11. Analytic Methods In Sports

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11. Analytic Methods In Sports



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Preface xi
About the Author xiii
List of Tables xv
1 Introduction 1
1.1 Analytic Methods 1
1.2 Organization of the Book 2
1.3 Data 3
1.4 Computation 4
1.5 Suggestions for Further Reading 5
2 Describing and Summarizing Sports Data 7
2.1 Introduction 7
2.2 Types of Data Encountered in Sports 8
2.3 Frequency Distributions 10
2.4 Summarizing Results by a Single Number: Mean and Median 16
2.5 Measuring the Variation in Sports Data 20
2.6 Sources of Variation: Comparing Between-Team and
Within-Team Variation 23
2.7 Measuring the Variation in a Qualitative Variable Such as Pitch Type 25
2.8 Using Transformations to Improve Measures of Team and Player
Performance 26
2.9 Home Runs per At Bat or At Bats per Home Run? 30
2.10 Computation 33
2.11 Suggestions for Further Reading 39
3 Probability 41
3.1 Introduction 41
3.2 Applying the Rules of Probability to Sports 41
3.3 Modeling the Results of Sporting Events as Random Variables 44
3.4 Summarizing the Distribution of a Random Variable 46
3.5 Point Distributions and Expected Points 48
3.6 Relationship between Probability Distributions and Sports Data 49
3.7 Tailoring Probability Calculations to Specific Scenarios:
Conditional Probability 51
3.8 Relating Unconditional and Conditional Probabilities: The Law of
Total Probability 54
3.9 The Importance of Scoring First in Soccer 56

3.10 Win Probabilities 57
3.11 Using the Law of Total Probability to Adjust Sports Statistics 58
3.12 Comparing NFL Field Goal Kickers 61
3.13 Two Important Distributions for Modeling Sports Data: The
Binomial and Normal Distributions 62
3.14 Using Z-Scores to Compare Top NFL Season Receiving Performances 66
3.15 Applying Probability Theory to Streaks in Sports 70
3.16 Using Probability Theory to Evaluate “Statistical Oddities” 73
3.17 Computation 75
3.18 Suggestions for Further Reading 77
4 Statistical Methods 79
4.1 Introduction 79
4.2 Using the Margin of Error to Quantify the Variation in Sports
Statistics 79
4.3 Calculating the Margin of Error of Averages and Related Statistics 82
4.4 Using Simulation to Measure the Variation in More
Complicated Statistics 87
4.5 The Margin of Error of the NFL Passer Rating 89
4.6 Comparison of Teams and Players 92
4.7 Could This Result Be Attributed to Chance? Understanding
Statistical Significance 94
4.8 Comparing the American and National Leagues 95
4.9 Margin of Error and Adjusted Statistics 98
4.10 Important Considerations When Applying Statistical Methods
to Sports 100
4.11 Computation 101
4.12 Suggestions for Further Reading 104
5 Using Correlation to Detect Statistical Relationships 105
5.1 Introduction 105
5.2 Linear Relationships: The Correlation Coefficient 105
5.3 Can the “Pythagorean Theorem” Be Used to Predict a Team’s
Second-Half Performance? 111
5.4 Using Rank Correlation for Certain Types of Nonlinear
Relationships 112
5.5 The Importance of a Top Running Back in the NFL 113
5.6 Recognizing and Removing the Effect of a Lurking Variable 114
5.7 The Relationship between Earned Run Average and Left-on-Base
Average for MLB Pitchers 116
5.8 Using Autocorrelation to Detect Patterns in Sports Data 117
5.9 Quantifying the Effect of the NFL Salary Cap 120
5.10 Measures of Association for Categorical Variables 121
5.11 Measuring the Effect of Pass Rush on Brady’s Performance 126
5.12 What Does Nadal Do Better on Clay? 127

5.13 A Caution on Using Team-Level Data 129
5.14 Are Batters More Successful If They See More Pitches? 130
5.15 Computation 132
5.16 Suggestions for Further Reading 136
6 Modeling Relationships Using Linear Regression 139
6.1 Introduction 139
6.2 Modeling the Relationship between Two Variables Using
Simple Linear Regression 139
6.3 The Uncertainty in Regression Coefficients: Margin of Error and
Statistical Significance 145
6.4 The Relationship between Wins above Replacement and
Team Wins 147
6.5 Regression to the Mean: Why the Best Tend to Get Worse and
the Worst Tend to Get Better 148
6.6 Trying to Detect Clutch Hitting 152
6.7 Do NFL Coaches Expire? A Case of Missing Data 154
6.8 Using Polynomial Regression to Model Nonlinear Relationships 155
6.9 The Relationship between Passing and Scoring in the English
Premier League 160
6.10 Models for Variables with a Multiplicative Effect on
Performance Using Log Transformations 161
6.11 An Issue to Be Aware of When Using Multiyear Data 168
6.12 Computation 170
6.13 Suggestions for Further Reading 175
7 Regression Models with Several Predictor Variables 177
7.1 Introduction 177
7.2 Multiple Regression Analysis 178
7.3 Interpreting the Coefficients in a Multiple Regression Model 178
7.4 Modeling Strikeout Rate in Terms of Pitch Velocity and Movement 181
7.5 Another Look at the Relationship between Passing and Scoring
in the English Premier League 183
7.6 Multiple Correlation and Regression 184
7.7 Measuring the Offensive Contribution of Players in La Liga 185
7.8 Models for Variables with a Synergistic or Antagonistic Effect
on Performance Using Interaction 187
7.9 A Model for 40-Yard Dash Times in Terms of Weight and Strength 189
7.10 Interaction in the Model for Strikeout Rate in Terms of Pitch
Velocity and Movement 192
7.11 Using Categorical Variables, Such as League or Position,
as Predictors 193
7.12 The Relationship between Rebounding and Scoring in the NBA 196
7.13 Identifying the Factors That Have the Greatest Effect on
Performance: The Relative Importance of Predictors 199

7.14 Factors Affecting the Scores of PGA Golfers 202
7.15 Choosing the Predictor Variables: Finding a Model for Team
Scoring in the NFL 204
7.16 Using Regression Models for Adjustment 208
7.17 Adjusted Goals-Against Average for NHL Goalies 210
7.18 Computation 211
7.19 Suggestions for Further Reading 214
References 217
Available Datasets 219



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