Curve Ball: Baseball, Statistics, and the Role of Chance in the Game

Front Cover
Springer Science & Business Media, Jun 8, 2001 - Mathematics - 350 pages
In its formative years, from the 1970s through the 1990s, sabermetrics was p- marily an amateur undertaking. Publications were aimed at a relatively small audience of baseball fans. To be sure, this ever-growing group of aficionados brought a lot of sophistication to baseball analysis, and were constantly looking for statistical insights beyond the listings of the top ten batters found in popular newspapers and magazines. But their influence on the baseball profession was very limited. A few consultants like Craig Wright developed temporary relati- ships with various teams, but none were able to stay long enough to create a p- manent sabermetrician staff position. (See Rob Neyer’s November 11, 2002, arti- 1 cle on ESPN. com. ) All of this changed, however, in 2002 with the hiring of Bill James by the Boston Red Sox. With that move, we have seen the admittance of the foremost proponent of sabermetrics into the top echelon of professional ba- ball management. The art and science of careful statistical analysis, it now seems, had made it into the big leagues. Since the publication of the first edition of Curve Ball in 2001, we have been overwhelmed by the positive responses from readers and critics. We’re pleased with the reception, of course, but we don’t want to rest on our laurels. Like a pitcher refining his repertoire, we’ve revised, expanded, and updated the book for its publication in this paperback edition. Several readers and critics took us 1 http://espn. go. com/mlb/columns/neyer_rob/1456664.
 

Contents

SIMPLE MODELS from Tabletop Baseball Games
xvii
Model Assumptions of AllStar Baseball
6
Introducing the Pitcher
7
The Independent Model
13
The Interactive Model
18
Which Model Is Best?
22
EXPLORING Baseball Data
25
Simple Graphs
27
OnBase Plus Slugging OPS
162
Batters Run Average BRA and Scoring lndex DX
166
Runs Created RC
167
More Analytic Models
170
AVERAGE RUNS per Play
173
Least Squares Linear Regression LSLR
174
Adding Caught Stealing to the LSLR Model
180
Adding Sacrifice Flies to the LSLR Model
183

Typical Valuesthe Mean and the Median
29
Measures of SpreadQuartiles and the Standard Deviation
30
Interesting Values
32
A FiveNumber Summary
33
OBPs of Offensive and Defensive Players
35
Relationships Between Batting Measures
36
Relating OBP and SLG
37
What about Pitching Data?
39
Strikeouts and Walks
40
Looking at Strikeout Totals
41
Defining a Strikeout Rate
42
Comparing Strikeout Rates of Starters and Relievers
45
Association Between Strikeouts and Walks?
46
Exploring Walk Rates
47
Comparing Walk Rates of Starters and Relievers
48
INTRODUCING Probability
49
Looking for Real Effects
51
Predicting OBPs
53
Probability Models
55
Observed and True OBPs
57
Learning about Batting Ability
60
Estimating Batting Ability Using a Confidence Interval
64
Comparing Hitters
66
SITUATIONAL EFFECTS
69
Surveying the Situation
70
Looking for Real Effects
72
Observed and True Batting Averages
73
Batting Averages of the 1998 Regulars
76
Two Models for Batting Averages
77
Do All Players Have the Same Ability?
78
A Model Using a Set of Random Spinners
79
Situational Effects
84
Turf vs Grass
85
Scenario 1 No Situational Effect
87
Scenario 2 Situational Bias
88
Scenario 3 Situational Effect Depends on Ability
89
Finding Good Models
90
What Do Observed Situational Effects Look Like When There Is No Effect?
91
The Last Five Years Data
93
The No Effect Situations
94
The Bias Situations
94
The Ability Situations
97
How Large Are the True Ability Effects?
102
Game Situation Effects
103
A Lot of Noise
104
STREAKINESS or The Hot Hand
107
Thinking about Streakiness
108
Moving AveragesLooking at Short lntervals
112
Runs of Good and Bad Games
115
Numbers of Good and Poor Hitting Days
116
Mr Consistent
118
Mr Streaky
122
How Does Mr Streaky Perform During a Season?
125
Mr Consistent or Mr Streaky?
128
Team Play
130
A Consistent Team
134
A Streaky Team
137
Thinking About Streakiness Again
139
MEASURING Offensive Performance
141
The Green Quest
142
Runs Scored per Game
144
Batting Average and Runs Scored per Game
149
Slugging Percentage and OnBase Percentage
153
Intuitive Techniques
161
The LindseyPalmer Models
185
Palmer Enters the Picture
195
Comparing the LSLR and LindseyPalmer Models
198
THE CURVATURE of Baseball
203
The DLSI Simulation Model
204
The Probability of Scoring Two Runs
205
The Probability of Scoring No Runs
207
A DLSI Example
211
Lessons from the Simulation
215
DLSI and Runs per Play
220
Where Do We Stand?
222
Additive Models
223
Product Models
224
Player Evaluations in the Best Models
226
Player Evaluations on an Average Team
229
Sorting Out Strengths and Weaknesses
236
MEASURING CLUTCH PLAY
239
Clutch Hits
241
Leading Off an Inning vs Not Leading Off
245
Two Outs vs NoneOne Out
247
Situation Evaluation of Run Production
249
A New Criterion for Performance
255
The Calculation of Win Probabilities
262
Player Game Percentage PGP
268
World Series Most Valuable Players
275
Looking to the Future
278
PREDICTION
281
Guessing
282
Predicting 1999 Game Results
283
How Good Were Our Predictions?
285
Predicting the Number of McGwire and Sosa Home Runs
287
Whats Wrong with This Prediction?
288
A Spinner Model for HomeRun Hitting
289
How Many AtBats?
290
Binomial Probabilities
291
What If We Dont Know Sosas True HomeRun Rate?
292
Revising Our Beliefs about Sosas HomeRun Probability
294
One Prediction
295
Many Predictions
298
Predicting Career Statistics
301
Sosas HomeRun Probabilities
302
How Long and How Many AtBats?
303
Making the Predictions
305
DID THE BEST Team Win?
307
The Big Question
308
Describing a Teams Ability
310
1871 to the Present
311
Explanations for the Winning Percentages
313
A Normal Curve Model
315
Team Performances over Time Revisited
317
A Mediocrity Model for Abilities
319
A Normal Model for Abilities
320
Weak Average and Strong Teams
321
A Model for Playing a Season
322
Simulating a Season
323
Simulating an American League Season
324
Simulating Many American League Seasons
328
Performances and Abilities of Different Types of Teams
329
Simulating an Entire Season
333
Chance
336
POSTGAME COMMENTS A Brief Afterword
339
Bibliography
343
Copyright

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Page i - The difference between a ballplayer's ability and his performance, and how probability is used to model the role of chance in performance.‎

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