, 109, 110 non-cooperative equilibrium, 115 penalty kick, 9, 106, 107, 109, 110, 137 prisoner’s dilemma, 115, 116, 137 Garrincha, 394 gate revenue, 9, 18, 139, 159, 162, 163, 165, 168, 170, 184, 187, 268, 324, 351, 394 German Bundesliga, 111, 210, 211, 241, 257, 258, 274, 275, 289, 299, 300, 301, 332, 336, 386 German Football Association, 385, 387 German Football League, 387 Germany, 11, 15, 45, 47, 48, 49, 56, 59, 176, 183, 184, 215, 231, 232, 235, 241, 275, 380, 385, 402, 407, 417, 418, 419 Gillett, George, 193 Gillingham, 264 Gini coefficient, 45, 46, 47, 48, 77 Glazer, Malcolm, 192 goals scored forecasting model, 79, 80, 82, 86, 96, 98, 100, 104, 122, 135, 358 statistical properties, 63, 77 timings of, 107, 127, 137 golden goal rule, 112, 138 Gradi, Dario, 260 Granada Media, 190 Granger causality tests, 324 Grant, Avram, 264 Grayson, Simon, 264 Greece, 47, 231, 302, 418 Greenwood, Ron, 262 Guangzhou GPC, 402 Gumbel distribution, 82 Hakuhodo, 398 Hamburg, 387, 390 Harris, Rob, 313 Haynes, Johnny, 181

450

Index

hazard function, 122, 124, 137, 250, 274, 275, 276, 277, 278, 281, 285 Hereford United, 196 Herfindahl index, 47, 48, 77 Heysel, 142, 157, 195 Hicks, Tom, 193 Hiddink, Guus, 264, 266 Hillsborough, 157, 195, 326, 350 hockey, 2, 51, 322 home-field advantage, 42, 43, 50, 51, 52, 53, 56, 59, 73, 77, 78, 112, 119, 123, 131, 260, 288, 291, 296, 300, 301, 309, 319, 369 hooliganism, 154, 155, 156, 157, 189, 195, 326 Hoyzer, Robert, 387 Huddersfield Town, 143, 146, 251 Hull City, 88, 91, 92, 93, 94, 98, 99, 100, 105, 157 human capital, 257, 277, 281, 287, 294 Hungary, 399 imperfect substitution, 201, 202 Ince, Paul, 266 Independent Television (ITV), 171, 172, 173, 174, 175, 177, 190, 204, 334 input-output models, 406, 411, 412, 415 invariance proposition, 29, 37 Ipswich Town, 146, 149, 191, 310 Ireland Northern, 220, 221, 242, 364 Republic of, 220, 221, 242, 418 Israel, 220 Italy, 15, 45, 47, 48, 49, 82, 175, 212, 215, 231, 232, 235, 236, 259, 289, 299, 302, 319, 336, 386, 394, 395, 407, 418 ITV, see Independent Television ITV Digital, 159, 175, 186, 193, 268, 334 J. League, 397, 398 Japan, 11, 275, 380, 394, 395, 398, 402, 403, 406, 408, 413 Japan Football League, 396, 398 Japanese Football Association (JFA), 395 JEF United Ichihara, 398 Jensen, John, 220 Juventus, 157 Kaka, 395 Kanchelskis, Andrei, 220 Kashima Antlers, 398 Keegan, Kevin, 264 Kendall’s tau statistic, 49 Kidderminster Harriers, 196 Kroenke, Stan, 190 LA Galaxy, 198 Ladbrokes, 367 Lampard, Frank, 198 Latin America, 51, 230, 231, 232, 241, 336 League Cup, 87, 141, 143, 170, 175 Leeds United, 146, 183, 190, 191, 253, 262, 264, 313 Leicester City, 157, 189, 190, 191, 264, 301 Libarski, Pierre, 398

Limpar, Anders, 220 Lincoln City, 157 linear probability model, 109, 273, 357 Lineker, Gary, 398 Liverpool, 47, 140, 143, 146, 155, 157, 158, 161, 172, 177, 181, 190, 193, 220, 253, 262, 264, 294, 301, 313, 328, 344, 371 London Stock Exchange, 188, 189 London Weekend Television, 172 Lorenz curve, 45, 46, 48, 77 Louis Schmelling Paradox, 4 Love, Vagner, 395 Luton Town, 52 Luxembourg, 418 luxury tax, 16, 17, 33, 34, 35, 41 Lyon, 383, 385 Macclesfield Town, 196 Maidstone United, 196 Major League Baseball, see baseball Major League Soccer, 209, 210, 212, 258, 336 Malta, 231 managers, see football managers Manchester City, 153, 157, 190, 191, 192, 193, 198, 344, 371 Manchester United, 47, 101, 105, 140, 142, 143, 146, 153, 156, 158, 161, 170, 172, 177, 178, 181, 183, 188, 189, 190, 192, 193, 194, 198, 201, 220, 252, 254, 264, 310, 326, 344 Mansour bin Zayed Al Nahyan, Sheik, 192 marginal revenue product, 12, 200, 204, 212, 213 Marseille, 383, 384, 385 maximum likelihood, 81, 278, 367 maximum wage, 165, 179, 180, 181, 195, 197 mean-reversion, 285, 287, 290, 294 Messi, Lionel, 198 Mexican League, 18 Mexico, 319, 336, 394, 396 Middlesbrough, 100, 149, 157, 190 migration, 9, 10, 216, 217, 227, 228, 232, 235, 248 Miller, Charles, 391 Millwall, 157, 188, 189 minimum admission price, 163 Minor League Baseball, see baseball Mitsubuishi Motors, 398 MK Dons, 157, 266 Mobray, Tony, 266 Molby, Jan, 220 Monopolies and Mergers Commission (MMC), 178, 190 monopoly, 3, 4, 5, 14, 15, 18, 19, 177, 179 natural, 5, 6, 202 rent, 213 monopsony, 2, 3, 5, 208, 209, 213, 238 moral hazard, 250 Morecambe, 196 Morocco, 220 Mourinho, Jose, 264 Moyes, David, 262 multi-plant firm, 5 Murdoch, Rupert, 18, 171

Index Nash equilibrium, 23, 31, 41, 115, 116, 117, 118, 207 National Basketball Association (NBA), 14, 16, 17, 18, 41, 43, 51, 53, 237, 238, 239, 256, 272, 274, 350, 356 National Collegiate Athletic Association (NCAA), 43 National Football Institute, 383 National Football League (NFL), 14, 16, 17, 18, 43, 51, 53, 238, 239, 256, 257, 272, 275, 286, 354, 355, 356 National Hockey League (NHL), 43, 51, 53, 112, 238, 287, 356 National League, 5, 14, 18, 19, 212 National Measure of Seasonal Imbalance, 45 National Rugby League, 48 Nayim, 220 NBA, see National Basketball Association NBC, 18 NCAA, see National Collegiate Athletic Association NFL, see National Football League NHL, see National Hockey League negative binomial distribution, 42, 59, 63, 64, 77, 80, 82, 304, 306, 357 bivariate, 306, 320 neoclassical theory, 249 Netherlands, 45, 47, 232, 302, 319, 418 New York Giants, 18 New York Yankees, 4, 17 Newcastle United, 100, 135, 136, 146, 149, 153, 181, 189, 190, 191, 251, 264, 294, 328, 344 Newton Heath, see Manchester United Nicholson, Bill, 262, 270 Nigeria, 231 Nimes, 183 Nippon Shinpan, 398 Nolan, Kevin, 136 non-stationary, 328, 330, 349, 350 normal distribution, 71, 73, 95, 100, 242, 366 Norway, 220, 302 Norwich City, 149, 191, 310, 345 Nottingham Forest, 146, 157, 253, 262 Notts County, 194 NTL, 190 Oceania, 230, 409 Ofex Market, see Plus Market Office of Fair Trading, 172, 179 Oldham Athletic, 52, 262 Olympic Games, 78, 176, 396, 405, 409, 415, 418, 420, 421, 422 ONDigital, 175 Opta Index, 259 ordered probit, 45, 73, 82, 241, 358 overdispersion, 64, 67, 77, 304, 307 Oxford United, 196 Oxford University, 140 Pacific Coast League, 18 Pacific League, 396 Paisley, Bob, 143

451

Paraguay, 51 Paris Saint Germain, 384 Paulistano, 391 payroll cap, 8, 13, 14, 16, 17, 20, 33, 35, 36, 37, 40 Payssandu Cricket Club, 391 Pearson, Nigel, 264 Pele, 394 Peru, 51 Peterborough United, 196 Peugeot, 381 Pirelli, 402 player dismissals timings of, 107, 124, 126, 137 player sale-and-leaseback, 191, 192 player transfers, 160, 182, 194, 253, 394 player wages and salaries, 3, 27, 33, 35, 40, 139, 159, 160, 180, 181, 189, 192, 194, 197, 208, 209, 210, 212, 213, 215, 240, 390, 398, 407 determination of, 197, 200, 205, 209, 210, 212 Plus Market, 189 Poisson distribution, 42, 59, 63, 64, 77, 80, 304, 306, 357, 362 bivariate, 78, 81, 82, 299, 306, 320 Port Vale, 262 Portsmouth, 100, 146, 149, 193 Portugal, 47, 198, 231, 235, 395, 418 Premier League Austrian, 288 Dutch, 288 English, 1, 9, 32, 49, 46, 93, 104, 119, 141, 157, 159, 160, 162, 170, 173, 174, 177, 179, 183, 184, 186, 189, 190, 191, 193, 194, 195, 196, 198, 201, 204, 206, 216, 217, 220, 223, 226, 235, 241, 297, 299, 323, 328, 335, 358, 363, 402 Scottish, 45, 47, 323, 328, 334, 363 Premiership, see Premier League: English Preston North End, 52, 140, 171, 189 production frontier, 250, 255, 256 data envelopment analysis (DEA), 256, 258, 258, 259 random frontier model, 257 stochastic frontier analysis, 256, 257, 273 Professional Footballers Association, 181 professional sports leagues, organisation European model, 14 North American model, 13, 14 professional sports leagues, theory closed model, 13, 21, 22, 24, 25, 27, 28, 32, 34, 36, 37, 38, 39, 40 open model, 13, 22, 26, 27, 29, 32, 34, 35, 36, 37, 39, 40 profit maximisation, 6, 15, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 37, 40, 41, 200, 249, 254 Pulis, Tony, 262 Queens Park Rangers, 52, 149, 189 Rangers, 335, 363 rank-order tournament model, 9, 198, 205, 206, 209, 213, 215 RC Paris, 381 Reading, 155, 157

452

Index

Real Madrid, 198, 363, 383, 395 Redknapp, Harry, 294 Reed, Mike, 313, 315 referees, see football referees Regional Industrial Multiplier System, 411, 412 regression binary logit, 273, 274, 275, 357 binary probit, 241, 273, 274, 275, 334, 364 bivariate Poisson, 309 bivariate probit, 300 cross-sectional, 84, 93, 237, 346 discrete-time logit, 274 fixed effects, 289, 338, 417 instrumental variables, 328, 350 mixed logit, 275 OLS, 210, 211, 272, 324, 328, 334, 350, 351, 357 ordered logit, 80, 418 ordered probit, 79, 80, 81, 95, 104, 241, 242, 288, 353, 365, 378 Poisson, 79, 83, 104 quantile, 210, 211, 237, 332 random effects, 211 random effects logit, 111, 236 simultaneous equations, 109 time-series, 333 tobit, 324, 326 Weibull, 274 Reith, John, 171 relative competitive inequality measure, 43 Rennie, Uriah, 315 reservation wage, 3, 4, 12, 200 reserve clause, 2, 3, 4, 7, 8, 12, 13, 15, 200, 212, 213 Restrictive Practices Court (RPC), 179 retain-and-transfer system, 179, 180, 181, 195 returns to scale constant, 258 variable, 259 revenue functions, 12, 20, 24, 28, 29 revenue maximisation, 169 revenue sharing, 4, 7, 8, 13, 14, 16, 18, 20, 27, 28, 29, 30, 31, 32, 40, 170 Revie, Don, 253, 262, 270, 293 Riley, Mike, 315 Rimet, Jules, 381 Robinho, 395 Romania, 231, 302 Ronaldo, Christiano, 198 Rosenior, Leroy, 262 Rosenthal, Ronnie, 220 Rotherham United, 142 Royal Engineers, 140 Royle, Joe, 262 Rudge, John, 262 rugby league, 11, 176, 324, 350 Rugby school, 140 rugby union, 11, 176 runs test, 73, 110 Rushden and Diamonds, 196 Russia, 232 salary cap, see payroll cap Santos, 395

Sao Paulo, 391, 394, 395 Scarborough, 196 Schalke 04, 390 Schmeichel, Peter, 220 Scholar, Irving, 188 Scolari, Phil, 264, 266, 394 Scotland, 11, 56, 59, 158, 171, 220, 225, 242, 248, 253, 279, 302, 335, 363, 364 Scunthorpe United, 196 securitisation, 190, 191 Serbia-Montenegro, 231 Setanta, 173 Sete, 381 Shakhtar Donetsk, 105 Shanghai Shenhua, 402 Shanghai United, 402 Shankly, Bill, 143, 253, 254, 262, 270, 293 share prices, 189, 364 Sheffield United, 105, 161, 171, 402 Sheffield Wednesday, 157 Shrewsbury Town, 196 Sichuan Guancheng, 402 Siemens, 402 simulation Monte Carlo, 42, 73, 74, 76, 81 numerical, 119 stochastic, 107, 131, 137 Sky, 171, 172, 173 Small Heath, see Birmingham City Sochaux, 381 Sony Creative Products, 398 South Africa, 395, 406, 407, 408, 413, 414, 415 South America, 236, 240, 392, 396, 409 South Korea, 394, 406, 408, 413 Southampton, 149, 157, 191, 262, 371 Southend United, 264 Southern League, 141 Southport, 345 Spain, 15, 45, 47, 48, 49, 56, 59, 176, 196, 215, 231, 232, 235, 259, 275, 288, 319, 328, 363, 386, 418 Spearman rank correlation coefficient, 49 sponsorship, 162, 170, 198, 214, 236, 254, 384, 397, 398, 401, 402, 408 St Etienne, 384 Stade Reims, 383 stadium capacity, 153, 168, 202, 240, 258, 301, 321, 324, 326, 337, 349, 350, 397, 412 Standard AC, 380 StanleyBet, 367 Stein, Jock, 253, 254 Stockport County, 194 Stoke City, 100, 157, 310 Stuttgart, 387 Sumitomo Metals, 398 Sunderland, 149, 153, 157, 171, 190, 328, 344 Suntory, 398 superstars economics of, 9, 201, 203, 204, 212, 213, 214 Supporters Direct, 194 surprise index, 48 survivor function, 273, 277, 279 Swansea City, 157, 262

Index Sweden, 47, 220, 302, 394 Swindon Town, 149, 155 Switzerland, 231, 232, 235, 275, 335, 419 Tapie, Bernard, 384 Taylor, Graham, 262 Taylor, Lord Justice, 157 Taylor, Peter, 264 TBS, 18 television, 5, 139, 142, 154, 155, 157, 171, 172, 179, 195, 204, 253, 297, 321, 333, 396, 407, 418 Tevez, Carlos, 198 Thatcher, Margaret, 156 Thorstvedt, Eric, 220 Tokyo Giants, 396 Torquay United, 262 Tottenham Hotspur, 88, 91, 92, 93, 94, 98, 99, 100, 105, 172, 188, 189, 191, 220, 262, 344 transactions costs, 249, 265 transfer expenditure, 139, 159, 184, 186, 193, 385 transfer fees, 8, 160, 182, 189, 401 transfer market, 10, 139, 143, 184, 185, 210, 217, 228, 229, 252, 255, 293, 401, 408 transfers, see player transfers two-part tariff, see discrimination: price UEFA, see Union of European Football Associations UEFA Cup, 87, 92, 105, 142, 146, 257, 302, 313 UEFA Pro-Licence, 251, 294 Ukraine, 220, 231 uncertainty of outcome, 3, 8, 42, 45, 50, 332, 333, 335 Union of European Football Associations (UEFA), 182, 231, 251 United Arab Emirates, 395 Urawa Red Diamonds, 398 Uruguay, 51, 381, 407 utility function, 7, 27, 113, 200, 254, 298, 354 utility maximisation, 7, 200 Van Den Hauwe, Pat, 220 Vasco da Gama, 391, 392 Verdy Kawasaki, 398 vertical integration, 178, 190 Vietnam, 395 Villa, Ricardo, 220 Virgin Media, 179

453

Wales, 364 Walker, Jack, 146 Wanderers, The, 140 Watford, 161, 189, 262 Weibull distribution, 82 weighted least squares (WLS), 347, 357 Wenger, Arsène, 254, 262, 264, 398 Werder Bremen, 387 West Bromwich Albion, 71, 100, 135, 155, 161, 266, 344 West Ham United, 262, 313, 344, 371 Western Europe, 11, 231, 232, 236, 241 Wigan Athletic, 100, 150, 157, 196 Willard, Gary, 313 William Hill, 358, 359, 367 Wimbledon, 194, 196 win percent, see win ratio win ratio, 19, 20, 41, 42, 43, 44, 45, 46, 47, 53, 59, 77, 96, 250, 255, 262, 269, 272, 274, 286, 310 win-percent maximisation, 21, 22, 23, 24, 25, 26, 27, 29, 30, 32, 33, 35, 37, 39, 40 Wolverhampton Wanderers, 143, 149, 251, 294, 344 Woolwich Arsenal, see Arsenal Workington, 345 World Cup, 11, 51, 153, 176, 232, 235, 236, 319, 335, 336, 380, 381, 384, 386, 394, 395, 396, 402, 405, 406, 407, 409, 413, 415, 416, 417, 418, 419, 420, 421 economic benefits, 11, 405, 406, 411, 417, 420, 421 intangible benefits, 407, 417, 418, 421, 422 prospective economic impact studies, 405, 406, 410, 411, 412, 413, 421 retrospective economic impact studies, 415, 416, 421 World Series, 4, 5 World Youth Championship, 396 Wrexham, 345 Wycombe Wanderers, 196, 264 Yeovil Town, 196 Yomiuro FC, 398 York City, 194 zero conjectural variations, 23, 31 Zico, 398 Zidane, Zinedine, 394 Zimbabwe, 414