We explore models for performance in athletic (running) events at a range of different distances and suggest a parametric form which can be useful for characterizing the change in performance with distance. This model is fitted to 1996 world records for various distances. Performance is expressed as the average speed for each distance, which is a more natural variable than time, when considering different distances, with widely varying times. We apply the model to compare performances by the same athlete at different distances, and so to determine an athlete's strengths, or to assess the effect of training. This requires that we also examine times near the world records to characterize this change in performance. Another application of our model is to describe jointly the decrease in several world records over several years and so to predict lower bounds on these records. We demonstrate this using some simple parametric forms with asymptotes.
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