ESTIMATING ECONOMIC IMPACTS OF TOMMY JOHN SURGERY ON MAJOR LEAGUE BASEBALL PITCHERS by Finn Ottey McMichael A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science In Applied Economics MONTANA STATE UNIVERSITY Bozeman, Montana April 2018 ©COPYRIGHT by Finn Ottey McMichael 2018 All Rights Reserved ii ACKNOWLEDGEMENTS I would like to thank my thesis committee: chair Dr. Randal Rucker, Dr. Rodney Fort, and Dr. Gregory Gilpin. They provided an immense amount of feedback and guidance throughout this process, and they were essential to the completion of this thesis. I would also like to thank my family for their support and my classmates for making the whole experience more enjoyable. iii TABLE OF CONTENTS 1. INTRODUCTION .......................................................................................................... 1 2. BACKGROUND ............................................................................................................ 3 History of Tommy John Surgery .................................................................................... 3 Wins Above Replacement (WAR) ................................................................................. 4 Baseball-Reference: BR-WAR ................................................................................... 6 FanGraphs: FG-WAR ................................................................................................. 9 Two WAR Measures: Discussion ............................................................................. 12 Chapter Two Figures and Tables .................................................................................. 13 3. RELATED LITERATURE ........................................................................................... 15 Medical Literature ......................................................................................................... 15 Economic Literature on Marginal Revenue Product .................................................... 19 Wins Above Replacement (WAR) Literature ............................................................... 23 Chapter Three Figures and Tables ................................................................................ 27 4. IMPACT OF TOMMY JOHN SURGERY ON PITCHER MARGINAL PRODUCT ............................................................................................. 29 Estimating the Impact of TJS on Pitcher Productivity ................................................. 30 Empirical Specification ............................................................................................. 30 Data ........................................................................................................................... 33 Results ....................................................................................................................... 35 Estimating the Marginal Product of Pitcher WAR on Team Wins ............................... 42 Chapter Four Figures and Tables .................................................................................. 47 5. ESTIMATING MARGINAL REVENUE OF A WIN ................................................. 65 Theory and Empirical Specification ............................................................................. 65 Data ............................................................................................................................... 68 Results ........................................................................................................................... 69 Chapter Five Figures and Tables .................................................................................. 72 iv TABLE OF CONTENTS (CONTINUED) 6. MARGINAL REVENUE PRODUCT CALCULATION ............................................ 78 General Estimate for Average Pitcher .......................................................................... 79 Specific Estimates for Three Hypothetical Pitchers ..................................................... 83 Pitcher A Estimation: ................................................................................................ 84 Pitcher B Estimation: ................................................................................................ 85 Pitcher C Estimation: ................................................................................................ 87 Discussion ..................................................................................................................... 88 7. CONCLUSION ............................................................................................................. 90 REFERENCES CITED ..................................................................................................... 94 APPENDICES .................................................................................................................. 97 A. ADDITIONAL DETAILS ON ESTIMATION OF WAR FOR POSITION PLAYERS ........................................................................................ 98 Appendix A Tables ..................................................................................................... 102 B. ATTEMPT AT REPLICATING MEDICAL STUDY METHODS AND RESULTS ..................................................................................... 103 Appendix B Tables ..................................................................................................... 106 C. ESTIMATION OF MARGINAL REVENUE USING GATE REVENUE INSTEAD OF TOTAL REVENUE ....................................................... 108 Appendix C Figures and Tables.................................................................................. 110 v LIST OF TABLES Table Page 1. Comparison of Medical Journal Analyses of Tommy John Surgery ................ 27 2. Summary Statistics – Pitchers 1996-2016 ........................................................ 47 3. Summary Statistics – All Pitcher-years 1996-2016 .......................................... 48 4. Summary Statistics – All TJS Pitcher-years 1996-2016 ................................... 48 5. Summary Statistics – Non-TJS Pitcher-years 1996-2016 ................................. 49 6. Impact of TJS on WAR..................................................................................... 51 7. Age Subsamples (Young = Age < 28, Old = Age >= 28) ................................. 52 8. Starter and Reliever Sub-samples ..................................................................... 53 9. Impact of TJS of ERA, WHIP and Innings Pitched for Starting Pitchers ........ 54 10. Impact of TJS of ERA, WHIP and IP for Relief Pitchers ................................ 55 11. Breakdown of WAR into standard pitching statistics ...................................... 56 12. Impact of TJS on Games Pitched, Innings Pitched and ERA for All Pitchers ................................................................................................ 57 13. Impact of TJS on WHIP, Strikeouts, Walks and Homeruns Allowed for All Pitchers ................................................................................................ 58 14. Summary Statistics – Pitchers and Position Player-years ................................ 59 15. Team Wins as a Function of Individual FG-WAR ........................................... 61 16. Team Wins as a Function of Individual BR-WAR .......................................... 62 17. Team Wins as a Function of Team FG-WAR .................................................. 63 18. Team Wins as a Function of Team BR-WAR .................................................. 64 19. Summary Statistics by Team ............................................................................ 74 vi LIST OF TABLES (CONTINUED) Table Page 20. MR of a Win, Quantile Regression with Time Trend and Team Fixed Effects .......................................................................................... 75 21. MR of a Win, Quantile Regression with Team and Year Fixed Effects ......... 76 22. MR of a Win, Quantile Regression with Time Trend and Yankee Dummy ................................................................................................ 77 23. Positional Adjustment Runs ........................................................................... 102 24. Summary Stats for Case (TJS) Group (343 pitchers) ..................................... 106 25. Summary Stats for Control Group (595) ........................................................ 107 26. Comparison of Means for Case and Control Groups ..................................... 107 27. MR of a Win, Quantile Regression with Time Trend and Team Fixed Effects ........................................................................................ 112 28. MR of a Win, Quantile Regression with Team and Year Fixed Effects ................................................................................................... 113 29. MR of aWin, Quantile Regression with Time Trend and Yankee Dummy .............................................................................................. 114 vii LIST OF FIGURES Figure Page 1. Number of Tommy John Surgeries in MLB by Year ....................................... 13 2. Ratio of Players who Return to Same Level after TJS ..................................... 13 3. Average Months to Return to the Same Level after TJS .................................. 14 4. Distribution of FG-WAR Values ...................................................................... 49 5. Distribution