Tail Modeling, Track and Field Records, and Bolt's Effect
In recent years predictions of athletic records have acquired a special significance in the scientific community. This article presents a method for calculation of probabilities of future records through modeling the tail of the distribution for performance measures. It utilizes an estimation method based on ideas from classical extreme-value theory that avoids difficulties associated with the maximum likelihood estimation. To improve the predictions, whenever possible, it utilizes information such as the survival time of the latest record and the time interval between the last two records. The article also presents alternative prediction methods based on order statistics and the theory of records, and includes a method for prediction of ultimate records. Application of tail modeling to men's long jump produces reasonable results. For long jump the last two records 8.95 meters and 8.90 meters are significantly greater than the third best record, 8.35 meters, which indicates a medium or long tail model. Data for 100 and 200 meter runs exhibit a similar characteristic as the present records for these events, 9.58 seconds and 19.19 seconds respectively, are significantly lower than the previous records. Application to the men's 100 meter data for the period starting January 1, 1977, when IAAF required fully automatic timing, to September 1, 2009 shows that the probabilities of setting a new record such as 9.55 seconds or less or 9.5 seconds or less are respectively:A. 0.0102 and 0.0052, when Bolt's three records are included.B. 0.0043 and 0.0023, when Bolt's three records are excluded.Also, excluding Bolt's records the probability of setting a record of 9.58 seconds or less by other runners is only 0.0064. Application of the method to Bolt's individual performance prior to the 2008 Olympics reveals the following:A. For him, the probability of running the 200 meter in the 19.30 seconds or less was only 0.00257, indicating that his Olympic record, 19.30 seconds, was completely unexpected.B. The probability of breaking his own best record, 19.75 seconds, was only 0.0738, indicating that his Olympic performance was exceptional.Also, application of the method to his individual performance including his 2008 Olympic record reveals that his new record 19.19 seconds was even more astonishing.Application of the method for estimation of ultimate record produces the following 90% prediction intervals:A. (9.40, 9.58) when Bolt's three records are included,B. (9.62, 9.71) when Bolt's three records are excluded.Note that Bolt's last record 9.58, falls outside the interval B. This demonstrates that Bolt is in a different league.
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Volume (Year): 6 (2010)
Issue (Month): 3 (July)
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