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Abstract:
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The International Swimming Federation’s simple points system aims to rank swimmers across all swimming events. The points acquired is a function of the recorded time and the current world record for that event, which introduces bias between events due to the differing “quality” of world records. A model based on extreme value theory is introduced, where swim-times are modeled through their rate of occurrence, and with the distribution of the best times following a generalized Pareto distribution. The swimmers’ times are considered as longitudinal data, capturing each swimmer’s natural progression and the dependence between swims. The model parameters vary smoothly across all events, allowing for unbiased comparison between events, including para-swimming. From the model it is possible to estimate other features of interest, such as the ultimate possible time, the distribution of new world records, and to correct swim times for the effect of full body suits. The model provides a novel single unified description of swim quality over all events and time, and more generally, a novel approach for dealing with longitudinal analysis of extremes, applicable in a wide range of applications.
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