A Monte Carlo comparison of alternative methods of maximum likelihood ranking in racing sports

Aaron Anderson

Journal of Applied Statistics, 2015, vol. 42, issue 8, 1740-1756

Abstract: Applications of maximum likelihood techniques to rank competitors in sports are commonly based on the assumption that each competitor's performance is a function of a deterministic component that represents inherent ability and a stochastic component that the competitor has limited control over. Perhaps based on an appeal to the central limit theorem, the stochastic component of performance has often been assumed to be a normal random variable. However, in the context of a racing sport, this assumption is problematic because the resulting model is the computationally difficult rank-ordered probit. Although a rank-ordered logit is a viable alternative, a Thurstonian paired-comparison model could also be applied. The purpose of this analysis was to compare the performance of the rank-ordered logit and Thurstonian paired-comparison models given the objective of ranking competitors based on ability. Monte Carlo simulations were used to generate race results based on a known ranking of competitors, assign rankings from the results of the two models, and judge performance based on Spearman's rank correlation coefficient. Results suggest that in many applications, a Thurstonian model can outperform a rank-ordered logit if each competitor's performance is normally distributed.

Date: 2015
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DOI: 10.1080/02664763.2015.1005065

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