Defining a historic football team: Using Network Science to analyze Guardiola's F.C. Barcelona

Passing path predicts shooting outcome in football

What determines the outcome of a shot (scored or unscored) in football (soccer)? Numerous studies have investigated various aspects of this question, including the skills and physical/mental state of the shooter or goalkeeper, the positional information of shots, as well as the attacking styles and defensive formations of the opposing team. However, a critical question has received limited attention: How does the passing path affect the outcome of a shot? In other words, does the path of the ball before shooting significantly influence the result when the same player takes two shots from the same location? This study aims to fill the gap in the literature by conducting qualitative studies using a dataset comprising 34,938 shots, along with corresponding passing paths from top-tier football leagues and international competitions such as the World Cup. Eighteen path features were extracted and applied to three different machine-learning models. The results indicate that the passing path, whether with or without the positional information of shots, can indeed predict shooting outcomes and reveal influential path features. Moreover, it suggests that taking quick actions to move the ball across areas with a high probability of scoring a goal can significantly increases the chance of a successful shot. Interestingly, certain path features that are commonly considered important for team performance, such as the distribution of passes among players and the overall path length, were found to be less significant for shooting outcomes. These findings enhance our understanding of the effective ball-passing and provide valuable insights into the critical factors for achieving successful shots in football games.

Technical and tactical evolution of the offensive team sequences in LaLiga between 2008 and 2021. Is Spanish football now a more associative game?

The aim of this investigation was to study the technical and tactical evolution of the offensive team sequences in the Spanish football teams from 2008/09 to 2020/21. A comparative analysis including twelve variables related to the development of offensive sequences in 4940 matches was performed from 2008/09 to 2020/21 seasons of the Spanish professional football league (LaLiga). All match observations were recorded using a validated video tracking system. Multilevel linear mixed models were used to examine the differences across seasons, considering the effects of contextual variables. The number of passes per sequence (2.4 [CI: 2.2-2.5] vs 3.2 [CI: 3.0-3.4]; +33.3%), the passing accuracy (72.1 [CI: 70.6-73.5] vs 76.9 [CI: 75.4-78.3]%; +6.8%) and the average duration of the team sequences (6.4 [CI: 5.9-6.8] vs 8.3 [CI: 7.8-8.7] seconds; +25.76%) showed a small increasing trend over the seasons (P < 0.05). In contrast, variables such as the direct speed of progression (2.2 [CI: 2.1-2.3] vs 1.6 [CI: 1.5-1.7] metres/second; -24.5%), key passes (8.1 [CI: 7.6-8.5] vs 6.8 [CI: 6.3-7.2]; -15.8%), and the sequences that ended in the attacking third (64.8 [CI: 62,7-66.8] vs 57.1 [CI: 55.1-59.2]; -11.7%) or in a shot (13.0 [CI: 12.4-13.6] vs 10.2 [CI: 9.6-10.8]; -21.6%) showed a small decreasing trend from 2008/09 to 2020/21 (P < 0.05). Spanish professional football teams slightly evolved technically and tactically towards a more associative style of play that includes longer passing sequences. This evolution also involved a decreasing speed of progression and fewer technical actions such as through balls, key passes and shots.

Theory and data analysis of player and team ball possession time in football

In this study, the stochastic properties of player and team ball possession times in professional football matches are examined. Data analysis shows that player possession time follows a gamma distribution and the player count of a team possession event follows a mixture of two geometric distributions. We propose a formula for expressing team possession time in terms of player possession time and player count in a team's possession, verifying its validity through data analysis. Furthermore, we calculate an approximate form of the distribution of team possession time and study its asymptotic property.

Study State Dynamics of Team Passing Networks in Soccer Games

Complex networks have been widely used in studying collective behaviours in soccer sports, such as examining tactical strategies, recognizing team characteristics, and discovering topological determinants for high team performance. The passing network of a team evolves and displays different temporal patterns, that are strongly linked to team status, tactical strategies, attacking/defending transitions, etc. Nevertheless, existing research has not illuminated the state dynamics of team passing networks, whereas similar methods have been extensively used in examining the dynamical brain networks constructed from human brain neuroimage data. This study aims to investigate the state dynamics of team passing networks in soccer sports. The introduced method incorporates multiple techniques, including sliding time window, network modeling, graph distance measure, clustering, and cluster validation. The final match of the FIFA World Cup 2018 was taken as an example, and the state dynamics of teams Croatia and France were analyzed respectively. Additionally, the effects of the time windows and graph distance measures on the results were briefly discussed. This study presents a novel outlook on examining the dynamics of team passing networks, as it facilitates the recognition of important team states or state transitions in soccer and other team ball-passing sports for further analysis.

Representing melodic relationships using network science

Music is a complex system consisting of many dimensions and hierarchically organized information-the organization of which, to date, we do not fully understand. Network science provides a powerful approach to representing such complex systems, from the social networks of people to modelling the underlying network structures of different cognitive mechanisms. In the present research, we explored whether network science methodology can be extended to model the melodic patterns underlying expert improvised music. Using a large corpus of transcribed improvisations, we constructed a network model in which 5-pitch sequences were linked depending on consecutive occurrences, constituting 116,403 nodes (sequences) and 157,429 edges connecting them. We then investigated whether mathematical graph modelling relates to musical characteristics in real-world listening situations via a behavioral experiment paralleling those used to examine language. We found that as melodic distance within the network increased, participants judged melodic sequences as less related. Moreover, the relationship between distance and reaction time (RT) judgements was quadratic: participants slowed in RT up to distance four, then accelerated; a parallel finding to research in language networks. This study offers insights into the hidden network structure of improvised tonal music and suggests that humans are sensitive to the property of melodic distance in this network. More generally, our work demonstrates the similarity between music and language as complex systems, and how network science methods can be used to quantify different aspects of its complexity.

Validation of a motion model for soccer players' sprint by means of tracking data

In soccer game analysis, the widespread availability of play-by-play and tracking data has made it possible to test mathematical models that have been discussed mainly theoretically. One of the essential models in soccer game analysis is a motion model that predicts the arrival point of a player in t s. Although many space evaluation and pass prediction methods rely on motion models, the validity of each has not been fully clarified. This study focuses on the motion model proposed by Fujimura and Sugihara (Fujimura-Sugihara model) under sprint conditions based on the equation of motion. A previous study indicated that the Fujimura-Sugihara model is ineffective for soccer games because it generates a circular arrival region. This study aims to examine the validity of the Fujimura-Sugihara model using soccer tracking data. Specifically, we quantitatively compare the arrival regions of players between the model and real data. We show that the boundary of the player's arrival region is circular rather than elliptical, which is consistent with the model. We also show that the initial speed dependence of the arrival region satisfies the solution of the model. Furthermore, we propose a method for estimating valid kinetic parameters in the model directly from tracking data and discuss the limitations of the model for soccer games based on the estimated parameters.

Complexity emerges in measures of the marking dynamics in football games

In this article, we study the dynamics of marking in football matches. To do this, we survey and analyze a database containing the trajectories of players from both teams on the field of play during three professional games. We describe the dynamics through the construction of temporal bipartite networks of proximity. Based on the introduced concept of proximity, the nodes are the players, and the links are defined between opponents that are close enough to each other at a given moment. By studying the evolution of the heterogeneity parameter of the networks during the game, we characterize a scaling law for the average shape of the fluctuations, unveiling the emergence of complexity in the system. Moreover, we propose a simple model to simulate the players' motion in the field from where we obtained the evolution of a synthetic proximity network. We show that the model captures with a remarkable agreement the complexity of the empirical case, hence it proves to be helpful to elucidate the underlying mechanisms responsible for the observed phenomena.

Variations in the physical demands and technical performance of professional soccer teams over three consecutive seasons

The purpose of this study was twofold: (i) to analyze the seasonal variations in the physical demands of Turkish Super League teams considering their status in the final rankings and (ii) to analyze the seasonal variations in the technical performance of Turkish Super League teams considering their status in the final rankings. This study followed an observational analytic retrospective design. In the last three seasons of the Turkish Super League (2015-2016, 2016-2017 and 2017-2018), 918 football matches, 54 teams, 25,029 observations were made. The Sentio Sports optical tracking system was used to quantify the physical demands and technical execution of players in all matches. No significant differences of external load were found between seasons analyzed (p > 0.05). The number of lost balls, ball touches in the central corridor, and goals from set pieces increased from season one to the others (p < 0.05), while the number of successful dribbles reduced over time (p < 0.05). As conclusion, it seems not occurred a progressive change in external load over the seasons, while an evolutionary trends regarding technical variables were observed.

Guardiola, Klopp, and Pochettino: The Purveyors of What? The Use of Passing Network Analysis to Identify and Compare Coaching Styles in Professional Football

We applied social networks analysis to objectively discriminate and describe interpersonal interaction dynamics of players across different top-coaching styles. The aim was to compare metrics in the passing networks of Jürgen Klopp, Pep Guardiola, and Mauricio Pochettino across the UEFA Champions League seasons from 2017 to 2020. Data on completed passes from 92 games were gathered and average passing networks metrics were computed. We were not only able to find the foundations on which these elite coaches build the passing dynamics in their respective teams, but also to determine important differences that represent their particular coaching signatures. The local cluster coefficient was the only metric not significantly different between coaches. Still, we found higher average shortest-path length for Guardiola's network (mean ± std = 3.00 ± 0.45 a.u.) compared to Klopp's (2.80 ± 0.52 a.u., p = 0.04) and Pochettino's (2.70 ± 0.39 a.u., p = 0.01). Density was higher for Guardiola's (64.16 ± 20.27 a.u.) than for Pochettino's team (51.42 ± 17.28 a.u., p = 0.008). The largest eigenvalue for Guardiola's team (65.95 ± 16.79 a.u.) was higher than for Klopp's (47.06 ± 17.25 a.u., p < 0.001) and Pochettino's (42,62 ± 12.01 a.u., p < 0.001). Centrality dispersion was also higher for Guardiola (0.14 ± 0.02 a.u.) when compared to Klopp (0.12 ± 0.03 a.u., p = 0.008). The local cluster coefficient seems to build the foundation for passing work, however, cohesion characteristics among players in the three teams of the top coaches seems to characterize their own footprint regarding passing dynamics. Guardiola stands out by the high number of passes and the enhanced connection of the most important players in the network. Klopp and Pochettino showed important similarities, which are associated to preferences toward more flexibility of interpersonal linkages synergies.

Stochastic model for football's collective dynamics

In this paper, we study collective interaction dynamics emerging in the game of football (soccer). To do so, we surveyed a database containing body-sensor traces measured during three professional football matches, where we observed statistical patterns that we used to propose a stochastic model for the players' motion in the field. The model, which is based on linear interactions, captures to a good approximation the spatiotemporal dynamics of a football team. Our theoretical framework, therefore, can be an effective analytical tool to uncover the underlying cooperative mechanisms behind the complexity of football plays. Moreover, we showed that it can provide handy theoretical support for coaches to evaluate teams' and players' performances in both training sessions and competitive scenarios.

Explaining the difference between men's and women's football

Women's football is gaining supporters and practitioners worldwide, raising questions about what the differences are with men's football. While the two sports are often compared based on the players' physical attributes, we analyze the spatio-temporal events during matches in the last World Cups to compare male and female teams based on their technical performance. We train an artificial intelligence model to recognize if a team is male or female based on variables that describe a match's playing intensity, accuracy, and performance quality. Our model accurately distinguishes between men's and women's football, revealing crucial technical differences, which we investigate through the extraction of explanations from the classifier's decisions. The differences between men's and women's football are rooted in play accuracy, the recovery time of ball possession, and the players' performance quality. Our methodology may help journalists and fans understand what makes women's football a distinct sport and coaches design tactics tailored to female teams.

Preferential model for the evolution of pass networks in ball sports

We propose a theoretical model to evaluate the temporally evolving ball-passing networks whose number of edges increases with time. The model incorporates a preferential selection of edges that chooses an edge based on its frequency of selection. The results are in good agreement with the corresponding ball-passing networks of association football, basketball, and rugby matches, and they enable a quantitative comparison of the passing activity among different teams or ball sports.

Coexistence of Distinct Performance Models in High-Level Women's Volleyball

In performance analysis, and most notably in match analysis, generalizing game patterns in a sport or competition may result in formulating generic models and neglecting relevant variability in benefit of average or central values. Here, we aimed to understand how different game models can coexist at the same competitive level using social network analysis with degree centrality to obtain systemic mappings for six volleyball matches, one for each of the six national teams playing in the 2014 World Grand Prix Finals, guaranteeing a homogeneous game level and balanced matches. Although the sample was not recent, this was not relevant for our purposes, since we aimed to merely expose a proof of concept. A total of 56 sets and 7,176 ball possessions were analysed through Gephi Software, considering game actions as nodes and the interaction between them as edges. Results supported the coexistence of different performance models at the highest levels of practice, with each of the six teams presenting a very distinct game model. For example, important differences in eigenvector centrality in attack zones (ranging from 0 to 34) and tempos (20 to 38) were found between the six teams, as well as in defensive lines (20 to 39) and block opposition (22 to 37). This further suggests that there may be multiple pathways towards expert performance within any given sport, inviting a re-conceptualization of monolithic talent identification, detection and selection models. Future studies could benefit from standardizing the metrics in function of the number of ball possessions.

Space evaluation in football games via field weighting based on tracking data

In football game analysis, space evaluation is an important issue because it is directly related to the quality of ball passing or player formations. Previous studies have primarily focused on a field division approach wherein a field is divided into dominant regions in which a certain player can arrive prior to any other players. However, the field division approach is oversimplified because all locations within a region are regarded as uniform herein. The objective of the current study is to propose a fundamental framework for space evaluation based on field weighting. In particular, we employed the motion model and calculated a minimum arrival time [Formula: see text] for each player to all locations on the football field. Our main contribution is that two variables [Formula: see text] and [Formula: see text] corresponding to the minimum arrival time for offense and defense teams are considered; using [Formula: see text] and [Formula: see text], new orthogonal variables [Formula: see text] and [Formula: see text] are defined. In particular, based on real datasets comprising of data from 45 football games of the J1 League in 2018, we provide a detailed characterization of [Formula: see text] and [Formula: see text] in terms of ball passing. By using our method, we found that [Formula: see text] and [Formula: see text] represent the degree of safety for a pass made to [Formula: see text] at t and degree of sparsity of [Formula: see text] at t, respectively; the success probability of passes could be well-fitted using a sigmoid function. Moreover, a new type of field division approach and evaluation of ball passing just before shots using real game data are discussed.

Identification of skill in an online game: The case of Fantasy Premier League

In all competitions where results are based upon an individual's performance the question of whether the outcome is a consequence of skill or luck arises. We explore this question through an analysis of a large dataset of approximately one million contestants playing Fantasy Premier League, an online fantasy sport where managers choose players from the English football (soccer) league. We show that managers' ranks over multiple seasons are correlated and we analyse the actions taken by managers to increase their likelihood of success. The prime factors in determining a manager's success are found to be long-term planning and consistently good decision-making in the face of the noisy contests upon which this game is based. Similarities between managers' decisions over time that result in the emergence of 'template' teams, suggesting a form of herding dynamics taking place within the game, are also observed. Taken together, these findings indicate common strategic considerations and consensus among successful managers on crucial decision points over an extended temporal period.

Sports Injury Forecasting and Complexity: A Synergetic Approach

The understanding that sports injury is the result of the interaction among many factors and that specific profiles could increase the risk of the occurrence of a given injury was a significant step in establishing programs for injury prevention. However, injury forecasting is far from being attained. To be able to estimate future states of a complex system (forecasting), it is necessary to understand its nature and comply with the methods usually used to analyze such a system. In this sense, sports injury forecasting must implement the concepts and tools used to study the behavior of self-organizing systems, since it is by self-organizing that systems (i.e., athletes) evolve and adapt (or not) to a constantly changing environment. Instead of concentrating on the identification of factors related to the injury occurrence (i.e., risk factors), a complex systems approach looks for the high-order variables (order parameters) that describe the macroscopic dynamic behavior of the athlete. The time evolution of this order parameter informs on the state of the athlete and may warn about upcoming events, such as injury. In this article, we describe the fundamental concepts related to complexity based on physical principles of self-organization and the consequence of accepting sports injury as a complex phenomenon. In the end, we will present the four steps necessary to formulate a synergetics approach based on self-organization and phase transition to sports injuries. Future studies based on this experimental paradigm may help sports professionals to forecast sports injuries occurrence.

Consistency and identifiability of football teams: a network science perspective

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.

Modeling ball possession dynamics in the game of football

In this paper, we study interaction dynamics in the game of football-soccer in the context of ball possession intervals. To do so, we analyze a database comprising one season of the five major football leagues of Europe. Using this input, we developed a stochastic model based on three agents: two teammates and one defender. Despite its simplicity, the model is able to capture, in good approximation, the statistical behavior of possession times, pass lengths, and number of passes performed. In the last section, we show that the model's dynamics can be mapped into a Wiener process with drift and an absorbing barrier.

Passing Networks and Tactical Action in Football: A Systematic Review

The aim of this study is to examine the most significant literature on network analyses and factors associated with tactical action in football. A systematic review was conducted on Web of Science, taking into account the PRISMA guidelines using the keyword “network”, associated with “football” or “soccer”. The search yielded 162 articles, 24 of which met the inclusion criteria. Significant results: (a) 50% of the studies ratify the importance of network structures, quantifying and comparing properties to determine the applicability of the results instead of analyzing them separately; (b) 12.5% analyze the process of offensive sequences and communication between teammates by means of goals scored; (c) the studies mainly identify a balance in the processes of passing networks; (d) the variables allowed for the interpretation of analyses of grouping metrics, centralization, density and heterogeneity in connections between players of the same team. Finally, a systematic analysis provides a functional understanding of knowledge that will help improve the performance of players and choose the most appropriate response within the circumstances of the game.

Tactical Variables Related to Gaining the Ball in Advanced Zones of the Soccer Pitch: Analysis of Differences Among Elite Teams and the Effect of Contextual Variables

Attacking tactical variables have been commonly studied in soccer to analyze teams’ performance. However, few studies investigated defensive tactical variables during match-play and the influence of contextual variables on them. The aims of the present study were (1) to examine the defensive behaviors of soccer teams when gaining the ball in advanced zones of the pitch and (2) to evaluate the effect of contextual variables on these defensive behaviors. A sample of 1,095 defensive pieces of play initiated in the opposing half of the pitch obtained from 10 matches of the season 2010/11 of La Liga and involving 13 teams was collected using the semiautomated tracking system Amisco Pro. Five defensive tactical variables, the outcome of defensive pieces of play, and contextual variables (i.e., match status, venue, quality of opposition, and match period) were recorded for every defensive piece initiated in the opposing half of the pitch. Results showed that there were significant differences among teams in the outcome of defensive pieces of play originating from the opposing half (χ² = 111.87, p < 0.01, φ_c = 0.22), and in the outcome of offensive pieces of play following ball gains (χ² = 49.92, p < 0.001, φ_c = 0.22). Cluster analysis revealed four groups describing different defensive behaviors from high-pressure to a defense close to their own goal. Match status (χ² = 25.87, p < 0.05, φ_c = 0.11) and quality of opposition (χ² = 21.19, p < 0.05, φ_c = 0.10) were the contextual variables that showed a significant effect on defensive pieces of play initiated in the opposite half of the pitch. Teams winning gained more balls in the zone close to their own goal, and losing teams gained more balls in advanced zones of the pitch. Moreover, the greater the quality of the opponent the lesser the chance of gaining the ball in advanced zones of the pitch. Neither venue or match period influenced the defensive pieces of play analyzed. Soccer teams could employ a similar analysis to improve their performance and prepare for opposition teams in competition.

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

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.