Entropy scaling of high resolution systems—Example from football

Wand, Tobias

Abstract

This comment on the article “Hidden power law patterns in the top European football leagues” written by Da Silva et al. derives a universal logarithmic scaling behaviour of Shannon entropy with respect to the system size that holds for sufficiently smooth distributions. Taking this scaling behaviour into account allows to compare the entropy of ensembles with different sizes, e.g. if they have the same underlying distribution, but are sampled at different resolutions. As an example, these findings help to improve Da Silva's method that uses entropy as a measure of competitiveness to compare European football leagues.