Entropy Analysis of Soccer Dynamics
1
UISPA–LAETA/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
2
Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, 4249-015 Porto, Portugal
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Entropy 2019, 21(2), 187; https://doi.org/10.3390/e21020187
Received: 27 January 2019 / Revised: 8 February 2019 / Accepted: 13 February 2019 / Published: 16 February 2019
(This article belongs to the Special Issue The Fractional View of Complexity)
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.
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Keywords:
entropy; mutual information; Jensen–Shannon divergence; fractional calculus; multidimensional scaling; complex systems
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MDPI and ACS Style
Lopes, A.M.; Tenreiro Machado, J.A. Entropy Analysis of Soccer Dynamics. Entropy 2019, 21, 187. https://doi.org/10.3390/e21020187
AMA Style
Lopes AM, Tenreiro Machado JA. Entropy Analysis of Soccer Dynamics. Entropy. 2019; 21(2):187. https://doi.org/10.3390/e21020187
Chicago/Turabian StyleLopes, António M.; Tenreiro Machado, J. A. 2019. "Entropy Analysis of Soccer Dynamics" Entropy 21, no. 2: 187. https://doi.org/10.3390/e21020187
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