Multifractal Analysis of Marathon Pacing—Physiological Background and Practical Implications

Marathons are one of the ultimate challenges of human endeavor. As a consequence of the growing passion of amateur runners for this discipline, a strong need has been shown for counselling during the preparation and for advice on how to manage their efforts during the race. This monitoring should be based on parameters collected during the race and correctly interpreted. Multifractality parameters, which have proved their relevance in many other areas of signal processing, are natural candidates for this purpose. This paper shows that, due to the extreme irregularity of the data, the previously used multifractal techniques cannot be applied in this context, in contrast with the recently introduced parameters based on the weak scaling exponent, which require no a priori assumptions for their use; these parameters yield new classification parameters in the processing of physiological data captured on marathon runners. The comparison of their values reveals how marathon runners handle variations in the irregularity of their races and therefore gives a new insight on the way that runners of different levels conduct their run; therefore, this study shows that the use of these parameters offers a promising tool in order to give advice on how to improve performances.