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.