The limitations of scaling laws in the prediction of performance in endurance events

In the twentieth century, scientists have examined running speed over various distances, analyzing world records and studying the ability of an athlete to sustain a given speed. Assuming that running speed expresses the response of a non-linear multisystemic behavior, the relationship between these two variables (distance vs. velocity) can therefore be evaluated by applying scaling laws that fulfill the key principles of specificity and individuality of each athlete, yet responding to bioenergetic and functional patterns that are well-known to sports physiology. Since speed loss as distance increases exhibits fractal behavior, with small changes in the speed-reduction curve due to the effect of fatigue, it must be recognized that no universal scaling law can account, with acceptable precision, for the effect exerted by fatigue on potential speed at any given moment in a race. Power laws using a range of scaling exponents provide technical staff and athletes with a reliable, non-invasive tool for planning of training schedules, predicting athletes' performances over various distances and comparing the performance of specialists in different track events. The equations for the scaling laws for the distances investigated here were: V1500=15.00×D−0.10 (R2=0.99); V3000=12.76×D−0.08 (R2=0.99); V5000=11.55×D−0.07 (R2=0.99); V10,000=11.59×D−0.07 (R2=0.99); V21,095=10.78×D−0.06 (R2=0.97); V42,175=10.27×D−0.057 (R2=0.99).

► The relationship between distance and speed can be studied with scaling laws offering specificity and individuality.
► This discards a universal scaling that may explain the effect of fatigue on potential speed at each race distance.
► Power laws are highly reliable, non-invasive tools for designing training regimes and predicting athletes' performance.