Predicting new sports records: Bootstrap enhancements in extreme value analysis

A new world record in athletics represents an extreme event, occurring in the tails of the distribution of peak performances. Therefore, extreme value theory provides a natural framework for modeling the distribution of sports records. The commonly used plug-in approach for predicting future records, which replaces unknown parameters with sample estimates in the model, can be unreliable, particularly when sample sizes are small. To address this limitation, two bootstrap-based corrections proposed in the literature are employed: One improves predicted quantiles, while the other, more recent, enhances predicted probabilities, providing more reliable predictions in small-sample contexts. The proposal builds on these two corrections by incorporating the possibility of serial correlation between consecutive annual records in an autoregressive fashion. Applications to records in athletics reveal substantial differences between predictions obtained using the classical plug-in approach and those obtained by the bootstrap methods. These discrepancies highlight the impact of small samples. As a result, the classical method suggests that records are very hard to break, while the bootstrap-based corrections suggest a near future richer in new records.