Lower Bounds for Athletic Performance

Abstract

This paper analyses a set of world records in athletic running events to extract long-term bounds for those events. The approach adopted is to identify a single parameter to represent the achieved standard of athletic performance at a series of fixed intervals. The long-term behaviour of this single parameter is then investigated by fitting a variety of nonlinear models and restrictions on the accuracy of the fits are discussed. The paper concludes with a range of estimates for each of the events considered in the original data set.

Power laws and athletic performance

“…T hus a graph of c versus the date show s how the 1-km regression value for T changed over the years. Blest (1996) perform ed a sim ilar analysis using m etres instead of kilom etres, resulting in the loss of som e useful inform ation, which we discuss later. Record run times for this analysis were taken from the Prog ressive World Record Lists 1913± 1970(IAAF, 1972.…”

“…T he regression lines through the data are displayed in Figs 2a and 2b. We analysed the world running records reported in Blest (1996) to determ ine if his data also exhibited the sam e general shape in the distribution of c i values. We also tried to select data from Blest for years that we did not analyse.…”

“…Since then, others (Lietzke, 1954;Henry, 1955;Riegel, 1981;Blest, 1996) have used this equation because of its excellent W t to the data. T he large range of event times and distances involved in these analyses (over two orders of m agnitude) and the general m onotonic character of the data have resulted in the power law equation W tting the data with R 2 values (coeY cients of determ ination) ver y close to 1.…”

Performance et vieillissement sportif

“…Après plus de 100 ans de compétition, de nombreux records ont été battus dans de nombreuses disciplines et permettent aujourd'hui d'avoir une idée très précise des capacités humaines sous différentes contraintes. Différentes analyses portant sur le développement historique des performances sportives mettent en évidence deux faits majeurs : la performance physique est limitée (Berthelot et al, 2008Blest, 1996 ;El Helou, 2011 ;El Helou et al, 2010 ;Nevill et Whyte, 2005) et dépendante d'un nombre considérable de paramètres. Les hypothèses avancées pour expliquer l'apparente limitation des performances sportives incluent une meilleure implication et structuration des organismes de lutte contre le dopage, un épuisement du vivier mondial (c'est-à-dire un ralentissement dans le développement des processus de détection et de sélection des morphotypes les plus adaptés à une contrainte spécifique : grands -mais pas trop -athlètes africains sur le marathon, etc.…”

Correspondence

“…In 'Focus on sport', Blest (1996) examined the problem of determining lower bounds for athletic performances, a topical question and of interest not only to statisticians. There are three points that I believe are worthy of brief comment.…”