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A stochastic rank ordered logit model for rating multi-competitor games and sports

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  • Glickman Mark E.

    (Center for Healthcare Organization and Implementation Research, Edith Nourse Rogers Memorial Hospital (152), Bldg 70, 200 Springs Road, Bedford, MA 01730, USA Department of Health Policy and Management, Boston University School of Public Health, 715 Albany Street, Boston, MA 02118, USA)

  • Hennessy Jonathan

    (The Houston Rockets, 1510 Polk Street, Houston, TX 77002, USA)

Abstract

Many games and sports, including races, involve outcomes in which competitors are rank ordered. In some sports, competitors may play in multiple events over long periods of time, and it is natural to assume that their abilities change over time. We propose a Bayesian state-space framework for rank ordered logit models to rate competitor abilities over time from the results of multi-competitor games. Our approach assumes competitors’ performances follow independent extreme value distributions, with each competitor’s ability evolving over time as a Gaussian random walk. The model accounts for the possibility of ties, an occurrence that is not atypical in races in which some of the competitors may not finish and therefore tie for last place. Inference can be performed through Markov chain Monte Carlo (MCMC) simulation from the posterior distribution. We also develop a filtering algorithm that is an approximation to the full Bayesian computations. The approximate Bayesian filter can be used for updating competitor abilities on an ongoing basis. We demonstrate our approach to measuring abilities of 268 women from the results of women’s Alpine downhill skiing competitions recorded over the period 2002–2013.

Suggested Citation

  • Glickman Mark E. & Hennessy Jonathan, 2015. "A stochastic rank ordered logit model for rating multi-competitor games and sports," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 11(3), pages 131-144, September.
    • Handle: RePEc:bpj:jqsprt:v:11:y:2015:i:3:p:131-144:n:5
    DOI: 10.1515/jqas-2015-0012
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    References listed on IDEAS

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    1. Rose D. Baker & Ian G. McHale, 2015. "Deterministic Evolution of Strength in Multiple Comparisons Models: Who is the Greatest Golfer?," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 180-196, March.
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    Cited by:

    1. Santos-Fernandez Edgar & Wu Paul & Mengersen Kerrie L., 2019. "Bayesian statistics meets sports: a comprehensive review," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 15(4), pages 289-312, December.

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