Contents

Preface to the First Edition ix

Preface to the Second Edition xi

1 An Introduction to Baseball Statistics 1

2 Exploring a Single Batch of Baseball Data 13 2.1 Looking at Teams’ Offensive Statistics ...... 13 2.2 A Tribute to Derek Jeter...... 17 2.3 A Tribute to Randy Johnson...... 20 2.4 Analyzing Baseball Attendance...... 23 2.5 Manager Statistics: the Use of Sacrifice Bunts...... 26 2.6 Exercises...... 28

3 Comparing Batches and Standardization 45 3.1 Albert Pujols and Manny Ramirez...... 45 3.2 Robin Roberts and Whitey Ford...... 50 3.3 Home Runs: A Comparison of Four Seasons...... 54 3.4 Slugging Percentages are Normal ...... 57 3.5 Great Batting Averages ...... 59 3.6 Exercises...... 61

4 Relationships Between Measurement Variables 73 4.1 Relationships in Team Offensive Statistics...... 73 4.2 Runs and Offensive Statistics...... 78 4.3 Most Valuable Hitting Statistics ...... 80 4.4 A New Measure of Offensive Performance ...... 86 4.5 How Important is a Run?...... 88 4.6 Baseball Players Regress to the Mean...... 91 4.7 Exercises...... 94

vii viii Contents

5 Introduction to Probability Using Tabletop Games 111 5.1 What is Chris Davis’ Home Run Probability?...... 111 5.2 Big League Baseball...... 114 5.3 All-Star Baseball...... 116 5.4 Strat-O-Matic Baseball ...... 119 5.5 Exercises...... 124

6 Probability Distributions and Baseball 139 6.1 The Binomial Distribution and Hits per Game...... 139 6.2 Modeling Runs Scored: Getting on Base...... 142 6.3 Modeling Runs Scored: Advancing the Runners to Home...... 144 6.4 Exercises...... 148

7 Introduction to Statistical Inference 155 7.1 Ability and Performance...... 155 7.2 Simulating a Batter’s Performance if His Ability is Known...... 157 7.3 Learning About a Batter’s Ability...... 159 7.4 Interval Estimates for Ability...... 161 7.5 Comparing Wade Boggs and Tony Gwynn...... 165 7.6 Exercises...... 168

8 Topics in Statistical Inference 175 8.1 Situational Hitting Statistics for Mike Trout...... 176 8.2 Observed Situational Effects for Many Players ...... 178 8.3 Modeling On-Base Percentages for Many Players...... 181 8.4 Models for Situational Effects...... 185 8.5 Is Michael Brantley Streaky?...... 188 8.6 A Streaky Die...... 191 8.7 Exercises...... 193

9 Modeling Baseball Using a Markov Chain 211 9.1 Introduction to a Markov Chain...... 211 9.2 A Half-inning of Baseball as a Markov Chain...... 215 9.3 Useful Markov Chain Calculations...... 217 9.4 The Value of Different On-base Events...... 222 9.5 Answering Questions About Baseball Strategy ...... 224 9.6 Exercises...... 225

A An Introduction to Baseball 233 A.1 The Game of Baseball...... 233 A.2 One Half-Inning of Baseball...... 234 A.3 The Boxscore: A Statistical Record of a Baseball Game...... 235

Bibliography 239

Index 241