Modelling between- and within-season trajectories in elite athletic performance data

TL;DR

This paper introduces a Bayesian hierarchical model that captures both between- and within-season performance trajectories in elite athletes, accounting for confounding factors and providing detailed individual and population-level insights.

Contribution

It develops a continuous-time Bayesian hierarchical model with a novel decomposition of performance trajectories, enabling detailed analysis of seasonal and career performance patterns.

Findings

Model effectively separates seasonal and career effects.

Application to swimming data reveals distinct performance patterns.

Provides individual and population-level performance trajectories.

Abstract

Athletic performance follows a typical pattern of improvement and decline during a career. This pattern is also often observed within-seasons, as an athlete aims for their performance to peak at key events such as the Olympic Games or World Championships. A Bayesian hierarchical model is developed to analyse the evolution of athletic sporting performance throughout an athlete's career and separate these effects whilst allowing for confounding factors such as environmental conditions. Our model works in continuous time and estimates both $g(t)$, the average performance level of the population at age $t$, and $f_i(t)$, the difference of the $i$-th athlete from this average. We further decompose $f_i(t)$ into a season-to-season trajectory and a within-season trajectory, which is modelled by a restricted Bernstein polynomial. The model is fitted using an adaptive Metropolis-within-Gibbs algorithm with a carefully chosen blocking scheme. The model allows us to understand seasonal patterns in athlete performance, how these differ between athletes, and provides individual fitted and trend performance trajectories. The properties of the model are illustrated using a simulation study and an application to 100 metres and 200 metres freestyle swimming for both female and male athletes.