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Extended Use of Paired Comparison Models, with Application to Chess Rankings

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  • Harry Joe

Abstract

Linear paired comparison models are studied when ties or draws are allowed, where the probability of a win plus half the probability of a draw is modelled as a symmetric cumulative function evaluated at the difference of strength parameters. These models are extended to make use of covariate information and used for ranking 64 top chess players since 1800 with information on career periods. The Davidson model which allows for draws does not fit chess data well because of the large variability in draw percentages from player to player. Some new methodology including an analysis of an appropriate goodness‐of‐fit test is given for this extended use of the linear model.

Suggested Citation

  • Harry Joe, 1990. "Extended Use of Paired Comparison Models, with Application to Chess Rankings," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 39(1), pages 85-93, March.
    • Handle: RePEc:bla:jorssc:v:39:y:1990:i:1:p:85-93
    DOI: 10.2307/2347814
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    Cited by:

    1. Hankin, Robin K.S., 2020. "A generalization of the Bradley–Terry model for draws in chess with an application to collusion," Journal of Economic Behavior & Organization, Elsevier, vol. 180(C), pages 325-333.
    2. 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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