Sports and Games

• Baseball - Can you define a single ranking function which accurately assigns value to hitters and/or pitchers on the basis of their statistics, ranking them from best to worst? Can you find the best batting order for a given team, the ordering of its hitters which maximizes the expected number of runs the team scores? How does this total compare to the worst possible order?   

  Batting averages give many children their first inkling of the power of mathematics. Complete team by team baseball statistics can be found at http://www.baseball-reference.com. Check http://www.usatoday.com/sports/baseball/sbstats.htm for player statistics since 1992.

• Football - Can you write an improved Clyde-like program for predicting the outcome of football games? What fraction of the games can you pick correctly, and how do you do against the spread? Are College Football games easier or harder to predict than the pros?   

  Last season's NFL statistics are available at http://www.sportingnews.com/nfl/statistics/ The official NFL site is www.nfl.com. Complete college football records are harder to find, but http://www.washingtonpost.com/ offers standings for all teams at all levels of play.

• Basketball - Being a game of individual player matchups and discrete shot attempts, basketball lends itself to Monte Carlo simulation in addition to Clyde-type prediction programs. Can you write a good basketball simulation?  

  What about predicting the outcome of the NCAA college basketball tournament, by assigning a probability of who wins each game based on statistics and rerunning the entire tourney many times?   

  Last season's NBA statistics are available at http://www.sportingnews.com/nba/statistics/ The official NBA site is www.nba.com. Complete college basketball records are available from http://www.washingtonpost.com/.

• Board Games - Many interesting board games are controlled by dice, implying that an accurate knowledge of the probabilities of certain events is essential for accurate play. Monte Carlo simulations can be used to gain insight into these events.  

  Take Monopoly as an example. Which properties are worth the most? This is a function of how often people land there as well as what the rents/costs are. Such probabilities can be easily by simulation. The results of one such study appears at http://www.teleport.com/$\sim$tcollins/monopoly.shtml.  

  What about the simpler board game of Chutes and Ladders or the card game War? What is the expected number of rolls/turns you will be committed to when your five-year old nephew demands just one more game?  

I hope you have enjoyed this excerpt from Calculated Bets: Computers, Gambling, and Mathematical Modeling to Win!, by Steven Skiena, copublished by Cambridge University Press and the Mathematical Association of America. This is a book about a gambling system that works. It tells the story of how the author used computer simulation and mathematical modeling techniques to predict the outcome of jai-alai matches and bet on them successfully -- increasing his initial stake by over 500% in one year! His method can work for anyone: at the end of the book he tells the best way to watch jai-alai, and how to bet on it. With humor and enthusiasm, Skiena details a life-long fascination with the computer prediction of sporting events. Along the way, he discusses other gambling systems, both successful and unsuccessful, for such games as lotto, roulette, blackjack, and the stock market. Indeed, he shows how his jai-alai system functions just like a miniature stock trading system. Do you want to learn about program trading systems, the future of Internet gambling, and the real reason brokerage houses don't offer mutual funds that invest at racetracks and frontons? How mathematical models are used in political polling? The difference between correlation and causation? If you are curious about gambling and mathematics, odds are this is the book for you! This book is available in both hardcover and paperback.