To develop a statistical model of winning times for international swimming events with the aim of predicting winning time distributions and the probability of winning for the 2020 and 2024 Olympic Games. The data set included first and third place times from all individual swimming events from the Olympics and World Championships from 1990 to 2019. We compared different model formulations fitted with Bayesian inference to obtain predictive distributions; comparisons were based on mean percentage error in out-of-sample predictions of Olympics and World Championships winning swim times from 2011 to 2019. The Bayesian time series regression model, comprising auto-regressive and moving average terms and other predictors, had the smallest mean prediction error of 0.57% (CI 0.46-0.74%). For context, using the respective previous Olympics or World Championships winning time resulted in a mean prediction error of 0.70% (CI 0.59-0.82%). The Olympics were on average 0.5% (CI 0.3-0.7%) faster than World Championships over the study period. The model computes the posterior predictive distribution, which allows coaches and athletes to evaluate the probability of winning given an individual's swim time, and the probability of being faster or slower than the previous winning time or even the world record.