Affiliation:
1. Department of Mathematics , Western Washington University , Bellingham 98225 , WA , USA
Abstract
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.
Subject
Decision Sciences (miscellaneous),Social Sciences (miscellaneous)
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