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. 2021 Aug 19;23(8):1072.
doi: 10.3390/e23081072.

Mathematical Models to Measure the Variability of Nodes and Networks in Team Sports

Fernando Martins  1   2   3 , Ricardo Gomes  1   3   4 , Vasco Lopes  5 , Frutuoso Silva  2   5 , Rui Mendes  1   3   4
Affiliations

Mathematical Models to Measure the Variability of Nodes and Networks in Team Sports

Fernando Martins et al. Entropy (Basel). .

Abstract

Pattern analysis is a widely researched topic in team sports performance analysis, using information theory as a conceptual framework. Bayesian methods are also used in this research field, but the association between these two is being developed. The aim of this paper is to present new mathematical concepts that are based on information and probability theory and can be applied to network analysis in Team Sports. These results are based on the transition matrices of the Markov chain, associated with the adjacency matrices of a network with n nodes and allowing for a more robust analysis of the variability of interactions in team sports. The proposed models refer to individual and collective rates and indexes of total variability between players and teams as well as the overall passing capacity of a network, all of which are demonstrated in the UEFA 2020/2021 Champions League Final.

Keywords: Markov chain; dynamical systems; entropy; football; performance analysis; social network analysis.

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Conflict of interest statement

The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analysis, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

Figures

Figure 1
Figure 1
Chelsea’s rate of passing and reception.
Figure 2
Figure 2
Mancester City’s Rate of passing and reception.
Figure 3
Figure 3
Chelsea’s index of rate of passing and reception.
Figure 4
Figure 4
Mancester City’s index of rate of passing and reception.
See this image and copyright information in PMC

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