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Monte Carlo Tennis: A Stochastic Markov Chain Model

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Author Info

  • Newton Paul K

    (University of Southern California)

  • Aslam Kamran

    (University of Southern California)

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    Abstract

    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.

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    Bibliographic Info

    Article provided by De Gruyter in its journal Journal of Quantitative Analysis in Sports.

    Volume (Year): 5 (2009)
    Issue (Month): 3 (July)
    Pages: 1-44

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

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    Web page: http://www.degruyter.com

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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 09:29:00

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