Power laws and athletic performance.

In a previous study, we showed that the 1992 men's world record running times in the 100 m to 200 km could be represented accurately by the equation T = cDn, where T is the calculated record time for distance D, and c and n are positive constants. Here, we extend that to cover the years 1925-65 at 10-year intervals and 1970-95 in 5-year intervals for distances of 100 m to 10 km. Values of n for all years lie along a straight line with a small negative slope. A regression analysis yields an equation for values of n covering the period 1925-95. Values of c from 1925 to 1995 were fitted by a quadratic equation. These two equations define a surface in three-dimensional space (log(T), log(D), data) for all men's world record runs over the 70-year period for distances of 100 m to 10 km. We also demonstrated previously that event times, t, do not scatter randomly with respect to the values of T but form a consistent pattern about the straight lines in log(T) versus log(D) plots. In this study, we show that the pattern of (t-T)/t as a function of date has remained constant for the past 70 years.

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