Tài liệu MATHLETICS How Gamblers, Managers, and Sports Enthusiasts Use Mathematics in Baseball,

MATHLETICS

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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

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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

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
/ 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

viii CONTENTS

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

CONTENTS ix

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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

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).

xii PREFACE

AC KNOW LEDG 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

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