MATHLETICS This page intentionally left blank MATHLETICS How Gamblers, Managers, and Sports Enthusiasts Use Mathematics in Baseball, Basketball, and Football WAYNE WINSTON PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD Copyright © 2009 by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TW All Rights Reserved Library of Congress Cataloging-in-Publication Data Winston, Wayne L. Mathletics : how gamblers, managers, and sports enthusiasts use mathematics in baseball, basketball, and football / Wayne Winston. p. cm. Includes bibliographical references and index. ISBN 978-0-691-13913-5 (hardcover : alk. paper) 1. Sports—Mathematics. I. Title. GV706.8.W56 2009 796.0151—dc22 2008051678 British Library Cataloging- in- Publication Data is available This book has been composed in ITC Galliard Printed on acid- free paper. ∞ press.princeton.edu Printed in the United States of America 1 3 5 7 9 10 8 6 4 2 To Gregory, Jennifer, and Vivian This page intentionally left blank CONTENTS Preface xi Ac know ledg ments xiii List of Abbreviations xv Part I. Baseball 1 1. Baseball’s Pythagorean Theorem 3 2. Who Had a Better Year, Nomar Garciaparra 11 or Ichiro Suzuki? The Runs- Created Approach 3. Evaluating Hitters by Linear Weights 17 4. Evaluating Hitters by Monte Carlo Simulation 30 5. Evaluating Baseball Pitchers and Forecasting Future Pitcher Per for mance 41 6. Baseball Decision- Making 52 7. Evaluating Fielders 64 Sabermetrics’ Last Frontier 8. Player Win Averages 71 9. The Value of Replacement Players 79 Evaluating Trades and Fair Salary 10. Park Factors 84 11. Streakiness in Sports 87 12. The Platoon Effect 102 13. Was Tony Perez a Great Clutch Hitter? 106 14. Pitch Count and Pitcher Effectiveness 110 15. Would Ted Williams Hit .406 Today? 113 16. Was Joe DiMaggio’s 56- Game Hitting Streak the Greatest Sports Record of All Time? 116 17. Major League Equivalents 123 Part II. Football 125 18. What Makes NFL Teams Win? 127 19. Who’s Better, Tom Brady or Peyton Manning? 132 viii CONTENTS 20. Football States and Values 138 21. Football Decision- Making 101 143 22. A State and Value Analysis of the 2006 Super Bowl 151 Champion Colts 23. If Passing Is Better Than Running, Why Don’t 158 Teams Always Pass? 24. Should We Go for a One- Point or Two- Point Conversion? 165 25. To Give Up the Ball Is Better Than to Receive 172 The Case of College Football Overtime 26. Why Is the NFL’s Overtime System Fatally Flawed? 175 27. How Valuable Are High Draft Picks in the NFL? 180 Part III. Basketball 185 28. Basketball Statistics 101 187 The Four- Factor Model 29. Linear Weights for Evaluating NBA Players 195 30. Adjusted ϩ/ Ϫ Player Ratings 202 31. NBA Lineup Analysis 224 32. Analyzing Team and Individual Matchups 228 33. NBA Players’ Salaries and the Draft 233 34. Are NBA Officials Prejudiced? 237 35. Are College Basketball Games Fixed? 242 36. Did Tim Donaghy Fix NBA Games? 244 37. End-Game Basketball Strategy 248 Part IV. Playing with Money, and Other Topics for Serious Sports Fans 253 38. Sports Gambling 101 255 39. Freakonomics Meets the Bookmaker 262 40. Rating Sports Teams 266 41. Which League Has Greater Parity, The NFL or the NBA? 283 42. The Ratings Percentage Index (RPI) 287 43. From Point Ratings to Probabilities 290 44. Optimal Money Management 298 The Kelly Growth Criteria 45. Ranking Great Sports Collapses 303 46. Can Money Buy Success? 311 47. Does Joey Crawford Hate the Spurs? 319 CONTENTS ix 48. Does Fatigue Make Cowards of Us All? 321 The Case of NBA Back- to- Back Games and NFL Bye Weeks 49. Can the Bowl Championship Series Be Saved? 324 50. Comparing Players from Different Eras 331 51. Conclusions 335 Index of Databases 341 Annotated Bibliography 343 Index 353 This page intentionally left blank PREFACE If you have picked up this book you surely love sports and you probably like math. You may have read Michael Lewis’s great book Moneyball, which describes how the Oakland A’s used mathematical analysis to help them compete successfully with the New York Yankees even though the average annual payroll for the A’s is less than 40 percent of that of the Yan- kees. After reading Moneyball, you might have been curious about how the math models described in the book actually work. You may have heard how a former night watchman, Bill James, revolutionized the way baseball professionals evaluate players. You probably want to know exactly how James and other “sabermetricians” used mathematics to change the way hitters, pitchers, and fielders are evaluated. You might have heard about the analysis of Berkeley economic professor David Romer that showed that NFL teams should rarely punt on fourth down. How did Romer use mathematics to come up with his controversial conclusion? You might have heard how Mark Cuban used math models (and his incredible busi- ness savvy) to revitalize the moribund Dallas Mavericks franchise. What mathematical models does Cuban use to evaluate NBA players and line- ups? Maybe you bet once in a while on NFL games and wonder whether math can help you do better financially. How can math determine the true probability of a team winning a game, winning the NCAA tournament, or just covering the point spread? Maybe you think the NBA could have used math to spot Tim Donaghy’s game fixing before being informed about it by the FBI. This book will show you how a statistical analysis would have “red flagged” Donaghy as a potential fixer. If Moneyball or day-to- day sports viewing has piqued your interest in how mathematics is used (or can be used) to make decisions in sports and sports gambling, this book is for you. I hope when you finish reading the book you will love math almost as much as you love sports. To date there has been no book that explains how the people running Major League Baseball, basketball, and football teams and Las Vegas sports bookies use math. The goal of Mathletics is to demonstrate how simple xii PREFACE arithmetic, probability theory, and statistics can be combined with a large dose of common sense to better evaluate players and game strategy in America’s major sports. I will also show how math can be used to rank sports teams and evaluate sports bets. Throughout the book you will see references to Excel files (e.g., Standings.xls). These files may be downloaded from the book’s Web site, http:// www.waynewinston.edu). AC KNOWLEDG MENTS I would like to acknowledge George Nemhauser of Georgia Tech, Michael Magazine of the University of Cincinnati, and an anonymous re- viewer for their extremely helpful suggestions. Most of all, I would like to recognize my best friend and sports handicapper, Jeff Sagarin. My discus- sions with Jeff about sports and mathematics have always been stimulating, and this book would not be one- tenth as good if I did not know Jeff. Thanks to my editor, Vickie Kearn, for her unwavering support through- out the project. Also thanks to my outstanding production editor, Debbie Tegarden. Thanks to Jenn Backer for her great copyediting of the manu- script. Finally, a special thanks to Teresa Reimers of Microsoft Finance for coming up with the title of the book. All the math you need to know will be developed as you proceed through the book. When you have completed the book, you should be capable of do- ing your own mathletics research using the vast amount of data readily avail- able on the Internet. Even if your career does not involve sports, I hope working through the logical analyses described in this book will help you think more logically and analytically about the decisions you make in your own career. I also hope you will watch sporting events with a more analytical perspective. If you enjoy reading this book as much as I enjoyed writing it, you will have a great time. My contact information is given below. I look for- ward to hearing from you. Wayne Winston Kelley School of Business Bloomington, Indiana This page intentionally left blank ABBREVIATIONS 2B Double 3B Triple AB At Bats BA Batting Average BABIP Batting Average on Balls in Play BB Bases on Balls (Walks) BCS Bowl Championship Series BFP Batters Faced by Pitchers CS Caught Stealing D Down DICE Defense- Independent Component ERA DIPS Defense- Independent Pitching Statistics DPAR Defense Adjusted Points above Replacement DPY/A Defense- Passing Yards Per Attempt DRP Defensive Rebounding Percentage DRY/A Defense Rushing Yards Per Attempt DTO Defensive Turnover DTPP Defensive Turnovers Caused Per Possession DVOA Defense Adjusted Value over Average EFG Effective Field Goal Percentage ERA Earned Run Average EXTRAFG Extra Field Goal FP Fielding Percentage FG Field Goal FT Free Throw FTR Free Throw Rate GIDP Ground into Double Play GO Ground Out HBP Hit by Pitch HR Home Run xvi ABBREVIATIONS IP Innings Pitched K Strikeout MAD Mean Absolute Deviation MLB Major League Baseball OBP On- Base Percentage OEFG Opponent’s Effective Field Goal Percentage OFTR Opponent’s Free Throw Rate ORP Offensive Rebounding Percentage OPS On- Base Plus Slugging PAP Pitcher Abuse Points PENDIF Penalty Differential PER Player Efficiency Rating PO Put Out PORP Points over Replacement Player PRESSURE TD Pressure Touchdown PY/A Passing Yards Per Attempt QB Quarterback RET TD Return Touchdown RF Range Factor RPI Ratings Percentage Index RSQ R-Squared Value RY/A Rushing Yards Per Attempt SAC Sacrifice Bunt SAFE Spatial Aggregate Fielding Evaluation SAGWINPOINTS Number of total points earned by player during