This book is an eclectic compendium of the essays solicited for the 2010 Mathematics Awareness Month web page on the theme of Mathematics and Sports. In keeping with the goal of promoting mathematics awareness to a broad audience, all of the articles are accessible to college level mathematics students and many are accessible to the general public.

The book is divided into sections by the type of sports. The section on football includes an article that evaluates a method for reducing the advantage of the winner of a coin flip in an NFL overtime game; the section on track and field examines the ultimate limit on how fast a human can run 100 meters; the section on baseball includes an article on the likelihood of streaks; the section on golf has an article that describes the double-pendulum model of a golf swing and an article on modeling Tiger Woods’ career.

The articles provide source material for classroom use and student projects. Many students will find mathematical ideas motivated by examples taken from sports more interesting than the examples selected from traditional sources. Among the authors are five women, five graduate students, and two undergraduate students.

### Table of Contents

Preface

**I Baseball**

1. Sabremetrics: The Past, the Present, and the Future (Jim Albert)

2. Surprising Streaks and Playoff Parity: Probability Problems in a Sports Context (Rick Cleary)

3. Did Humidifying the Baseball Decrease the Number of Homers at Coors Field? (Howard Penn)

4. Streaking: Finding the Probability for a Batting Streak (Stanley Rothman and Quoc Le)

**II Basketball**

5. Bracketology: How can math help? (Tim Chartier, Erich Kreutzer, Amy Langville, and Kathryn Pedings)

6. Down 4 with a Minute to Go (G. Edgar Parker)

7. Jump Shot Mathematics (Howard Penn)

**III Football**

8. How Deep Is Your Playbook? (Tricia Muldoon Brown and Eric B. Kahn)

9. A Look at Overtime in the NFL (Chris Jones)

10. Extending the Colley Method to Generate Predictive Football Rankings (R. Drew Pasteur)

11. When Perfect Isn?t Good Enough: Retrodictive Rankings in College Football (R. Drew Pasteur)

**IV Golf**

12.The Science of a Drive (Douglas N. Arnold)

13. Is Tiger Woods a Winner? (Scott M. Berry)

14. G. H. Hardy?s Golfing Adventure (Roland Minton)

15. Tigermetrics (Roland Minton)

**V NASCAR**

16. Can Mathematics Make a Difference? Exploring Tire Troubles in NASCAR (Cheryll E. Crowe)

**VI Schedulin**g

17. Scheduling a Tournament (Dalibor Froncek)

**VII Soccer**

18. Bending a Soccer Ball with Math (Tim Chartier)

**VIII Tennis**

19. Teaching Mathematics and Statistics Using Tennis (Reza Noubary)

20. Percentage Play in Tennis (G. Edgar Parker) IX Track and Field

21. The Effects of Wind and Altitude in the 400m Sprint with Various IAAF Track Geometries (Vanessa Alday and Michael Frantz)

23. What is the Speed Limit for Men's 100 Meter Dash? (Reza Noubary)

24. May the Best Team Win: Determining the Winner of a Cross Country Race (Stephen Szydlik)

25. Biomechanics of Running and Walking (Anthony Tongen and Roshna E. Wunderlich)

### Excerpt: (p.152)

*Mathematician Douglas N. Arnold, in his essay "The Science of a Drive," reviews how mathematics elucidates common physical phenomena in the context of a golf drive. He describes the double-pendulum model of a golf swing; the transfer of energy and momentum in the impact between club head and ball; and drag and lift in the flight of a golf ball.*

Once the ball is in flight, its trajectory is completely determined by its launch velocity and launch angle and the forces acting on it. The most important of these forces is, of course, the force of gravity, which is accelerating the ball back down toward the ground at 9.8 meters per second per second. But the forces exerted on the ball by the air it is passing through are important as well. To clarify this, we choose a coordinate system with one axis aligned with the direction of flight of the ball and the others perpendicular to it. Then the forces exerted by the atmosphere on the ball are decomposed into the drag, which is a force impeding the ball in its forward motion, and the *lift*, which helps the ball fight gravity and stay aloft longer. Drag is the same force you feel pushing on your arm if you stick it out of the window of a moving car. Lift is a consequence of the back spin of the ball, which speeds the air passing over the top of the ball and slows the air passing under it. By Bernoulli’s principle the result is lower pressure above and therefore an upward force on the ball.

### About the Editor

**Joseph A. Gallian** was born in Arnold, Pennsylvania on January 5, 1942. He obtained a BA from Slippery Rock University in 1966, an MA from the University of Kansas in 1968 and a PhD from the University of Notre Dame in 1971. After serving as a visiting Assistant Professor at Notre Dame for one year, he went to the University of Minnesota Duluth where he is a University Distinguished Professor of Teaching.

Among his honors are the MAA’s Haimo Award for distinguished teaching, the MAA Allendoerfer and Evans awards for exposition, MAA Pólya Lecturer, MAA Second Vice President, MAA President, co-director of the MAA Project NExT, associate editor of *The American Mathematical Monthly* and the *Mathematics Magazine*, advisory board member for *Math Horizons*, the Carnegie Foundation for the Advancement of Teaching Minnesota Professor of the Year, and recipient of the University of Minnesota Duluth Chancellor’s Award for Distinguished Research.

Over 150 research papers written under Gallian’s supervision by undergraduates have been published in mainstream journals. He has given more than 250 invited lectures at conferences and colleges and universities and written more than 100 articles. He is the author of *Contemporary Abstract Algebra*, Cengage, 7th edition, coauthor of *For All Practical Purposes*, W.H. Freeman, 8th edition, and coauthor of *Principles and Practices of Mathematics*, Springer. He is the editor of two conference preceedings published by the American Mathematical Society and the Executive Producer of the documentary film *Hard Problems: The Road to the World’s Toughest Math Contest*. Gallian has received more than $4,000,000 in grants.

Besides the usual math courses, Gallian has taught a Humanities course called the “The Lives and Music of the Beatles” for more than 30 years and a liberal arts course on math and sports. In 2000 a Duluth newspaper cited him as one of the “100 Great Duluthians of the 20th Century.”