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.

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We investigated the ability of football teams to develop a particular playing style by looking at their passing patterns. Using the information contained in the pass sequences during matches, we constructed the pitch passing networks of teams, whose nodes are the divisions of the pitch for a given spatial scale and links account for the number of passes from region to region. We translated football passings networks into their corresponding adjacency matrices. We calculated the correlations between matrices of the same team to quantify how consistent the passing patterns of a given team are. Next, we quantified the differences with other teams’ matrices and obtained an identifiability parameter that indicates how unique are the passing patterns of a given team. Consistency and identifiability rankings were calculated during a whole season, allowing to detect those teams of a league whose passing patterns are different from the rest. Furthermore, we found differences between teams playing at home or away. Finally, we used the identifiability parameter to investigate what teams imposed their passing patterns over the rivals during a given match.

We investigate the relation between the number of passes made by a football team and the number of goals. We analyze the 380 matches of a complete season of the Spanish national league “LaLiga" (2018/2019). We observe how the number of scored goals is positively correlated with the number of passes made by a team. In this way, teams on the top (bottom) of the ranking at the end of the season make more (less) passes than the rest of the teams. However, we observe a strong asymmetry when the analysis is made depending on the part of the match. Interestingly, fewer passes are made in the second half of a match, while, at the same time, more goals are scored. This paradox appears in the majority of teams, and it is independent of the number of passes made. These results confirm that goals in the first half of matches are more “costly” in terms of passes than those scored in second halves.

In this study, we analyse the proximity between professional players during a soccer match. Specifically, we are concerned about the time a player remains at a distance to a rival that is closer than 2 m, which has a series of consequences, from the risk of contagion during a soccer match to the understanding of the tactical performance of players during the attacking/defensive phases. Departing from a dataset containing the Euclidean positions of all players during 60 matches of the Spanish national league (30 from LaLiga Santander and 30 from LaLiga Smartbank, respectively, the first and second divisions), we analysed 1,670 participations of elite soccer players. Our results show a high heterogeneity of both the player-player interaction time (from 0 to 14 min) and the aggregated time with all opponents (from <1 to 44 min). Furthermore, when the player position is taken into account, we observe that goalkeepers are the players with the lowest exposure (lower than 1 min), while forwards are the players with the highest values of the accumulated time (~21 min). In this regard, defender-forward interactions are the most frequent. To the best of our knowledge, this is the largest dataset describing the proximity between soccer players. Therefore, we believe these results may be crucial to the development of epidemiological models aiming the predict the risk of contagion between players and, furthermore, to understand better the statistics of all actions that involve proximity between players.

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