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- Node and network entropy : a novel mathematical model for pattern analysis of team sports behaviorPublication . M. L. Martins, Fernando; Gomes, Ricardo; Lopes, Vasco; G. M. Silva, Frutuoso; Mendes, RuiPattern analysis is a well-established topic in team sports performance analysis, and is usually centered on the analysis of passing sequences. Taking a Bayesian approach to the study of these interactions, this work presents novel entropy mathematical models for Markov chain-based pattern analysis in team sports networks, with Relative Transition Entropy and Network Transition Entropy applied to both passing and reception patterns. To demonstrate their applicability, these mathematical models were used in a case study in football—the 2016/2017 Champions League Final, where both teams were analyzed. The results show that the winning team, Real Madrid, presented greater values for both individual and team transition entropies, which indicate that greater levels of unpredictability may bring teams closer to victory. In conclusion, these metrics may provide information to game analysts, allowing them to provide coaches with accurate and timely information about the key players of the game.
- Social network analysis : mathematical models for understanding professional football in game critical moments : an exploratory studyPublication . A, Diana; Pedrosa, Isabel; Mendes, Rui; M. L. Martins, Fernando; Francisco, João; Gomes, Ricardo; Dias, GonçaloConsidering the Social Network Analysis approach and based on the creation of mathematical models, the aim of this study is to analyze the players’ interactions of professional football teams in critical moments of the game. The sample consists in the analysis of a 2019/2020 season UEFA Champions League match. The mathematical models adopted in the analysis of the players (micro analysis) and the game (macro analysis) were obtained through the uPATO software. The results of the networks indicated a performance pattern trend more robust in terms of the mathematical model: Network Density. As far as it concerned, we found that the Centroid Players had a decisive role in the level of connectivity and interaction of the team. Regarding the main critical moments of the game, the results showed that these were preceded by periods of great instability, obtaining a differentiated performance in the following mathematical models: Centrality, Degree Centrality, Closeness Centrality, and Degree Prestige. We concluded that the networks approach, in concomitance with the dynamic properties of mathematical models, and the critical moments of the game, can help coaches to better evaluate the level of interaction and connectivity of their players toward the actions imposed by opponents.
- Mathematical models to measure the variability of nodes and networks in team sportsPublication . M. L. Martins, Fernando; Gomes, Ricardo; Lopes, Vasco; Silva, Frutuoso G. M.; Mendes, RuiPattern 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.