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Probability Formulas and Statistical Analysis in Tennis

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  • O'Malley A. James

    (Harvard Medical School)

Abstract

In this paper an expression for the probability of winning a game in a tennis match is derived under the assumption that the outcome of each point is identically and independently distributed. Important properties of the formula are evaluated and presented pictorially. The accuracy of this formula is tested by comparing observed proportions against predicted values using data from the 2007 Wimbledon Tennis Championships. We also derive expressions for the probability of several other milestones in a tennis match including winning a tiebreaker, winning a set, winning a match, and recovering from a break of serve down to win a set. The resulting "tennis formulas" are used to evaluate the implications of possible rule changes, to demonstrate how broadcasts of tennis matches could be made more interesting and informative, and to potentially improve a player's chance of winning a match.

Suggested Citation

  • O'Malley A. James, 2008. "Probability Formulas and Statistical Analysis in Tennis," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 4(2), pages 1-23, April.
    • Handle: RePEc:bpj:jqsprt:v:4:y:2008:i:2:n:15
    DOI: 10.2202/1559-0410.1100
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    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. On probability of winning a tennis match
      by Daniel Korzekwa in Betting Exchange Research Blog on 2012-02-04 15:29:00

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    Cited by:

    1. Bizzozero, Paolo & Flepp, Raphael & Franck, Egon, 2016. "The importance of suspense and surprise in entertainment demand: Evidence from Wimbledon," Journal of Economic Behavior & Organization, Elsevier, vol. 130(C), pages 47-63.
    2. Kovalchik, Stephanie & Reid, Machar, 2019. "A calibration method with dynamic updates for within-match forecasting of wins in tennis," International Journal of Forecasting, Elsevier, vol. 35(2), pages 756-766.
    3. Noubary Reza D. & Coles Drue, 2011. "Rule of Tangent for Win-By-Two Games," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 7(4), pages 1-18, October.
    4. Newton Paul K & Aslam Kamran, 2009. "Monte Carlo Tennis: A Stochastic Markov Chain Model," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 5(3), pages 1-44, July.
    5. Chan Timothy C.Y. & Singal Raghav, 2018. "A Bayesian regression approach to handicapping tennis players based on a rating system," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 14(3), pages 131-141, September.

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