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Monte Carlo Tennis: A Stochastic Markov Chain Model


  • Newton Paul K

    (University of Southern California)

  • Aslam Kamran

    (University of Southern California)


We develop a stochastic Markov chain model to obtain the probability density function (pdf) for a player to win a match in tennis. By analyzing both individual player and 'field' data (all players lumped together) obtained from the 2007 Men's Association of Tennis Professionals (ATP) circuit, we show that a player's probability of winning a point on serve and while receiving serve varies from match to match and can be modeled as Gaussian distributed random variables. Hence, our model uses four input parameters for each player. The first two are the sample means associated with each player's probability of winning a point on serve and while receiving serve. The third and fourth parameter for each player are the standard deviations around the mean, which measure a player's consistency from match to match and from one surface to another (e.g. grass, hard courts, clay). Based on these Gaussian distributed input variables, we use Monte Carlo simulations to determine the probability density functions for each of the players to win a match. By using input data for each of the players vs. the entire field, we describe the outcome of simulations based on head-to-head matches focusing on four top players currently on the men's ATP circuit. We also run full tournament simulations of the four Grand Slam events and gather statistics for each of these four player's frequency of winning each of the events and we describe how to use the results as the basis for ranking methods with natural probabilistic interpretations.

Suggested Citation

  • 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.
  • Handle: RePEc:bpj:jqsprt:v:5:y:2009:i:3:n:7

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    References listed on IDEAS

    1. Mark Glickman, 2001. "Dynamic paired comparison models with stochastic variances," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(6), pages 673-689.
    2. Mark Walker & John Wooders, 2001. "Minimax Play at Wimbledon," American Economic Review, American Economic Association, vol. 91(5), pages 1521-1538, December.
    3. Mark E. Glickman, 1999. "Parameter Estimation in Large Dynamic Paired Comparison Experiments," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(3), pages 377-394.
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    Blog mentions

    As found by, 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. Pettigrew Stephen, 2014. "How the West will be won: using Monte Carlo simulations to estimate the effects of NHL realignment," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 10(3), pages 1-11, September.
    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. Goldner Keith, 2012. "A Markov Model of Football: Using Stochastic Processes to Model a Football Drive," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 8(1), pages 1-18, March.
    5. Pasteur R. Drew & Janning Michael C., 2011. "Monte Carlo Simulation for High School Football Playoff Seed Projection," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 7(2), pages 1-10, May.
    6. Heiny Erik L. & Heiny Robert Lowell, 2014. "Stochastic model of the 2012 PGA Tour season," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 10(4), pages 1-13, December.

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