運動的數學 (Mathletics)

如何幫助 Dallas Mavericks 得到 2011 NBA 冠軍？ 

全書共分成四大部份：棒球、橄欖球、籃球、和賭錢 (註 1)。

例如第 1 章中，使用得分平方除以 (得分平方 + 失分平方）來預估棒球隊伍贏的機率。根據 2006 年美國大聯盟的記錄，圖 1.1 說明其平均絕對誤差 (mean absolute deviation, MAD) 為 2%。

第 3 章考慮線性迴歸，使用 (各種) 安打、全壘打、保送、和盜壘，來預測棒球球員的得分數。以 2001 - 6 球季為例，表現最好的前 25 名中，Barry Bonds 佔據了前四名和第 16 名，Albert Pujols 則出現了四次。書的第 4 章使用蒙地卡羅模擬法 (Monte Carlo simulation)，以瞭解某球員對球隊得分的貢獻。

第 30 章中，根據籃球隊員的攻防能力、場上的隊友和對手，決定其分數高低 (註 2)；以 2006 - 7 球季為例，最好的球員是 Kevin Garnett。Dallas Mavericks 就是利用此套系統，決定先發球員，和用誰替換誰，以最大化得分數；球隊老闆在記者會中強調分析 (analytics) 對他們的重要性，也聘請統計學家 Ronald Beech 當全職的顧問。

至於書中的 Excel 檔可至 www.waynewinston.com 處下載，並參考更多的資訊。

有興趣的老師可以將之使用在教學上，例如機率 (含模擬) 或統計。同學們可以考慮做畢專，針對台灣的 (棒) 球隊做分析，或異常狀況的偵測與預警。如果您是球隊的老闆，更應該看看這本有趣且重要的書。

(註 1) Wayne L. Winston, Mathletics: How Gamblers, Managers, and Sports Enthusiasts Use Mathematics in Baseball, Basketball, and Football, Princeton University Press, 2012.

書商的介紹 

Mathletics is a remarkably entertaining book that shows readers how to use simple mathematics to analyze a range of statistical and probability-related questions in professional baseball, basketball, and football, and in sports gambling. How does professional baseball evaluate hitters? Is a singles hitter like Wade Boggs more valuable than a power hitter like David Ortiz? Should NFL teams pass or run more often on first downs? Could professional basketball have used statistics to expose the crooked referee Tim Donaghy? Does money buy performance in professional sports?

In Mathletics, Wayne Winston describes the mathematical methods that top coaches and managers use to evaluate players and improve team performance, and gives math enthusiasts the practical tools they need to enhance their understanding and enjoyment of their favorite sports--and maybe even gain the outside edge to winning bets. Mathletics blends fun math problems with sports stories of actual games, teams, and players, along with personal anecdotes from Winston's work as a sports consultant. Winston uses easy-to-read tables and illustrations to illuminate the techniques and ideas he presents, and all the necessary math concepts--such as arithmetic, basic statistics and probability, and Monte Carlo simulations--are fully explained in the examples.

After reading Mathletics, you will understand why baseball teams should almost never bunt, why football overtime systems are unfair, why points, rebounds, and assists aren't enough to determine who's the NBA's best player--and much, much more. In a new epilogue, Winston discusses the stats and numerical analysis behind some recent sporting events, such as how the Dallas Mavericks used analytics to become the 2011 NBA champions.

(註 2) 準則是最小平方法。是的，線性代數是有用的。