دانلود کتاب Mathematics and Sports

فهرست مطالب :

cover
copyright page
title page
Preface
Contents
I Baseball
Sabermetrics: The Past, the Present, and the Future Jim Albert
1.1 Introduction
1.2 Measuring Batting
1.3 Measuring Pitching
1.4 Measuring Fielding
1.5 New Measurements, New Data and Measures of Performance
1.6 Further Reading
About the Author
Surprising Streaks and Playoff Parity: Probability Problems in a Sports Context Rick Cleary
2.1 Problem 1: Rare Events
Example 1: Four homers in a row
Example 2: A streak of winless opponents
2.2 Problem 2: Playoff Series Length
References
About the Author
Did Humidifying the Baseball Decrease the Number of Homers at Coors Field? Howard Penn
3.1 Introduction
3.2 The Numbers
3.3 A Useful Statistic
3.4 Comparing the two sets of data
3.5 Summary of Conclusions
3.6 Exercises
References
About the Author
Streaking: Finding the Probability for a Batting Streak Stanley Rothman and Quoc Le
4.1 Introduction
4.2 A recursive function to calculate the probability of a player having a 56-game hitting streak at some point in a season
4.3 A non-recursive piecewise function, NR(n), to calculate the probability of a player having a 56-game hitting streak at some point in a season
4.4 The Error = |R(n) - NR(n)|
4.5 Generalizing the concept of a streak
4.5.1 Definitions
4.5.2 Inputs and calculations
4.5.3 Each Individual plate appearance is a game
4.5.4 Each Individual At-Bat is a Game
4.6 Comparing Ted Williams’ 84-game consecutive on-base streak to Joe DiMaggio’s 56-game consecutive hitting streak
4.7 These two streaks evaluated for other great hitters
4.8 Conclusion
References
About the Authors
II Basketball
Bracketology: How can math help? Tim Chartier & Erich Kreutzer & Amy Langville & Kathryn Pedings
5.1 Introduction
5.2 Colley Method
5.3 Massey Method
5.4 Weighting Methods
5.4.1 Linear weighting and the Colley method
5.4.2 Linear weighting in the Massey method
5.4.3 Alternative weightings — when life isn’t linear
5.5 2009 Results
5.6 Concluding Remarks
References
About the Authors
Down 4 with a Minute to Go G. Edgar Parker
6.1 Shoot the 3
6.2 Shoot the “easy” two
References
About the Author
Jump Shot Mathematics Howard Penn
7.1 Angle of elevation 60 degrees
7.2 Angle of elevation 30 degrees
7.3 Varying the distance
7.4 Varying the height
References
About the Author
III Football
How Deep Is Your Playbook? Tricia Muldoon Brown and Eric B. Kahn
8.1 Introduction
8.2 The Game of Football and Mathematics
8.3 Counting the Formations
The 3-4 Defense
The 4-3 Defense
The Nickel Defense
The Dime Defense
8.4 Conclusion
About the Authors
A Look at Overtime in the NFL Chris Jones
9.1 Introduction
9.2 Game Data
9.3 Analyzing the current system
9.4 An alternative proposal
9.5 Conclusion
About the Author
Extending the Colley Method to Generate Predictive Football Rankings R. Drew Pasteur
References
Appendix Top 25 ranking, at the end of the 2008 season, by this method
About the Author
When Perfect Isn\'t Good Enough: Retrodictive Rankingsin College Football R. Drew Pasteur
References
About the Author
Appendix Compilation of various rankings
IV Golf
The Science of a Drive Douglas N. Arnold
12.1 The double-pendulum approximation of the swing
12.2 The impact of the club head and the ball
12.3 The ball’s flight
References
About the Author
Is Tiger Woods a Winner? Scott M. Berry
G.H. Hardy\'s Golfing Adventure Roland Minton
14.1 Hardy’s Golf Problem
14.2 Hardy’s Analysis
14.3 Two Moments
14.4 Stroke Play
14.5 Skins Game
14.6 Tournament Golf
14.7 Handicaps
14.8 Laurels to Hardy
References
About the Author
Tigermetrics Roland Minton
15.1 How many putts do the pros make?
15.2 Is Tiger Woods the best putter on tour?
15.3 What is a reasonable system for ranking putters?
15.4 Who is the best at hitting irons from the fairway?
15.5 Is there a hidden flaw in Tiger’s game?
15.6 Who is the best golfer overall?
15.7 What else can be learned?
References
About the Author
V NASCAR
Can Mathematics Make a Difference? Exploring Tire Troubles in NASCAR Cheryll E. Crowe
16.1 Introduction
16.2 What happened?
16.3 Race Tires vs. Street Tires
16.4 Mathematics is Making a Difference
16.5 Problem Resolved? Looking Towards the Future
References
About the Author
VI Scheduling
Scheduling a Tournament Dalibor Froncek
17.1 Some small tournaments
17.2 Tournaments for any even number of teams
17.3 Some more tournament properties
References
About the Author
VII Soccer
Bending a Soccer Ball with Math Tim Chartier
References
About the Author
VIII Tennis
Teaching Mathematics and Statistics Using Tennis Reza Noubary
19.1 Introduction
19.1.1 General
19.1.2 Specific
19.2 An Illustrative Example
19.3 Activities
Activity 1: Bouncing Ball
Activity 2: Applying Binomial Distribution, Matrices, Markov Chain, and Derivatives
Activity 3: Calculations Based on Normal Distribution
Activity 4: Constructing Confidence Intervals and Testing Hypotheses
Activity 5: Applying Regression and Time Series for Prediction
Activity 6: Research topics
About the Author
Percentage Play in Tennis G. Edgar Parker
20.1 Introduction
20.2 The Model
20.3 The Calculations
20.4 Big Shot Strategies
20.5 Analyzing Serve
20.6 Afterthoughts
Reference
About the Author
IX Track and Field
The Effects of Wind and Altitude in the 400m Sprintwith Various IAAF Track Geometries Vanessa Alday and Michael Frantz
21.1 Introduction and an Early Model
21.2 Quinn’s Model
21.3 The Effects of Track Geometry on Running Performance
21.4 Computation of the Effect of Winds
21.5 Altitude and the Propulsive Force
21.6 Data Collected and Results from Quinn
21.7 Effects of Wind Direction on Overall Performance
21.8 Effects of Altitude and Air Density
21.9 The Equal Quadrant Track
21.10 Wind Effects on the Equal Quadrant Track
21.11 The Ancient Greek Olympiad Track
21.12 Summary of Results
21.13 Directions for Possible Future Work
References
About the Authors
Mathematical Ranking of the Division III Track and Field Conferences Chris Fisette
About the Author
What is the Speed Limit for Men\'s 100 Meter Dash Reza Noubary
23.1 Introduction
23.2 Methods Based on Trend Analysis
23.3 Methods Based on Outstanding Values
23.3.1 Methods Based on Threshold Theory
23.3.2 Methods Based on Theory of Records
23.4 Ultimate Record
References
About the Author
May the Best Team Win: Determining the Winner of a Cross Country Race Stephen Szydlik
24.1 Warming Up
24.2 Mile 1: Basic Terminology and Some Alternatives
24.3 Mile 2: Fairness Criteria and Other Scoring Methods
24.4 Mile 3: More Criteria and Alternative Scoring Methods
24.5 Mile 4: Some Social Choice Theory
24.6 Mile 5: Impossibility?
24.7 Warmdown: Some Concluding Remarks
References
About the Author
Biomechanics of Running and Walking Anthony Tongen and Roshna E. Wunderlich
25.1 Introduction
25.2 Applications
Numerically Calculating Impulse
Running Model
Walking Model
25.3 Conclusions
References
About the Authors
About the Editor