The power law model applied to the marathon world record

Abstract

In September 2013 the world record in the marathon men's race was broken. The aim of this study is to apply to the 2013 Berlin Marathon a mathematical model based on the power law that analyses the marks distribution and checks its connection. The results show that the correlations obtained in all the different categories have been very significant, with a result of (r ≥ 0.978; p < 0.000) and a linear determination coefficient of (R 2 ≥ 0.969). As a conclusion it could be said that the power law application to the 2013 Berlin Marathon Men's race has been an useful and feasible study, and the connection between the data and the mathematical model has been so accurate.

Scaling Invariance of Sports Sex Gap

“…To maintain consistency with the chronological records, such as running, swimming and hurdles, the records of high jump, long jump, and triple jump were rendered by the reciprocal transformation. In this study, it is used the power law equation ( Harte, 1999 ; Sylvan Katz and Katz, 1999 ; Hu et al, 2004 ; Fernández-Revelles and García Mármol, 2019 ), namely y = ax l , to describe sex differences in sports. We define variables x and y to represent the male and female sports records of an event, respectively.…”

“…Scale invariance describes phenomena that are not associated with a particular or characteristic scale of length, energy, or other variables, and is mathematically equivalent to power law behavior. Many studies have used power law to analyze the law of sport ( Katz and Katz, 1994 ; Sylvan Katz and Katz, 1999 ; Vincenzo and Sandra, 2001 ; Yamamoto, 2009 ; Fernández-Revelles and García Mármol, 2019 ). Among them, Katz’s research shown that the performance of male and female superior athletes exhibits a fractal relationship between world record running and swimming times and the distance of the even, and an exceptionally good linear fit ( R 2 ≥ 0.999) was observed in the log-log plot ( Katz and Katz, 1994 ).…”