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An iterative Markov rating method

Author

Listed:
  • Devlin Stephen

    (Mathematics, University of San Francisco, San Francisco, CA, USA)

  • Treloar Thomas

    (Mathematics, Hillsdale College, Hillsdale, MI, USA)

  • Creagar Molly

    (University of San Francisco, San Francisco, CA, USA)

  • Cassels Samuel

    (Hillsdale College, Hillsdale, MI, USA)

Abstract

We introduce a simple and natural iterative version of the well-known and widely studied Markov rating method. We show that this iterative Markov method converges to the usual global Markov rating, and shares a close relationship with the well-known Elo rating. Together with recent results on the relationship between the global Markov method and the maximum likelihood estimate of the rating vector in the Bradley–Terry (BT) model, we connect and explore the global and iterative Markov, Elo, and Bradley–Terry ratings on real and simulated data.

Suggested Citation

  • Devlin Stephen & Treloar Thomas & Creagar Molly & Cassels Samuel, 2021. "An iterative Markov rating method," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 17(2), pages 117-127, June.
    • Handle: RePEc:bpj:jqsprt:v:17:y:2021:i:2:p:117-127:n:4
    DOI: 10.1515/jqas-2019-0070
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    References listed on IDEAS

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    1. Julio González-Díaz & Ruud Hendrickx & Edwin Lohmann, 2014. "Paired comparisons analysis: an axiomatic approach to ranking methods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(1), pages 139-169, January.
    2. 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.
    3. Stefani Ray, 2011. "The Methodology of Officially Recognized International Sports Rating Systems," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 7(4), pages 1-22, October.
    4. Mark Glickman, 2001. "Dynamic paired comparison models with stochastic variances," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(6), pages 673-689.
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    Keywords

    Elo; Markov; ranking; rating;
    All these keywords.

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