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

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.