Bayesian additive regression trees (BART) for prediction and correction of winning times in kayak and canoe racing

Abstract This paper introduces a Bayesian Additive Regression Trees (BART) approach to correct sprint kayak and canoe race times for environmental conditions and predict future winning times using historical data. The model delivers refined estimates, enabling accurate forecasts and real-time adjustments under changing conditions. Trained on data from elite international and Olympic competitions over the past decade, BART achieved an out-of-sample mean relative error (MRE) of 3.8 % and an in-sample MRE of 1.4 % for 1,000 m, 500 m, and 200 m events at the 2022 Halifax Championships. Consistent with prior research, wind strength, air temperature, and water temperature were the most influential variables, while salinity, which is not generally used in the analysis, proved important, with event venues classified as freshwater or saltwater. A major strength of BART is its Bayesian framework, which yields predictive distributions that allow sport scientists to estimate probabilities such as achieving a target time. Model validation included meta-analysis of variable importance across 13 distance and boat-class sub-models, Gelman-Rubin MCMC convergence checks, and cross-validation for hyper-parameter tuning. Temporal hold-out validations for Halifax 2022 and the London 2012, Rio 2016, and Tokyo 2021 Olympics confirmed BART’s superior performance, with out-of-sample MRE less than half that of Bayesian linear models.