Sport and Games

Abstract

Mathematical ideas can give pointers to good tactics in a variety of sports and games. In lawn tennis, we assess how the proportion of points won on serve might translate into the proportion of games won, the respective merits of risky or safer serves, and how the scoring system adds to spectator enjoyment. In rugby, from where should a conversion be attempted after a try is scored? Snooker gives rise to applications of geometry and trigonometry, and the use of scalar products. Throwing events in athletics use differential equations, the formulae used to derive scores in the decathlon or heptathlon have interesting mathematical properties. The game of darts suggests diverse exercises in counting and logic, we show how the theory of zero-sum games can be applied to taking penalties in soccer, and we examine the trade-off between consistency and flamboyance in golf. We investigate how different tournaments, from soccer via chess to ice-skating, have been designed, and show how the Marriage Theorem helps avoid catastrophes when UEFA make the draw for the knockout round in soccer. Simple ideas of probability, recurrence relations, summing series, and matrix algebra arise naturally in many of these contexts.