Distribution of performances and scoring in athletics

Abstract

We address the question of scoring the athletic performance and claim that scoring should be linked to the distribution of performances among a selected population. We start by reviewing four different scoring methods (Letessier, Harder, Purdy and World Athletics) that have been proposed in the past. We proceed next to formulate the mathematical link between scoring and performance distributions. Based on the explicit expressions for the Purdy and World Athletics scoring tables we derive the corresponding performance distributions, finding that they involve the well-known Gompertz and Weibull distributions. Starting from a distribution assumption, we propose a new version of the Purdy scoring method, which could be the basis for new scoring tables for combined events, as well as for popular endurance events. Finally, we present a bold claim that the distribution of performances of a very large human population can be represented by a skew-logistic distribution.