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MSE-optimal K-factor of the Elo rating system for round-robin tournament

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  • Chan Victor

    (Department of Mathematics, Western Washington University, Bellingham, 98225, WA, USA)

Abstract

The Elo rating system contains a coefficient called the K-factor which governs the amount of change to the updated ratings and is often determined by empirical or heuristic means. Theoretical studies on the K-factor have been sparse and not much is known about the pertinent factors that impact its appropriate values in applications. This paper has two main goals: to present a new formulation of the K-factor that is optimal with respect to the mean-squared-error (MSE) criterion in a round-robin tournament setting and to investigate the effects of the relevant variables, including the number of tournament participants n, on the optimal K-factor (based on the model-averaged MSE). It is found that n and the variability of the deviation between the true rating and the pre-tournament rating have a strong influence on the optimal K-factor. Comparisons between the MSE-optimal K-factor and the K-factors from Elo and from the US Chess Federation as a function of n are also provided. Although the results are applicable to other sports in similar settings, the study focuses on chess and makes use of the rating data and the K-factor values from the chess world.

Suggested Citation

  • Chan Victor, 2022. "MSE-optimal K-factor of the Elo rating system for round-robin tournament," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 18(1), pages 59-72, March.
    • Handle: RePEc:bpj:jqsprt:v:18:y:2022:i:1:p:59-72:n:3
    DOI: 10.1515/jqas-2021-0079
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