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E-grāmata: Sports Math: An Introductory Course in the Mathematics of Sports Science and Sports Analytics

(Roanoke College, Salem, Virginia, USA)
  • Formāts: 278 pages
  • Izdošanas datums: 03-Nov-2016
  • Izdevniecība: Chapman & Hall/CRC
  • ISBN-13: 9781498706322
  • Formāts - EPUB+DRM
  • Cena: 55,09 €*
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  • Formāts: 278 pages
  • Izdošanas datums: 03-Nov-2016
  • Izdevniecība: Chapman & Hall/CRC
  • ISBN-13: 9781498706322

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Can you really keep your eye on the ball? How is massive data collection changing sports?

Sports science courses are growing in popularity. The authors course at Roanoke College is a mix of physics, physiology, mathematics, and statistics. Many students of both genders find it exciting to think about sports. Sports problems are easy to create and state, even for students who do not live sports 24/7. Sports are part of their culture and knowledge base, and the opportunity to be an expert on some area of sports is invigorating. This should be the primary reason for the growth of mathematics of sports courses: the topic provides intrinsic motivation for students to do their best work.

From the Author:

"The topics covered in Sports Science and Sports Analytics courses vary widely. To use a golfing analogy, writing a book like this is like hitting a drive at a driving range; there are many directions you can go without going out of bounds. At the driving range, I pick out a small target to focus on, and that is what I have done here. I have chosen a sample of topics I find very interesting. Ideally, users of this book will have enough to choose from to suit whichever version of a sports course is being run."

"The book is very appealing to teach from as well as to learn from. Students seem to have a growing interest in ways to apply traditionally different areas to solve problems. This, coupled with an enthusiasm for sports, makes Dr. Mintons book appealing to me."Kevin Hutson, Furman University

Recenzijas

The book is written at a level that is accessible to a large audience. It contains a small number of applications that make use of calculus; otherwise, only a high school level mathematics background is required. Furthermore, one can easily skip over those sections that require calculus and still have plenty of accessible material to read.

Sports Math is well written and easy to read. The book should appeal to anyone interested in the quantitative aspects of athletics. Each chapter of the books ends with a fairly large number of exercises and also pointers to further reading. Thus, the book could be used not only as a textbook for a course but also as a nice resource for student projects.

~Mathematical Reviews, 2017

Minton presents a textbook based on the current status of a sport science course that has evolved since he began teaching it in 1988. He offers a sample of topics that he knows something about and finds interesting, and hopes that instructors and students will find the book useful. His topics are projectile motion, rotational motion, sports illusions, collisions, ratings systems, voting systems, saber- and other metrics, randomness in sports, sports strategies, and big data and beyond.

~ProtoView, 2017

This work discusses how mathematics is used to analyze popular American sports like football, baseball, and basketball. Minton (mathematics, Roanoke College) has based this book on several of his undergraduate courses. The book covers two major aspects: the physics involved in sports (e.g., the motion of a ball) and the statistics used to make probabilistic ratings of performance and success. The beginning chapters consider topics from mechanics, such as Projectile Motion, Rotational Motion, and Collisions. The rest of the text is devoted to statistics used in sports ratings and analysis, with many examples from specific games played in the big leagues or by major colleges. The material covered is selective and quirky; the level of analytical mathematics and statistics ranges from simple to advanced, including calculus, matrixes, and game theory. Each chapter has solved examples and end-of-chapter questions, problems, and suggestions for projects. There are pictures and graphs interspersed throughout the text. The book is not suitable as a standard text in any conventional courseit will best serve as a supplement.

--N. Sadanand, Central Connecticut State University 2018 The book is written at a level that is accessible to a large audience. It contains a small number of applications that make use of calculus; otherwise, only a high school level mathematics background is required. Furthermore, one can easily skip over those sections that require calculus and still have plenty of accessible material to read.

Sports Math is well written and easy to read. The book should appeal to anyone interested in the quantitative aspects of athletics. Each chapter of the books ends with a fairly large number of exercises and also pointers to further reading. Thus, the book could be used not only as a textbook for a course but also as a nice resource for student projects.

~Mathematical Reviews, 2017

Minton presents a textbook based on the current status of a sport science course that has evolved since he began teaching it in 1988. He offers a sample of topics that he knows something about and finds interesting, and hopes that instructors and students will find the book useful. His topics are projectile motion, rotational motion, sports illusions, collisions, ratings systems, voting systems, saber- and other metrics, randomness in sports, sports strategies, and big data and beyond.

~ProtoView, 2017

This work discusses how mathematics is used to analyze popular American sports like football, baseball, and basketball. Minton (mathematics, Roanoke College) has based this book on several of his undergraduate courses. The book covers two major aspects: the physics involved in sports (e.g., the motion of a ball) and the statistics used to make probabilistic ratings of performance and success. The beginning chapters consider topics from mechanics, such as Projectile Motion, Rotational Motion, and Collisions. The rest of the text is devoted to statistics used in sports ratings and analysis, with many examples from specific games played in the big leagues or by major colleges. The material covered is selective and quirky; the level of analytical mathematics and statistics ranges from simple to advanced, including calculus, matrixes, and game theory. Each chapter has solved examples and end-of-chapter questions, problems, and suggestions for projects. There are pictures and graphs interspersed throughout the text. The book is not suitable as a standard text in any conventional courseit will best serve as a supplement.

--N. Sadanand, Central Connecticut State University 2018

Preface xiii
List of Figures
xvii
List of Tables
xxi
1 Projectile Motion
1(24)
Introduction
1(1)
Figuring with Newton
1(2)
Hangin' with MJ: 1-D Motion
3(1)
Raining 3's with Steph: 2-D Motion
4(2)
K's with Kershaw: Terminal Velocity and Drag Forces
6(1)
Calculus Box: Solving for Velocity
7(1)
Bending with Bubba: Magnus Force
8(3)
Smiling with Dimples
11(1)
Calculus Box: A General Model of a Ball in Flight
12(1)
The Effects of Drag and Lift
13(2)
Knuckling Down
15(2)
Calculus Box: Lateral Position of a Knuckleball
17(1)
Exercises
18(5)
Further Reading
23(2)
2 Rotational Motion
25(14)
Introduction
25(1)
Going in Circles
26(2)
Torquing Off Newton
28(1)
All About MOI
29(1)
Size Is Important
30(1)
Calculus Box: Calculating MOI
30(1)
Equipment Design
31(1)
Supercats and Tamedogs
32(1)
Keeping the Momentum
33(1)
Exercises
34(4)
Further Reading
38(1)
3 Sports Illusions
39(16)
Introduction
39(1)
You Can't Keep Your Eye on the Ball
39(2)
You Can't Touch This
41(1)
You Can't Teach Size
42(1)
You Can't Afford the Yardage
43(2)
You Can't Bend That Way
45(1)
You Can't Make That Call!
46(3)
You Can't Clear That Bar
49(1)
Exercises
50(4)
Further Reading
54(1)
4 Collisions
55(18)
Introduction
55(1)
Linear Momentum
56(1)
Impulse and Force
57(2)
Calculus Box: Integration
59(1)
Giving to Receive
60(1)
Tendons and Tennis
61(1)
Coefficient of Restitution
62(1)
Incoming and Outgoing
63(2)
Derivative Works
65(1)
The Way the Ball Bounces
66(1)
Freeze Frame
67(1)
Exercises
68(3)
Further Reading
71(2)
5 Ratings Systems
73(22)
Introduction
73(1)
Right versus Best
74(1)
Ratings versus Rankings
74(1)
The Massey System
75(2)
Connected Schedules
77(1)
Massey Win Ratings
78(1)
Offense and Defense
79(1)
Least Squares Equivalence
79(1)
Wins versus Points
80(1)
The Colley System
81(1)
A Flaky Scaling Problem
82(1)
The Elo System
83(2)
Strength of Schedule
85(1)
Computing Probabilities
85(1)
Weighty Issues
86(1)
Calculus Box: A Recipe for Reduction of Matrices
87(3)
Exercises
90(4)
Further Reading
94(1)
6 Voting Systems
95(26)
Introduction
95(1)
How They Vote
96(1)
Condorcet's Intransitive Attitude
97(2)
Preference Lists, Voting Systems, and Chaos
99(2)
Fairness and the Arrow of Impossibility
101(1)
Positional Voting Systems
102(1)
A Return to Sports Voting
103(1)
Simulations
104(2)
Range Voting
106(2)
PageRank and MVPassing
108(2)
Seeding of Tournaments
110(2)
Probability Box: Put Some Error Bars on Those Things
112(1)
Exercises
113(6)
Further Reading
119(2)
7 Saber- and Other Metrics
121(30)
Introduction
121(1)
The Pythagorean Cult
122(3)
When Good Statistics Go Bad
125(2)
Rates versus Numbers
127(1)
Persistence and Reliability
128(2)
On the Defensive
130(1)
Plus and Minus
131(1)
Park Factors
132(2)
Four Factors, Fenwick, and Football
134(3)
Evaluation and Prediction
137(1)
Regression to the Mean
138(1)
Linear Weights: A Prelude to WAR
139(2)
Calculus Box: Linear Regression
141(1)
Roger Maris and the Hall of Fame
141(1)
Now Trending
142(2)
Exercises
144(6)
Further Reading
150(1)
8 Randomness in Sports
151(28)
Introduction
151(1)
Summing Up the Basics
152(2)
Prediction is Difficult
154(1)
A Slump or a Disaster
155(1)
Calculus Box: Probability
156(1)
May the Best Team Win
157(1)
Measuring Parity: Gini in a Bottle
158(3)
Measuring Parity: Luck versus Skill
161(1)
The Paradox of Skill
162(1)
Measuring Parity: Entropy
163(1)
Declaration of Independence
164(1)
Conditional Probability
165(1)
The Hot Hands
166(1)
Not So Fast, My Friend
167(1)
Runs Tests
168(1)
Joltin Joe and The Streak
169(1)
Not Following the Rules
170(1)
BABIP and DIPS
171(1)
Random Thoughts
172(1)
Exercises
173(5)
Further Reading
178(1)
9 Sports Strategies
179(24)
Introduction
179(1)
Don't Punt, John!
180(1)
Bill Belichick's Gambles
181(2)
The Value of a Play
183(1)
Markov Chain Models
184(3)
The Expected Runs Matrix
187(1)
Win Probability and Leverage
187(1)
Game Control and the Story Stat
188(1)
Game Theory
189(4)
Upsetting the Game Theory
193(1)
Getting and Giving Two
194(1)
The Physical Challenge
195(1)
Personnel Decisions: Aging
196(1)
Personnel Decisions: Transfer Fees and Stars
197(2)
Exercises
199(3)
Further Reading
202(1)
10 Big Data and Beyond
203(50)
Introduction
203(1)
Big Data Is Watching You
204(1)
A Theory of Everything
205(2)
Catch Me If You Can
207(1)
Getting Framed
208(1)
Anonymous Field Goal Kicking
209(2)
On the Rebound
211(2)
Breaching the Convex Hull
213(2)
Calculus Box: A Goal-Scoring Model
215(2)
Showing Hot and Cold
217(1)
RIP to the RPI
218(2)
Blackbox Analytics
220(2)
PeeWee Analytics
222(1)
Wearable Tech
223(1)
Exercises
223(3)
Further Reading
226(1)
Answers and Selected Solutions
227(26)
Index 253
Roland Minton is professor of Mathematics at Roanoke College, Salem, Virginia. He has taught courses in sports science since 1987.