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

TL;DR

This paper introduces a probabilistic, model-based scoring system for comparing athletic performances across different events, outperforming traditional methods like the IAAF tables in predicting future performance quality.

Contribution

It proposes a new, objective algorithm for scoring athletic performances based on expected better performances, which is more versatile and predictive than existing scoring methods.

Findings

The proposed score predicts future performance quality better than IAAF tables.

The model allows for multiple interpretations, such as predicting top marks and record-breaking probabilities.

The scoring method is less dependent on small data sets like world records.

Abstract

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...