Player Productivity and Performance: An Econometric Approach to Team Management in Soccer by Guy Benedict Wilkinson A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Sport Management) in the University of Michigan 2017 Doctoral Committee: Professor Stefan Szymanski, Chair Professor Rodney D. Fort Professor Jeffrey A. Smith Assistant Professor Eric M. Schwartz Guy B. Wilkinson [email protected] ORCID iD: 0000-0002-3623-1914 © Guy B. Wilkinson 2017 DEDICATION To my father and Uncle Jim for taking me to my first Celtic game, and to Henrik Larsson for inspiring me to go to many more. ii ACKNOWLEDGEMENTS I would like to thank Professor Stefan Szymanski for taking me on as his doctoral student for the past four years. Without his guidance, I would not have been able to complete my research projects with the high quality I strive for. My thanks also go to my committee members, Professor Rodney Fort, Professor Jeffrey Smith and Assistant Professor Eric Schwartz for their guidance and suggestions throughout the duration of my degree. Finally, I want to thank my family, friends and cohort for helping me adapt to life in America and supporting me through both the good times and the bad. iii TABLE OF CONTENTS DEDICATION ........................................................................................................................... ii ACKNOWLEDGEMENTS ..................................................................................................... iii LIST OF TABLES ................................................................................................................... vii LIST OF FIGURES ................................................................................................................... x ABSTRACT .............................................................................................................................. xi CHAPTER I – THESIS MOTIVATION ................................................................................... 1 1. INTRODUCTION .......................................................................................................... 1 2. REFERENCES ............................................................................................................... 7 CHAPTER II – TESTING THE O-RING THEORY USING DATA FROM THE ENGLISH PREMIER LEAGUE ............................................................................................................... 12 1. INTRODUCTION ........................................................................................................ 13 2. LITERATURE REVIEW ............................................................................................. 13 2.1 O-RING THEORY ................................................................................................ 13 2.2 SALARY DISPERSION AND MOTIVATION ................................................... 15 2.3 WAGE PERFORMANCE RELATIONSHIP ....................................................... 17 3. THEORY ...................................................................................................................... 19 3.1 THE AGGREGATE MODEL ............................................................................... 19 3.2 THE VALUE MATCHING MODEL ................................................................... 20 4. DATA ........................................................................................................................... 23 iv 5. ESTIMATION .............................................................................................................. 27 5.1 EXOGENEITY IN WAGES ................................................................................. 27 5.2 DISPERSION ANALYSIS ................................................................................... 28 5.3 THE EFFICIENCY OF WAGES AND TPI IN PREDICTING RESULTS ......... 29 5.4 OPTIMALITY ....................................................................................................... 30 6. CONCLUSION ............................................................................................................. 33 7. APPENDIX A ............................................................................................................... 35 7.1 LAGRANGIAN DERIVATION ........................................................................... 35 7.2 INDIVIDUAL GAME OPTIMALITY ................................................................. 37 7.3 MODEL ROBUSTNESS ...................................................................................... 38 8. REFERENCES ............................................................................................................. 41 CHAPTER III – THE IMPACT OF REST PERIODS ON RESULTS IN THE ENGLISH PREMIER LEAGUE ............................................................................................................... 45 1. INTRODUCTION ........................................................................................................ 46 2. LITERATURE REVIEW ............................................................................................. 47 3. THEORY ...................................................................................................................... 49 3.1 PARAMETRIC LINEAR MODELS .................................................................... 51 3.1.1 RELATIVE REST MODEL .......................................................................... 52 3.1.2 MIDWEEK EFFECT MODEL ...................................................................... 52 3.1.3 WEEKEND EFFECT MODEL ..................................................................... 53 4. DATA ........................................................................................................................... 53 5. RESULTS ..................................................................................................................... 57 5.1 REGRESSION RESULTS .................................................................................... 57 5.2 PROPENSITY SCORE MATCHING................................................................... 65 v 5.3 ANALYSIS OF ECONOMIC SIGNIFICANCE .................................................. 68 6. CONCLUSION ............................................................................................................. 69 7. APPENDIX B ............................................................................................................... 71 8. REFERENCES ............................................................................................................. 82 CHAPTER IV – INDIVIDUAL PLAYER CONTRIBUTIONS IN EUROPEAN SOCCER 84 1. INTRODUCTION ........................................................................................................ 85 2. LITERATURE REVIEW ............................................................................................. 86 3. THEORY ...................................................................................................................... 88 4. DATA ........................................................................................................................... 91 5. RESULTS ..................................................................................................................... 94 5.1 PREDICTIONS ..................................................................................................... 94 5.2 BETTING ANALYSIS ......................................................................................... 99 5.3 ESTIMATIONS................................................................................................... 100 6. CONCLUSION ........................................................................................................... 106 7. APPENDIX C ............................................................................................................. 108 8. REFERENCES ........................................................................................................... 119 CHAPTER V – THESIS CONCLUSION ............................................................................. 122 1. CONCLUSION ........................................................................................................... 122 2. REFERENCES ........................................................................................................... 126 vi LIST OF TABLES Table 1 - Summary statistics of player share values; the proportion of a team's total spending each ranked player accounts for ............................................................................................... 26 Table 2 - Difference in the average proportion of resources allocated to player ranks by teams of different stature (standard error in brackets) ....................................................................... 27 Table 3 - Exogeneity analysis .................................................................................................. 28 Table 4 - Dispersion analysis ................................................................................................... 29 Table 5 - Betting odds comparison .......................................................................................... 30 Table 6 - The impact of results by the starting eleven players. Top 100 best fitting models are included to highlight the player ranks that contribute most to results ..................................... 31 Table 7 - Team and optimal