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

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 fi(t), the difference of the ith athlete from this average. We further decompose fi(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 and 200 m freestyle swimming for both female and male athletes.