Abstract
This paper addresses the dynamics of four European soccer teams over the season 2018–2019. The modeling perspective adopts the concepts of fractional calculus and power law. The proposed model embeds implicitly details such as the behavior of players and coaches, strategical and tactical maneuvers during the matches, errors of referees and a multitude of other effects. The scale of observation focuses the teams’ behavior at each round. Two approaches are considered, namely the evaluation of the team progress along the league by a variety of heuristic models fitting real-world data, and the analysis of statistical information by means of entropy. The best models are also adopted for predicting the future results and their performance compared with the real outcome. The computational and mathematical modeling lead to results that are analyzed and interpreted in the light of fractional dynamics. The emergence of patterns both with the heuristic modeling and the entropy analysis highlight similarities in different national leagues and point towards some underlying complex dynamics.
Highlights
Soccer is the most popular sport in Europe [1,2]
Each team includes 10 field players, that can maneuver the ball using any part of the body except hands and arms, and one goalkeeper, who is allowed to touch the ball with the whole body, as long as they stay in their penalty area
This paper studies the dynamical performance of soccer teams in a given league
Summary
Soccer is the most popular sport in Europe [1,2]. The game is played by two teams of 11 players, on a rectangular field with a goal placed at each end. Machado and Lopes [15] adopted distinct dissimilarity measures and multidimensional scaling to study the behavior of teams competing within soccer national leagues and related the generated loci with the teams’ performance over time. Lopes and Machado [17] studied the dynamics of national soccer leagues using information and fractional calculus tools In their approach, an entire soccer league season was treated as a complex system with a state observable at the time of rounds, consisting of the goals scored by the teams. The adoption of heuristic models, fitting real-world data, and the entropy analysis of statistical information, give a new perspective to a complex system that has been scarcely studied in the scientific literature Bearing these ideas in mind, this paper is organized as follows.
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