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MATHLETICS This page intentionally left blank MATHLETICS How Gamblers, Managers, and Sports Enthusiasts Use Mathematics in Baseball, Basketball, and Football WAYNE WINSTON PRINCETON UNIV ERSITY 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 Acknowledgments List of Abbreviations 1. 2. Part I. Baseball Baseball’s Pythagorean Theorem Who Had a Better Year, Nomar Garciaparra or Ichiro Suzuki? xi xiii xv 1 3 11 The Runs-Created Approach 3. 4. 5. 6. 7. Evaluating Hitters by Linear Weights Evaluating Hitters by Monte Carlo Simulation Evaluating Baseball Pitchers and Forecasting Future Pitcher Performance Baseball Decision-Making Evaluating Fielders 17 30 41 52 64 Sabermetrics’ Last Frontier 8. 9. Player Win Averages The Value of Replacement Players 71 79 Evaluating Trades and Fair Salary 10. 11. 12. 13. 14. 15. 16. 84 87 102 106 110 113 17. Park Factors Streakiness in Sports The Platoon Effect Was Tony Perez a Great Clutch Hitter? Pitch Count and Pitcher Effectiveness Would Ted Williams Hit .406 Today? Was Joe DiMaggio’s 56-Game Hitting Streak the Greatest Sports Record of All Time? Major League Equivalents 18. 19. Part II. Football What Makes NFL Teams Win? Who’s Better, Tom Brady or Peyton Manning? 125 127 132 116 123 viii 20. 21. 22. CONTENTS 24. 25. Football States and Values Football Decision-Making 101 A State and Value Analysis of the 2006 Super Bowl Champion Colts If Passing Is Better Than Running, Why Don’t Teams Always Pass? Should We Go for a One-Point or Two-Point Conversion? To Give Up the Ball Is Better Than to Receive 26. 27. Why Is the NFL’s Overtime System Fatally Flawed? How Valuable Are High Draft Picks in the NFL? 175 180 28. Part III. Basketball Basketball Statistics 101 185 187 23. 138 143 151 158 165 172 The Case of College Football Overtime The Four-Factor Model 29. 30. 31. 32. 33. 34. 35. 36. 37. Linear Weights for Evaluating NBA Players Adjusted
/  Player Ratings NBA Lineup Analysis Analyzing Team and Individual Matchups NBA Players’ Salaries and the Draft Are NBA Officials Prejudiced? Are College Basketball Games Fixed? Did Tim Donaghy Fix NBA Games? End-Game Basketball Strategy 195 202 224 228 233 237 242 244 248 38. 39. 40. 41. 42. 43. 44. Part IV. Playing with Money, and Other Topics for Serious Sports Fans Sports Gambling 101 Freakonomics Meets the Bookmaker Rating Sports Teams Which League Has Greater Parity, The NFL or the NBA? The Ratings Percentage Index (RPI) From Point Ratings to Probabilities Optimal Money Management 253 255 262 266 283 287 290 298 The Kelly Growth Criteria 45. 46. 47. Ranking Great Sports Collapses Can Money Buy Success? Does Joey Crawford Hate the Spurs? 303 311 319 ix CONTENTS 48. Does Fatigue Make Cowards of Us All? 321 The Case of NBA Back-to-Back Games and NFL Bye Weeks 49. 50. 51. Can the Bowl Championship Series Be Saved? Comparing Players from Different Eras Conclusions Index of Databases Annotated Bibliography Index 324 331 335 341 343 353