1 Introduction
Graphs or networks arise in the study of a variety of problems, ranging from technological and transport issues to social phenomena and biological problems [ 1, 2, 3]. Their prevalence is such that a rich mathematical theory has been developed around them, notably by Euler, in relation to the Königsberg bridge problem, Erdös and many others.
2 The network of a football team
Figure 1: Passing networks for the Netherlands and Spain drawn before the final game, using the passing data and tactical formations of the semi-finals.
3 Player performance
The individual contribution of a player in a team can be inferred from local network invariants of the passing network and, in particular, from centrality measures, which define the relevance or popularity of a player according to different parameters.
4 Clustering and communities
An interesting aspect of football is how tightly players interact in a team. The notion of clustering tells us precisely that: it is a measure of the degree to which nodes in a network tend to cluster together.
5 Results and analysis
We present in this section the results of the computation of the different measures presented in the previous sections for the teams that have participated in the 2010 FIFA World Cup.
6 Further work
The passing networks that we have presented provide an attractive visual summary or ‘snapshot’ of a football team’s style. The obvious limitation of these networks is of course that they are static.
Acknowledgements
We thank J.J. Merelo Güervós for introducing us to the possibility of using network theory in the context of football, C. Clanet for inviting us to the Euromech Physics of Sports Conference and encouraging us to write down the results of our analysis as a paper, and L. Mahadevan for suggesting to study communities within football teams.
How does social network analysis help in football?
The Social Network Analysis has been carried out in the investigations about passing distribution, improving the understanding on how players interact and cooperate during a match. In football official matches, studies have used the Social Network Analysis as a means of coding players’ cooperation and opposition patterns. However, situational variables such as match status were previously investigated and associated with changes on teams’ dynamics within and/or between matches, but were not considered in studies based on Social Network Analysis. This study aimed to analyze the influence of match status on teams’ cooperation patterns and players’ prominence according to playing positions during 2018 FIFA World Cup. Fourteen matches of the knockout stage were analyzed. Macro and micro network measures were obtained from adjacency matrixes collected for each team, in each match status (winning, drawing, and losing). A one-way ANOVA was used to compare teams’ networks (macro-analysis variables) within each match status, while a two-way ANOVA (match status x playing position) was used to compare the micro-analysis variables. Results showed no differences between match status for macro analysis. Winning situations induced higher prominence in central midfielders (0.107; p=0.001), wide midfielders (0.093; p=0.001), and centre forwards (0.085; p=0.001), while in losing situations lower prominence levels were observed for goalkeepers (0.044; p=0.001) and centre forwards (0.074; p=0.001). Data revealed that teams do not change macrostructures according to match status. On the other hand, the microstructures showed important adaptations regarding game styles, with changes in players’ behaviors according to playing positions. In general, the levels of centrality and prestige in players of different positions indicated a more direct play style in winning situations and a more build-up style in losing situations. These results allow a better understanding about the influence of match status on players’ and teams’ performance during high-level football competitions and may help coaches to improve athletes’ performance in these situations.
What is social network analysis in sports?
Recently, social network analysis has been introduced to the study of sports dynamics in order to quantify the involvement of individual players in the interplay and to characterize the organizational processes used by teams. Nonetheless, only a limited set of team sports has been assessed to date, and the focus of most studies has been on the application of small sets of network metrics to a single sport. Our study aims at comparing the network patterns of different team sports in order to contribute to the understanding of their underlying nature. It considers three invasion games, namely professional matches from basketball, football and handball. By applying relevant centrality measures and minimum spanning trees a first comparison between the nature of interplay in various team sports is offered as well as a deeper understanding of the role of different tactical positions in each sport. The point guard in basketball, defensive midfielder in football and center in handball are identified as the most central tactical positions. Direct interplay is most balanced in football followed by basketball and handball. A visualization of the basic structure of interplay for each sport is achieved through minimum spanning trees.
What is competition network?
Generally, competition networks are groups that compete against each other and their performance is dependent on that of opposing networks. This paper develops a methodology and an application to examine actions or decisions that reveal affiliation and competition when these are not explicitly defined. This was achieved by defining a cooperation threshold along with a visualization framework, which are the main contributions of this paper. The visualization identifies commonalities, differences, and attributes associated with the behavior and characteristics of the actors in each competition network. Data from the Mexican Senate bills from 2012-2015 were used to illustrate the contributions.
What is network science?
Network science is an emerging field . The purpose of this study is to investigate soccer attacks by using network science. In this study, by applying network science approach, four Turkish National Football Team's attacks analyzed with an open-source NodeXL program. We have focused on two types of attacks: the attacks that end with goals and the ones that don't. Our main aim is to see whether there is a difference between the network metrics of these two types of attacks? Using network metrics, for attacks in a same match we couldn't find important differences but we have found real differences for networks' metrics when opponent team changes. Our findings also support that micro measures can be used for new line-up's. First of all, it should be mentioned that our study is a case study and the results of this study should not be generalized. However, our findings can be the start point for further researches with larger samples sizes. With the help of network science approach, the most effective players could be found, the most compatible line-up for the future games could be chosen and the opponent team's key players could be analyzed.
How is soccer related to science?
Most of the scientific research on soccer is related to matches and game play analysis . In this paper, we propose a novel system for team performance analysis and visualization in terms of the structure of a team, and concentrate on cause-and-effect relationships between players and their teams based on player transfer data. Our system visualizes the individual player performance, team characteristics, comparisons between teams, and time varying changes of the team characteristics. The analyzed data are presented in two different ways (1) the system creates a pixel-grid visualization that presents the distinct characteristics of each player in a team. (2) A horizon graph is used to display the changes in team characteristics over time due to player transfers. This approach facilitates understanding the influence of player transfers on team characteristics in a very simple and straightforward manner.
