Teaching Statistics Using Baseball

257 Pages·2022·9.58 MB·English

by  Jim Albert

AMS / MAA TEXTBOOKS VOL 34
Teaching Statistics Using
Baseball
Second Edition
Jim Albert
Teaching Statistics Using
Baseball
Second Edition
Originallypublishedby
TheMathematicalAssociationofAmerica,2017.
SoftcoverISBN:978-1-4704-6938-2
LCCN:2017931120
Copyright©2017,heldbytheAmericanMathematicalSociety
PrintedintheUnitedStatesofAmerica.
ReprintedbytheAmericanMathematicalSociety,2022
TheAmericanMathematicalSocietyretainsallrights
exceptthosegrantedtotheUnitedStatesGovernment.
⃝1Thepaperusedinthisbookisacid-freeandfallswithintheguidelines
establishedtoensurepermanenceanddurability.
VisittheAMShomepageathttps://www.ams.org/
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AMS/MAA TEXTBOOKS
VOL 34
Teaching Statistics Using
Baseball
Second Edition
Jim Albert
CouncilonPublicationsandCommunications
JenniferJ.Quinn,Chair
CommitteeonBooks
JenniferJ.Quinn,Chair
MAATextbooksEditorialBoard
StanleyE.Seltzer,Editor
BelaBajnok
MatthiasBeck
RichardE.Bedient
OttoBretscher
HeatherAnnDye
WilliamGreen
CharlesR.Hampton
JacquelineA.Jensen-Vallin
SuzanneLynneLarson
JohnLorch
VirginiaA.Noonburg
SusanF.Pustejovsky
JeffreyL.Stuart
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Contents
PrefacetotheFirstEdition ix
PrefacetotheSecondEdition xi
1 AnIntroductiontoBaseballStatistics 1
2 ExploringaSingleBatchofBaseballData 13
2.1 LookingatTeams’OffensiveStatistics..................................................... 13
2.2 ATributetoDerekJeter........................................................................ 17
2.3 ATributetoRandyJohnson................................................................... 20
2.4 AnalyzingBaseballAttendance............................................................... 23
2.5 ManagerStatistics:theUseofSacrificeBunts............................................ 26
2.6 Exercises........................................................................................... 28
3 ComparingBatchesandStandardization 45
3.1 AlbertPujolsandMannyRamirez........................................................... 45
3.2 RobinRobertsandWhiteyFord.............................................................. 50
3.3 HomeRuns:AComparisonofFourSeasons.............................................. 54
3.4 SluggingPercentagesareNormal............................................................ 57
3.5 GreatBattingAverages......................................................................... 59
3.6 Exercises........................................................................................... 61
4 RelationshipsBetweenMeasurementVariables 73
4.1 RelationshipsinTeamOffensiveStatistics................................................. 73
4.2 RunsandOffensiveStatistics.................................................................. 78
4.3 MostValuableHittingStatistics.............................................................. 80
4.4 ANewMeasureofOffensivePerformance................................................ 86
4.5 HowImportantisaRun?....................................................................... 88
4.6 BaseballPlayersRegresstotheMean....................................................... 91
4.7 Exercises........................................................................................... 94
vii
viii Contents
5 IntroductiontoProbabilityUsingTabletopGames 111
5.1 WhatisChrisDavis’HomeRunProbability?............................................. 111
5.2 BigLeagueBaseball............................................................................. 114
5.3 All-StarBaseball................................................................................. 116
5.4 Strat-O-MaticBaseball......................................................................... 119
5.5 Exercises........................................................................................... 124
6 ProbabilityDistributionsandBaseball 139
6.1 TheBinomialDistributionandHitsperGame............................................ 139
6.2 ModelingRunsScored:GettingonBase................................................... 142
6.3 ModelingRunsScored:AdvancingtheRunnerstoHome.............................. 144
6.4 Exercises........................................................................................... 148
7 IntroductiontoStatisticalInference 155
7.1 AbilityandPerformance........................................................................ 155
7.2 SimulatingaBatter’sPerformanceifHisAbilityisKnown............................ 157
7.3 LearningAboutaBatter’sAbility............................................................ 159
7.4 IntervalEstimatesforAbility.................................................................. 161
7.5 ComparingWadeBoggsandTonyGwynn................................................. 165
7.6 Exercises........................................................................................... 168
8 TopicsinStatisticalInference 175
8.1 SituationalHittingStatisticsforMikeTrout............................................... 176
8.2 ObservedSituationalEffectsforManyPlayers........................................... 178
8.3 ModelingOn-BasePercentagesforManyPlayers........................................ 181
8.4 ModelsforSituationalEffects................................................................. 185
8.5 IsMichaelBrantleyStreaky?.................................................................. 188
8.6 AStreakyDie..................................................................................... 191
8.7 Exercises........................................................................................... 193
9 ModelingBaseballUsingaMarkovChain 211
9.1 IntroductiontoaMarkovChain............................................................... 211
9.2 AHalf-inningofBaseballasaMarkovChain............................................. 215
9.3 UsefulMarkovChainCalculations........................................................... 217
9.4 TheValueofDifferentOn-baseEvents..................................................... 222
9.5 AnsweringQuestionsAboutBaseballStrategy........................................... 224
9.6 Exercises........................................................................................... 225
A AnIntroductiontoBaseball 233
A.1 TheGameofBaseball........................................................................... 233
A.2 OneHalf-InningofBaseball................................................................... 234
A.3 TheBoxscore:AStatisticalRecordofaBaseballGame................................ 235
Bibliography 239
Index 241
Preface to the First Edition
Overtwentyyears,thisauthorhasbeenintheenterpriseofteachingintroductorystatisticstoan
audiencethatistakingtheclasstosatisfytheirmathematicsrequirement.Thisisachallenging
endeavor because the students have little prior knowledge about the discipline of statistics
and many of them are anxious about mathematics and computation. Statistical concepts and
examplesareusuallypresentedinaparticularcontext.However,oneobstacleinteachingthis
introductoryclassisthatweoftendescribethestatisticalconceptsinacontext,suchasmedicine,
law, or agriculture that is completely foreign to the undergraduate student. The student has a
muchbetterchanceofunderstandingconceptsinprobabilityandstatisticsiftheyaredescribed
inafamiliarcontext.
Manystudentsarefamiliarwithsportseitherasaparticipantoraspectator.Theyknowofthe
popularathletes,suchasTigerWoodsandBarryBonds,andtheyaregenerallyknowledgeable
withtherulesofthemajorsports,suchasbaseball,football,andbasketball.Formanystudents
sportsisafamiliarcontextinwhichaninstructorcandescribestatisticalthinking.
Thegoalofthisbookistoprovideacollectionofexamplesandexercisesapplyingproba-
bilityandstatisticstothesportofbaseball.Whybaseballinsteadofothersports?
(cid:4) BaseballisthegreatAmericangame.Baseballisgreatinthatithasarichhistoryofteams
andplayers,andmanypeoplearefamiliarwiththebasicrulesofthegame.Thepopularityof
baseball isreflected by thelarge number of movies thathave been produced about baseball
teamsandplayers.
(cid:4) Baseball is the most statistical of all sports. Hitters and pitchers are identified by their
correspondinghittingandpitchingstatistics.Forexample,BabeRuthisforeveridentifiedby
the statistic 60, which was the number of home runs hit in his 1927 season. Bob Gibson is
famous for his record low earned run average of 1.12 during the 1968 season. A flood of
differentstatisticalmeasuresareusedtorateplayersandsalariesofplayersaredeterminedin
partbythesestatistics.Thereisanactiveeffortamongbaseballwriterstolearnmoreabout
baseballissuesbyusingstatistics.
(cid:4) AwealthofbaseballdataiscurrentlyavailableovertheInternet.Playerandteamhittingand
pitchingstatisticscanbeeasilyfound.Comparisonsbetweenplayersofdifferenterascanbe
made using a downloadable dataset that gives hitting and pitching data for all players who
haveeverplayedprofessionalbaseball.
ix