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Entropy Analysis of Soccer Dynamics
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 s...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2019
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514670/ https://www.ncbi.nlm.nih.gov/pubmed/33266902 http://dx.doi.org/10.3390/e21020187 |
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author | Lopes, António M. Tenreiro Machado, J. A. |
author_facet | Lopes, António M. Tenreiro Machado, J. A. |
author_sort | Lopes, António M. |
collection | PubMed |
description | 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. |
format | Online Article Text |
id | pubmed-7514670 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2019 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-75146702020-11-09 Entropy Analysis of Soccer Dynamics Lopes, António M. Tenreiro Machado, J. A. Entropy (Basel) Article 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. MDPI 2019-02-16 /pmc/articles/PMC7514670/ /pubmed/33266902 http://dx.doi.org/10.3390/e21020187 Text en © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Lopes, António M. Tenreiro Machado, J. A. Entropy Analysis of Soccer Dynamics |
title | Entropy Analysis of Soccer Dynamics |
title_full | Entropy Analysis of Soccer Dynamics |
title_fullStr | Entropy Analysis of Soccer Dynamics |
title_full_unstemmed | Entropy Analysis of Soccer Dynamics |
title_short | Entropy Analysis of Soccer Dynamics |
title_sort | entropy analysis of soccer dynamics |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514670/ https://www.ncbi.nlm.nih.gov/pubmed/33266902 http://dx.doi.org/10.3390/e21020187 |
work_keys_str_mv | AT lopesantoniom entropyanalysisofsoccerdynamics AT tenreiromachadoja entropyanalysisofsoccerdynamics |