Modelling of Running Performances: Comparisons of Power-Law, Hyperbolic, Logarithmic, and Exponential Models in Elite Endurance Runners

Abstract EN

Many empirical and descriptive models have been proposed since the beginning of the 20th century.

In the present study, the power-law (Kennelly) and logarithmic (Péronnet-Thibault) models were compared with asymptotic models such as 2-parameter hyperbolic models (Hill and Scherrer), 3-parameter hyperbolic model (Morton), and exponential model (Hopkins).

These empirical models were compared from the performance of 6 elite endurance runners (P.

Nurmi, E.

Zatopek, J.

Väätäinen, L.

Virén, S.

Aouita, and H.

Gebrselassie) who were world-record holders and/or Olympic winners and/or world or European champions.

These elite runners were chosen because they participated several times in international competitions over a large range of distances (1500, 3000, 5000, and 10000 m) and three also participated in a marathon.

The parameters of these models were compared and correlated.

The less accurate models were the asymptotic 2-parameter hyperbolic models but the most accurate model was the asymptotic 3-parameter hyperbolic model proposed by Morton.

The predictions of long-distance performances (maximal running speeds for 30 and 60 min and marathon) by extrapolation of the logarithmic and power-law models were more accurate than the predictions by extrapolation in all the asymptotic models.

The overestimations of these long-distance performances by Morton’s model were less important than the overestimations by the other asymptotic models.