Scaling laws and forecasting in athletic world records

Abstract

In this study, we analysed running world records and found that the mean speed of the race, μ, as a function of the record time, τ, can be described asymptotically by two well-defined scaling laws of the form u ˜s τ - β. There is a break in the scaling laws (˜1000m) between the shorter and the longer races at a characteristic time of around 150-170 s, after which a new scaling regime emerges. This is the first occasion that this characteristic time has been clearly found in physical terms; we interpreted it as the transition time between the anaerobic and the aerobic energy expenditure of athletes. This phenomenon is independent of the athletes' sex and is also found in swimming races with similar values of the characteristic time. We also investigated the forecasting of world records using historical data. Using an approach based on the identification of non-Poissonian events for a sequence of temporal point processes, we found that the sequence of improvements in all athletic records from 1900 to the present day cannot be considered as a sequence of completely random events.

Keywords:

• Athletic World Records
• Forecasting
• Scaling Laws