Entropy Analysis of Soccer Dynamics

Entropy Analysis of Soccer Dynamics

António M. Lopes and J. A. Tenreiro Machado

Abstract

This paper adopts the information and fractional calculus tools for studying the dynamics of a national soccer league. A soccer league season is treated as a complex system (CS) with a state observable at discrete time instants, that is, at the time of rounds. The CS state, consisting of the goals scored by the teams, is processed by means of different tools, namely entropy, mutual information and Jensen–Shannon divergence. The CS behavior is visualized in 3-D maps generated by multidimensional scaling. The points on the maps represent rounds and their relative positioning allows for a direct interpretation of the results.

Keywords: entropy; mutual information; Jensen–Shannon divergence; fractional calculus; multidimensional scaling; complex systems

Full Paper can be downloaded at: https://www.mdpi.com/1099-4300/21/2/187

This article belongs to the Special Issue The Fractional View of Complexity

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