Comparing and Forecasting Performances in Different Events of Athletics Using a Probabilistic Model

Though athletics statistics are abundant, it is a difficult task to quantitatively compare performances from different events of track, field, and road running in a meaningful way. There are several commonly-used methods, but each has its limitations. Some methods, for example, are valid only for running events, or are unable to compare men's performances to women's, while others are based largely on world records and are thus unsuitable for comparing world records to one other. The most versatile and widely-used statistic is a set of scoring tables compiled by the IAAF, which are updated and published every few years. Unfortunately, these methods are not fully disclosed. In this paper, we propose a straight-forward, objective, model-based algorithm for assigning scores to athletic performances for the express purpose of comparing marks between different events. Specifically, the main score we propose is based on the expected number of athletes who perform better than a given mark within a calendar year. Computing this naturally interpretable statistic requires only a list of the top performances in each event and is not overly dependent on a small number of marks, such as the world records. We found that this statistic could predict the quality of future performances better than the IAAF scoring tables, and is thus better suited for comparing performances from different events. In addition, the probabilistic model used to generate the performance scores allows for multiple interpretations which can be adapted for various purposes, such as calculating the expected top mark in a given event or calculating the probability of a world record being broken within a certain time period. In this paper, we give the details of the model and the scores, a comparison with the IAAF scoring tables, and a demonstration of how we can calculate expectations of what might happen in the coming Olympic year. Our conclusion is that a probabilistic model such as the one presented here is a more informative and more versatile choice than the standard methods for comparing athletic performances.