10. Sports Math And Analytics

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10. Sports Math And Analytics

 

 

CATEGORY: Sports & Recreation 250 Courses

COURSE NUMBER: 10

FEES: 555/- INR only

CERTIFICATE VALIDITY: Lifetime

CERTIFICATES DELIVERY: In 48 hours

BOOKS/ MANUALS: Pages

Syllabus

Preface xiii
List of Figures xvii
List of Tables xxi
1 Projectile Motion 1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Figuring with Newton . . . . . . . . . . . . . . . . . . . . . . . . . 1
Hangin’ with MJ: 1-D Motion . . . . . . . . . . . . . . . . . . . . 3
Raining 3’s with Steph: 2-D Motion . . . . . . . . . . . . . . . . . 4
K’s with Kershaw: Terminal Velocity and Drag Forces . . . . . . . 6
Calculus Box: Solving for Velocity . . . . . . . . . . . . . . . 7
Bending with Bubba: Magnus Force . . . . . . . . . . . . . . . . . 8
Smiling with Dimples . . . . . . . . . . . . . . . . . . . . . . . . . 11
Calculus Box: A General Model of a Ball in Flight . . . . . . 12
The Effects of Drag and Lift . . . . . . . . . . . . . . . . . . . . . 13
Knuckling Down . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Calculus Box: Lateral Position of a Knuckleball . . . . . . . . 17
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2 Rotational Motion 25
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Going in Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Torquing Off Newton . . . . . . . . . . . . . . . . . . . . . . . . . 28
All About MOI . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Size Is Important . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Calculus Box: Calculating MOI . . . . . . . . . . . . . . . . . 30
Equipment Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Supercats and Tamedogs . . . . . . . . . . . . . . . . . . . . . . . 32
Keeping the Momentum . . . . . . . . . . . . . . . . . . . . . . . 33
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3 Sports Illusions 39
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
You Can’t Keep Your Eye on the Ball . . . . . . . . . . . . . . . . 39
You Can’t Touch This . . . . . . . . . . . . . . . . . . . . . . . . . 41
You Can’t Teach Size . . . . . . . . . . . . . . . . . . . . . . . . . 42
You Can’t Afford the Yardage . . . . . . . . . . . . . . . . . . . . 43
You Can’t Bend That Way . . . . . . . . . . . . . . . . . . . . . . 45
You Can’t Make That Call! . . . . . . . . . . . . . . . . . . . . . . 46
You Can’t Clear That Bar . . . . . . . . . . . . . . . . . . . . . . 49
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4 Collisions 55
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Linear Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Impulse and Force . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Calculus Box: Integration . . . . . . . . . . . . . . . . . . . . . . . 59
Giving to Receive . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Tendons and Tennis . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Coefficient of Restitution . . . . . . . . . . . . . . . . . . . . . . . 62
Incoming and Outgoing . . . . . . . . . . . . . . . . . . . . . . . . 63
Derivative Works . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
The Way the Ball Bounces . . . . . . . . . . . . . . . . . . . . . . 66
Freeze Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5 Ratings Systems 73
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Right versus Best . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Ratings versus Rankings . . . . . . . . . . . . . . . . . . . . . . . 74
The Massey System . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Connected Schedules . . . . . . . . . . . . . . . . . . . . . . . 77
Massey Win Ratings . . . . . . . . . . . . . . . . . . . . . . . 78
Offense and Defense . . . . . . . . . . . . . . . . . . . . . . . 79
Least Squares Equivalence . . . . . . . . . . . . . . . . . . . . 79
Wins versus Points . . . . . . . . . . . . . . . . . . . . . . . . . . 80
The Colley System . . . . . . . . . . . . . . . . . . . . . . . . . . 81
A Flaky Scaling Problem . . . . . . . . . . . . . . . . . . . . 82
The Elo System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
Strength of Schedule . . . . . . . . . . . . . . . . . . . . . . . . . 85
Computing Probabilities . . . . . . . . . . . . . . . . . . . . . . . 85

Weighty Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Calculus Box: A Recipe for Reduction of Matrices . . . . . . . . . 87
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6 Voting Systems 95
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
How They Vote . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Condorcet’s Intransitive Attitude . . . . . . . . . . . . . . . . . . 97
Preference Lists, Voting Systems, and Chaos . . . . . . . . . . . . 99
Fairness and the Arrow of Impossibility . . . . . . . . . . . . . . . 101
Positional Voting Systems . . . . . . . . . . . . . . . . . . . . . . 102
A Return to Sports Voting . . . . . . . . . . . . . . . . . . . . . . 103
Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
Range Voting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
PageRank and MVPassing . . . . . . . . . . . . . . . . . . . . . . 108
Seeding of Tournaments . . . . . . . . . . . . . . . . . . . . . . . . 110
Probability Box: Put Some Error Bars on Those Things . . . . . . 112
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
7 Saber- and Other Metrics 121
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
The Pythagorean Cult . . . . . . . . . . . . . . . . . . . . . . . . 122
When Good Statistics Go Bad . . . . . . . . . . . . . . . . . . . . 125
Rates versus Numbers . . . . . . . . . . . . . . . . . . . . . . . . . 127
Persistence and Reliability . . . . . . . . . . . . . . . . . . . . . . 128
On the Defensive . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Plus and Minus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Park Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
Four Factors, Fenwick, and Football . . . . . . . . . . . . . . . . . 134
Evaluation and Prediction . . . . . . . . . . . . . . . . . . . . . . 137
Regression to the Mean . . . . . . . . . . . . . . . . . . . . . . . . 138
Linear Weights: A Prelude to WAR . . . . . . . . . . . . . . . . . 139
Calculus Box: Linear Regression . . . . . . . . . . . . . . . . 141
Roger Maris and the Hall of Fame . . . . . . . . . . . . . . . . . . 141
Now Trending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

x Contents
8 Randomness in Sports 151
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Summing Up the Basics . . . . . . . . . . . . . . . . . . . . . . . . 152
Prediction is Difficult . . . . . . . . . . . . . . . . . . . . . . . . . 154
A Slump or a Disaster . . . . . . . . . . . . . . . . . . . . . . . . . 155
Calculus Box: Probability . . . . . . . . . . . . . . . . . . . . . . . 156
May the Best Team Win . . . . . . . . . . . . . . . . . . . . . . . 157
Measuring Parity: Gini in a Bottle . . . . . . . . . . . . . . . . . . 158
Measuring Parity: Luck versus Skill . . . . . . . . . . . . . . . . . 161
The Paradox of Skill . . . . . . . . . . . . . . . . . . . . . . . . . . 162
Measuring Parity: Entropy . . . . . . . . . . . . . . . . . . . . . . 163
Declaration of Independence . . . . . . . . . . . . . . . . . . . . . 164
Conditional Probability . . . . . . . . . . . . . . . . . . . . . . . . 165
The Hot Hands . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
Not So Fast, My Friend . . . . . . . . . . . . . . . . . . . . . . . . 167
Runs Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
Joltin Joe and The Streak . . . . . . . . . . . . . . . . . . . . . . 169
Not Following the Rules . . . . . . . . . . . . . . . . . . . . . . . . 170
BABIP and DIPS . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
Random Thoughts . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
9 Sports Strategies 179
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Don’t Punt, John! . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
Bill Belichick’s Gambles . . . . . . . . . . . . . . . . . . . . . . . . 181
The Value of a Play . . . . . . . . . . . . . . . . . . . . . . . . . . 183
Markov Chain Models . . . . . . . . . . . . . . . . . . . . . . . . . 184
The Expected Runs Matrix . . . . . . . . . . . . . . . . . . . . . . 187
Win Probability and Leverage . . . . . . . . . . . . . . . . . . . . 187
Game Control and the Story Stat . . . . . . . . . . . . . . . . . . 188
Game Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
Upsetting the Game Theory . . . . . . . . . . . . . . . . . . . . . 193
Getting and Giving Two . . . . . . . . . . . . . . . . . . . . . . . 194
The Physical Challenge . . . . . . . . . . . . . . . . . . . . . . . . 195
Personnel Decisions: Aging . . . . . . . . . . . . . . . . . . . . . . 196
Personnel Decisions: Transfer Fees and Stars . . . . . . . . . . . . 197
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

Contents xi
10 Big Data and Beyond 203
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
Big Data Is Watching You . . . . . . . . . . . . . . . . . . . . . . 204
A Theory of Everything . . . . . . . . . . . . . . . . . . . . . . . . 205
Catch Me If You Can . . . . . . . . . . . . . . . . . . . . . . . . . 207
Getting Framed . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
Anonymous Field Goal Kicking . . . . . . . . . . . . . . . . . . . 209
On the Rebound . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
Breaching the Convex Hull . . . . . . . . . . . . . . . . . . . . . . 213
Calculus Box: A Goal-Scoring Model . . . . . . . . . . . . . . . . 215
Showing Hot and Cold . . . . . . . . . . . . . . . . . . . . . . . . 217
RIP to the RPI . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
Blackbox Analytics . . . . . . . . . . . . . . . . . . . . . . . . . . 220
PeeWee Analytics . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
Wearable Tech . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
Answers and Selected Solutions 227
Index 253

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