Sport and Games

  • John HaighEmail author


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? Geometry, trigonometry and scalar products arise in snooker. 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 apply the theory of zero-sum games to taking penalties in soccer, note that the traditional order in a penalty shoot-out favours the team going first, and describe proposals to remedy this. We assess the trade-off between consistency and flamboyance in golf, and investigate the design of different tournaments in soccer, chess and ice-skating, and show how the Marriage Theorem helps UEFA avoid catastrophes. Simple ideas of probability, recurrence relations, summing series, and matrix algebra arise naturally.

References and Further Reading

  1. Bennett J (1998) Statistics in Sport. ArnoldGoogle Scholar
  2. Brahms S J and Ismael M (2018) Making the Rules of Sports Fairer SIAM Review 2018 60(1) pages 181–202Google Scholar
  3. Butenko S, Gil-Lafuente J and Pardalos P M (2004) Economics, Management and Optimization in Sports. SpringerGoogle Scholar
  4. Eastaway R and Haigh J (2011) The Hidden Mathematics of Sport. PorticoGoogle Scholar
  5. Haigh J (2003) Taking Chances. Winning with Probability. OUPzbMATHGoogle Scholar
  6. Haigh J (2009) Uses and Limitations of Mathematics in Sport. IMA Journal of Management Mathematics 2009 20(2) pages 97–108Google Scholar
  7. Kiesl H (2013) Match me if you can. Mitteilungen der DMV 21 pages 84–8Google Scholar
  8. Morris C (1977) The most important point in tennis. In “Optimal Strategies in Sports” edited by S P Lahany and R E Machol. ElsevierGoogle Scholar
  9. Palacios-Huerta I (2014) Beautiful game theory: how soccer can help economics. Princeton University PressGoogle Scholar
  10. Percy D (2012) The Optimal Dartboard? Mathematics Today 48(6) pages 268–70Google Scholar
  11. Singmaster D (1980) Arranging a dartboard. IMA Bulletin 16(4) pages 93–7Google Scholar
  12. Wallace M and Haigh J (2013) Football and marriage – and the UEFA draw. Significance 10(2) pages 47–8Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of SussexBrightonUK

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