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Journal of Quantitative Analysis in Sports

An official journal of the American Statistical Association

Editor-in-Chief: Mark Glickman PhD

SCImago Journal Rank (SJR) 2015: 0.288
Source Normalized Impact per Paper (SNIP) 2015: 0.358
Impact per Publication (IPP) 2015: 0.250

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

Tristan Barnett1 / John Zeleznikow2 / Clare MacMahon3

1Victoria University

2Victoria University

3Victoria University

Citation Information: Journal of Quantitative Analysis in Sports. Volume 6, Issue 2, ISSN (Online) 1559-0410, DOI: https://doi.org/10.2202/1559-0410.1228, April 2010

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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.

Keywords: game theory; tennis; optimization; scoring systems; risk taking

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