  The use of statistical methods in sport analytics has gained a rapidly
growing interest over the last decade, and nowadays is common practice. In
particular, the interest in understanding and predicting an athlete's
performance throughout his/her career is motivated by the need to evaluate the
efficacy of training programs, anticipate fatigue to prevent injuries and
detect unexpected of disproportionate increases in performance that might be
indicative of doping. Moreover, fast evolving data gathering technologies
require up to date modelling techniques that adapt to the distinctive features
of sports data. In this work, we propose a hierarchical Bayesian model for
describing and predicting the evolution of performance over time for shot put
athletes. To account for seasonality and heterogeneity in recorded results, we
rely both on a smooth functional contribution and on a linear mixed effect
model with heteroskedastic errors to represent the athlete-specific
trajectories. The resulting model provides an accurate description of the
performance trajectories and helps specifying both the intra- and
inter-seasonal variability of measurements. Further, the model allows for the
prediction of athletes' performance in future seasons. We apply our model to an
extensive real world data set on performance data of professional shot put
athletes recorded at elite competitions.
