Spatial and Temporal Entropies in the Spanish Football League: A Network Science Perspective

Abstract

We quantified the spatial and temporal entropy related to football teams and their players by means of a pass-based interaction. First, we calculated the spatial entropy associated to the positions of all passes made by a football team during a match, obtaining a spatial entropy ranking of Spanish teams during the 2017/2018 season. Second, we investigated how the player’s average location in the field is related to the amount of entropy of his passes. Next, we constructed the temporal passing networks of each team and computed the deviation of their network parameters along the match. For each network parameter, we obtained the permutation entropy and the statistical complexity of its temporal fluctuations. Finally, we investigated how the permutation entropy (and statistical complexity) of the network parameters was related to the total number of passes made by a football team. Our results show that (i) spatial entropy changes according to the position of players in the field, and (ii) the organization of passing networks change during a match and its evolution can be captured measuring the permutation entropy and statistical complexity of the network parameters, allowing to identify what parameters evolve more randomly.

Predicting Wins, Losses and Attributes’ Sensitivities in the Soccer World Cup 2018 Using Neural Network Analysis

“…In the last decade, there has been a plethora of research describing and analyzing the match performance data from soccer World Cups using several approaches such as multivariate analyses and machine learning [1][2][3][4][11][12][13][14][15], passing networks based on space, time and the multilayer nature of the game [16] or based on spatial and temporal entropy related to football teams and their players by means of a pass-based interaction [17] and social network analyzes to study the interaction between a player and their teammates (for example a ball passing network) through graph theory to assess the structural and topographical characteristics of personal interactions between team members [18]. This type of descriptive research provides important information that can be used to improve training and adapt tactics, however analyses, such as machine learning, can identify performance indicators, whether physical or technical that may predict what will occur during the match [19][20][21][22].…”

Complexity Evaluation of an Environmental Control and Life-Support System Based on Directed and Undirected Structural Entropy Methods

“…But the existing structural entropy model has no quantitative method for the uncertainty of the results [46,47]. In addition, there are many other fields of complexity evaluation based on information entropy, such as a stock network [50], a brain network [51], the spatial and temporal entropy of a football game [52], and species distribution [53]. The uncertainty of their calculation results originates from the uncertainty of test data, that was, the uncertainty of information.…”

Node and Network Entropy—A Novel Mathematical Model for Pattern Analysis of Team Sports Behavior

“…Real Madrid's unpredictability in passing may have increased the chances of goal-scoring opportunities, potentially having contributed to the win. The concept of entropy to model social interactions has already been used [26][27][28]. Newman and Vilenchik (2019) used the concept of relative entropy to model the interactions of players passing the ball in football, having found that when comparing two opposing teams, higher entropy values lead to more chances of creating goal-scoring opportunities [27].…”