Mathematics and Sports

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