Calibrated prediction of extremes with an application to sports records

Establishing a new world record in athletics can be viewed as an extreme event, occurring in the tails of the distribution of peak performances. It is thus natural to analyze sports records using models and methods from extreme value theory. The choice of the model is more or less natural, but we argue that the most popular approach to using models for prediction can be misleading: one is tempted to just replace the unknown parameter with an estimate (this is called the "estimative" approach), but the asymptotic theory shows that this is only a rough approximation to the true data generating process, especially when estimates are based on small datasets. When small sample issues are suspected, asymptotic corrections come to the rescue, but it can be rather tedious to apply them in practice. Fonseca, Giummole' and Vidoni (2014, 2025) recently provided two automatic corrections to improve the quality of probabilistic predictions based on bootstrap, to improve the reliability of either predicted probabilities or predicted quantiles.An analysis of world and annual records in athletics and aquatics illustrates the differences in the predictions of new world records obtained using either the classical approach or the bootstrap methods. Discrepancies in predictions can indicate small sample issues, which the improved methods aim to address, making them preferable to the potentially unreliable estimative approach. Yet distinct, the distributions for improved probabilities ad improved quantiles yield predictions that somewhat agree with each other in one respect: predictions should be more heavy-tailed than usually told by the estimative approach. As a side effect, while all records look hard to break under the estimative approach, the improved methods tell us of a near future richer in new records. More generally, the analysis of extreme values can hugely benefit from calibration methods, when the validity of predictions is at stake.