Using Network Science to Analyse Football Passing Networks: Dynamics, Space, Time, and the Multilayer Nature of the Game

Evolution of passing network in the Soccer World Cups 2010-2022

This study investigates the evolution of passing networks (PN) at both team and player levels in the FIFA World Cups (WC) from 2010 to 2022. Analyzing 256 matches (7328 player observations) using a multiple-camera tracking system across four WCs, we considered six playing positions: goalkeeper (n = 521), central defender (n = 1192), fullback (n = 1223), midfielder (n = 2039), winger (n = 1320), and central forward (n = 1033). We used 17 network metrics and considered contextual variables such as team formation, and team ranking. Linear mixed-effect models analyzed differences in team and player PN parameters by year and team strength. Results showed a shift from possession-play to direct-play from the 2010 to 2018 WCs, with possession-play returning in 2022. Specifically, high- and low-quality teams significantly decreased their density, average degree (AD), modularity, and average path length in 2018 (p < 0.05). High-quality teams showed increased density, AD, and average weighted degree in 2022 (p < 0.05). Midfielders and central forwards exhibited significantly lower centrality parameters, whereas central defenders and goalkeepers showed increased centrality parameters (p < 0.05). This study highlights the evolutionary trends of passing relationships from a network analysis perspective over twelve years, providing insights into the changing dynamics of team interactions and positional prominence in elite soccer.

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.

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.

The effects of scheduling network models in predictive processes in sports

In many sports disciplines, the schedule of the competitions is undeniably an inherent yet crucial component. The present study modeled sports competitions schedules as networks and investigated the influence of network properties on the accuracy of predictive ratings and forecasting models in sports. Artificial networks were generated representing competition schedules with varying density, degree distribution and modularity and embedded in a full rating and forecasting process using ELO ratings and an ordered logistic regression model. Results showed that network properties should be considered when tuning predictive ratings and revealed several aspects for improvement. High density does not increase rating accuracy, so improved rating approaches should increasingly use indirect comparisons to profit from transitivity in dense networks. In networks with a high disparity in their degree distribution, inaccuracies are mainly driven by nodes with a low degree, which could be improved by relaxing the rating adjustment functions. Moreover, in terms of modularity, low connectivity between groups (i.e., leagues or divisions) challenges correctly assessing a single group’s overall rating. The present study aims to stimulate discussion on network properties as a neglected facet of sports forecasting and artificial data to improve predictive ratings.

Combined effect of game position and body size on network-based centrality measures performed by young soccer players in small-sided games

This study verified the effects of body size and game position on interactions performed by young soccer players in small-sided games (SSG). The sample consisted of 81 Brazilian soccer players (14.4 ± 1.1 years of age). Height, body mass, and trunk-cephalic height were measured. SSG was applied in the GK + 3v3 + GK format, and Social Network Analyses were carried out through filming the games to obtain the following prominence indicators: degree centrality, closeness centrality, degree prestige, and proximity prestige, in addition to network intensity and number of goals scored. Factorial ANCOVA (bone age as covariate) was used to test the effects of game position, body size, and respective interaction on centrality measurements (p < 0.05). Similarity between game positions in body size indicators (p > 0.05) was observed. The game position affected degree centrality (p = 0.01, η² = 0.16), closeness centrality (p  = 0.01, η² = 0.11), and network intensity (p = 0.02, η² = 0.09), in which midfielders presented the highest network prominence values when compared to defenders and forwards. In conclusion, midfielders are players with high interaction patterns in the main offensive plays, which behavior is independent of body size.

Social Network Analysis: Mathematical Models for Understanding Professional Football in Game Critical Moments—An Exploratory Study

Considering 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.

Natural Gas Scarcity Risk in the Belt and Road Economies Based on Complex Network and Multi-Regional Input-Output Analysis

Natural gas scarcity poses a significant risk to the global economy. The risk of production loss due to natural gas scarcity can be transferred to downstream economies through globalized supply chains. Therefore, it is important to quantify and analyze how natural gas scarcity in some regions affects the Belt and Road (B&R) economies. The embodied natural gas scarcity risks (EGSRs) of B&R economies are assessed and the EGSR transmission network is constructed. The built network shows a small-world nature. This illustrates that any interruption in key countries will quickly spread to neighboring countries, potentially affecting the global economy. The top countries, including Turkey, China, Ukraine, and India are identified in EGSR exports, which also have relatively high values of closeness centrality. The findings illustrate that the shortage of natural gas supply in these countries may have a significant impact on downstream countries or sectors and the resulting economic losses spread rapidly. These countries are critical to the resilience of the B&R economies to natural gas scarcity. The top nations, including Turkmenistan, Macedonia, and Georgia are also identified in EGSR imports, highlighting their vulnerability to natural gas scarcity. Further, the community analysis of the network provides a fresh perspective for formulating fair and reasonable allocation policies of natural gas resources and minimizing the large-scale spread of economic losses caused by natural gas scarcity.

The effect of bio-banding on academy soccer player passing networks: Implications of relative pitch size

The primary aims of this study were to examine the effects of bio-banding players on passing networks created during 4v4 small-sided games (SSGs), while also examining the interaction of pitch size using passing network analysis compared to a coach-based scoring system of player performance. Using a repeated measures design, 32 players from two English Championship soccer clubs contested mixed maturity and bio-banded SSGs. Each week, a different pitch size was used: Week 1) small (36.1 m2 per player); week 2) medium (72.0 m2 per player); week 3) large (108.8 m2 per player); and week 4) expansive (144.50 m2 per player). All players contested 12 maturity (mis)matched and 12 mixed maturity SSGs. Technical-tactical outcome measures were collected automatically using a foot-mounted device containing an inertial measurement unit (IMU) and the Game Technical Scoring Chart (GTSC) was used to subjectively quantify the technical performance of players. Passing data collected from the IMUs were used to construct passing networks. Mixed effect models were used with statistical inferences made using generalized likelihood ratio tests, accompanied by Cohen's local f2 to quantify the effect magnitude of each independent variable (game type, pitch size and maturation). Consistent trends were identified with mean values for all passing network and coach-based scoring metrics indicating better performance and more effective collective behaviours for early compared with late maturation players. Network metrics established differences (f2 = 0.00 to 0.05) primarily for early maturation players indicating that they became more integral to passing and team dynamics when playing in a mixed-maturation team. However, coach-based scoring was unable to identify differences across bio-banding game types (f2 = 0.00 to 0.02). Pitch size had the largest effect on metrics captured at the team level (f2 = 0.24 to 0.27) with smaller pitch areas leading to increased technical actions. The results of this study suggest that the use of passing networks may provide additional insight into the effects of interventions such as bio-banding and that the number of early-maturing players should be considered when using mixed-maturity playing formats to help to minimize late-maturing players over-relying on their early-maturing counterparts during match-play.

Downtrends in Offside Offenses Among 'The Big Five' European Football Leagues

This study examined the evolution of offside offenses and pass performance across a 10-season period in the top five European soccer leagues. Match performance observations (n = 18 259) were analysed for emergent trends. Two-way ANOVA analyses revealed significant league and seasonal differences among the five leagues (medium effect size). The total offside offenses committed during a match experienced a clear decline during the 10 seasons. In contrast, moderate increases were evident for all passing differential variables. Offside offenses per match were higher in the German Bundesliga and Spanish La Liga than in the English Premier League and France Ligue 1. However, the English Premier League had the greatest value in the touch differential, pass differential, successful pass differential, and key pass differential among all leagues. It is important to note that the number of offside offenses fell after the implementation of VAR.

Distance Between Players During a Soccer Match: The Influence of Player Position

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.

Behavioral Spatial Segmentation and Its Application to Sports Dynamics

In this literature review and theoretical paper, I present a psychological interpretation of sports situations in which space becomes a fundamental element. For this, I employ Kupalov's studies regarding the conditioned place reflex and Gibson's field analysis about driving as locomotion and his later assumptions from his theory of affordances. I present Behavioral Spatial Segmentation as an analytical concept, and I apply it to a sports situation in soccer with some parameters offered for subsequent evaluation. I describe the utility of some modern analysis, measurement, and representation tools for investigating this type of situation. Finally, I present some conclusions and potential implications of this work for sports training.

Dodge and survive: Modeling the predatory nature of dodgeball

The analysis of games and sports as complex systems can give insights into the dynamics of human competition and has been proven useful in soccer, basketball, and other professional sports. In this paper, we present a model for dodgeball, a popular sport in U.S. schools, and analyze it using an ordinary differential equation (ODE) compartmental model and stochastic agent-based game simulations. The ODE model reveals a rich landscape with different game dynamics occurring depending on the strategies used by the teams, which can in some cases be mapped to scenarios in competitive species models. Stochastic agent-based game simulations confirm and complement the predictions of the deterministic ODE models. In some scenarios, game victory can be interpreted as a noise-driven escape from the basin of attraction of a stable fixed point, resulting in extremely long games when the number of players is large. Using the ODE and agent-based models, we construct a strategy to increase the probability of winning.

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.

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.

Asymmetries in Football: The Pass—Goal Paradox

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.

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

Predicting the results of soccer competitions and the contributions of match attributes, in particular, has gained popularity in recent years. Big data processing obtained from different sensors, cameras and analysis systems needs modern tools that can provide a deep understanding of the relationship between this huge amount of data produced by sensors and cameras, both linear and non-linear data. Using data mining tools does not appear sufficient to provide a deep understanding of the relationship between the match attributes and results and how to predict or optimize the results based upon performance variables. This study aimed to suggest a different approach to predict wins, losses and attributes' sensitivities which enables the prediction of match results based on the most sensitive attributes that affect it as a second step. A radial basis function neural network model has successfully weighted the effectiveness of all match attributes and classified the team results into the target groups as a win or loss. The neural network model's output demonstrated a correct percentage of win and loss of 83.3% and 72.7% respectively, with a low Root Mean Square training error of 2.9% and testing error of 0.37%. Out of 75 match attributes, 19 were identified as powerful predictors of success. The most powerful respectively were: the Total Team Medium Pass Attempted (MBA) 100%; the Distance Covered Team Average in zone 3 (15-20 km/h; Zone3_TA) 99%; the Team Average ball delivery into the attacking third of the field (TA_DAT) 80.9%; the Total Team Covered Distance without Ball Possession (Not in_Poss_TT) 76.8%; and the Average Distance Covered by Team (Game TA) 75.1%. Therefore, the novel radial based function neural network model can be employed by sports scientists to adapt training, tactics and opposition analysis to improve performance.

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.

A public data set of spatio-temporal match events in soccer competitions

Soccer analytics is attracting increasing interest in academia and industry, thanks to the availability of sensing technologies that provide high-fidelity data streams for every match. Unfortunately, these detailed data are owned by specialized companies and hence are rarely publicly available for scientific research. To fill this gap, this paper describes the largest open collection of soccer-logs ever released, containing all the spatio-temporal events (passes, shots, fouls, etc.) that occured during each match for an entire season of seven prominent soccer competitions. Each match event contains information about its position, time, outcome, player and characteristics. The nature of team sports like soccer, halfway between the abstraction of a game and the reality of complex social systems, combined with the unique size and composition of this dataset, provide an ideal ground for tackling a wide range of data science problems, including the measurement and evaluation of performance, both at individual and at collective level, and the determinants of success and failure.

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

The application of Network Science to social systems has introduced new methodologies to analyze classical problems such as the emergence of epidemics, the arousal of cooperation between individuals or the propagation of information along social networks. More recently, the organization of football teams and their performance have been unveiled using metrics coming from Network Science, where a team is considered as a complex network whose nodes (i.e., players) interact with the aim of overcoming the opponent network. Here, we combine the use of different network metrics to extract the particular signature of the F.C. Barcelona coached by Guardiola, which has been considered one of the best teams along football history. We have first compared the network organization of Guardiola's team with their opponents along one season of the Spanish national league, identifying those metrics with statistically significant differences and relating them with the Guardiola's game. Next, we have focused on the temporal nature of football passing networks and calculated the evolution of all network properties along a match, instead of considering their average. In this way, we are able to identify those network metrics that enhance the probability of scoring/receiving a goal, showing that not all teams behave in the same way and how the organization Guardiola's F.C. Barcelona is different from the rest, including its clustering coefficient, shortest-path length, largest eigenvalue of the adjacency matrix, algebraic connectivity and centrality distribution.