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Using Game Theory to Optimize Performance in a Best-of-N Set Match


  • Barnett Tristan

    (Victoria University)

  • Zeleznikow John

    (Victoria University)

  • MacMahon Clare

    (Victoria University)


This paper analyzes the situation in a best-of-N set match, where both players/teams are given the opportunity to increase their probability of winning a set (increase in effort) on one particular set. To gain insight to the problem, a best-of-3 set match (as typically used in tennis) is analyzed. Using game theory to obtain an optimal solution, the results indicate that both players should use a mixed strategy, by applying their increase in effort at each set with a probability of one third. A conjecture is devised to obtain an optimal solution for a best-of-N set match. Some applications are given to the theoretical results, which could be used by coaches and players to optimize performance.

Suggested Citation

  • Barnett Tristan & Zeleznikow John & MacMahon Clare, 2010. "Using Game Theory to Optimize Performance in a Best-of-N Set Match," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 6(2), pages 1-10, April.
  • Handle: RePEc:bpj:jqsprt:v:6:y:2010:i:2:n:2

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    References listed on IDEAS

    1. Tunaru, Radu & Clark, Ephraim & Viney, Howard, 2005. "An option pricing framework for valuation of football players," Review of Financial Economics, Elsevier, vol. 14(3-4), pages 281-295.
    2. Ian McHale & Phil Scarf, 2007. "Modelling soccer matches using bivariate discrete distributions with general dependence structure," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 61(4), pages 432-445.
    3. Oberstone Joel, 2009. "Differentiating the Top English Premier League Football Clubs from the Rest of the Pack: Identifying the Keys to Success," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 5(3), pages 1-29, July.
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