^{*}

Edited by: Silvan Steiner, University of Bern, Switzerland

Reviewed by: Julen Castellano, University of the Basque Country (UPV/EHU), Spain; Carlos Lago-peñas, University of Vigo, Spain

*Correspondence: Duarte Araújo

This article was submitted to Performance Science, a section of the journal Frontiers in Psychology

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

The synergistic interaction between teammates in association football has properties that can be captured by Social Network Analysis (SNA). The analysis of networks formed by team players passing a ball in a match shows that team success is correlated with high network density and clustering coefficient, as well as with reduced network centralization. However, oversimplification needs to be avoided, as network metrics events associated with success should not be considered equally to those that are not. In the present study, we investigated whether network density, clustering coefficient and centralization can predict successful or unsuccessful team performance. We analyzed 12 games of the Group Stage of UEFA Champions League 2015/2016 Group C by using public records from TV broadcasts. Notational analyses were performed to categorize attacking sequences as successful or unsuccessful, and to collect data on the ball-passing networks. The network metrics were then computed. A hierarchical logistic-regression model was used to predict the successfulness of the offensive plays from network density, clustering coefficient and centralization, after controlling for the effect of total passes on successfulness of offensive plays. Results confirmed the independent effect of network metrics. Density, but not clustering coefficient or centralization, was a significant predictor of the successfulness of offensive plays. We found a negative relation between density and successfulness of offensive plays. However, reduced density was associated with a higher number of offensive plays, albeit mostly unsuccessful. Conversely, high density was associated with a lower number of successful offensive plays (SOPs), but also with overall fewer offensive plays and “ball possession losses” before the attacking team entered the finishing zone. Independent SNA of team performance is important to minimize the limitations of oversimplifying effective team synergies.

The team, rather than the individual, has become the basic work unit in many activities and organizations (Balkundi and Harrison,

Individual and collective behavior has been intensively studied in team sports performance analysis. The behavior of an individual player affects the team's behavioral pattern (Vilar et al.,

Analyses of network heterogeneity and centrality reveal that team offensive play has many variations and short patterns that increase collective unpredictability (Clemente et al.,

Despite these recent advances, research in the field has remained focused on the association between ball-passing network metrics and coarse-grained team performance variables (e.g., goals scored, shots, shots on goal, or competition stage reached) (Grund,

This study deliberately focused on club-teams rather than on national teams because club-teams train and compete together for longer consecutive periods of time. Our sample comprises 12 matches played in Group C of the UEFA Champions League 2015/2016 Group Stage. The four teams analyzed are here identified as CAM, FCA, GSK, and SLB.

Our analysis focused on collective offensive processes. Offensive play is a set of attacking actions performed by a team between recovering and losing ball possession. According to Garganta (

The video footage used in the analysis was obtained from TV broadcasters. We started by categorizing all offensive plays as

The offensive plays were identified and categorized with

Density is the interconnectedness of nodes (players) in a network (team), i.e., it is the ratio of existing ties (passes) between teammates relative to the possible number of such ties (Balkundi and Harrison,

Clustering is a measure of the degree to which nodes in a network tend to cluster together (Peña and Touchette,

In directed graphs, the local clustering coefficient of a vertex expresses the ratio of the links between the vertices that are connected to it. Thus, local clustering coefficient (C) of a given vertex _{jk} between _{i} vertices in its neighborhood, divided by the maximum number _{i} (_{i} − 1) of possible links there between:

The centrality of a group or network is the degree of inequality of the distribution of positions/“weights” of different elements within the network. A network is therefore more centralized when one of its elements is clearly more central than all other group members. Conversely, a network is decentralized when all its elements have the same value of centrality (Grund,

There are several measures of centrality and researchers do not always agree on how “group centrality” or “centralization” should be assessed. We used degree centrality for quantifying the relative influence of each player on the total number of passes within a network. Thus, centralization conveys how central the most central player is when compared to the other players in the network. This metric was originally described by Freeman (^{*}) is the largest value of centrality degree in the network, deg (

In the context of a football match, zero centralization indicates that all players have the same level of interaction during the game. Conversely, a centralization value very close to one suggests that a player is the key-player of the team and that other players have a strong tendency to play with him (Clemente et al.,

A hierarchical logistic regression model using the logit link function was performed to predict the successfulness of offensive plays from the number of passes performed and the network metrics (density, clustering coefficient and centralization). Two blocks were defined. In thefirst block, only the predictor

In a logistic regression, Exp (β_{i}) represents the odds-ratio of success vs. failure (categories of the model's dependent variable) when variable _{i} increases by one unit with respect to the odds-ratio of success vs. failure, when _{i} stays constant. Density, clustering coefficient and centralization vary between zero and one, therefore, we converted these metrics to a scale of 0 to 10 to adjust to model sensitivity. Consequently, the odds ratios presented for these variables refer to a unit change of 0.1.

A two-block hierarchical logistic regression was used to predict the successfulness of offensive plays. In the first block, the total number of passes (hereafter referred to as ‘total passes’) was the only predictor-variable. This model performed significantly better than a constant-only model [^{2} of 0.035. Network metrics were added in a second block (Table ^{2} of 0.071. The first-block model correctly classified 56.2% of the known cases, 66.7% of the UOPs and 45.3% of the SOPs. The second-block model correctly classified 69.5% of the UOPs and 47.5% of the SOPs, with an overall correct classification of 58.7% of the cases. Thus, adding the second block to the model increased the number of correct classifications by 2.5%.

Binary Logistic Regression Model of offensive plays' successfulness.

Total number of passes | 0.079 (0.034) | 5.475 | 0.019 | 1.082 | 1.013 | 1.156 |

Density scores | –1.320 (0.591) | 4.994 | 0.025 | 0.267 | 0.084 | 0.850 |

Clustering coefficient scores | 0.179 (0.193) | 0.858 | 0.354 | 1.196 | 0.819 | 1.747 |

Centralization scores | 0.189 (0.143) | 1.759 | 0.185 | 1.208 | 0.914 | 1.597 |

Constant | –0.615 (0.469) | 1.719 | 0.190 | 0.541 |

Total number of passes and density were significant predictors among the four considered variables. The total number of passes was positively associated with the successfulness of offensive plays. A one-pass-increase augmented the probability of SOPs by 8.2% Exp (β) = 1.082; see Table

Depiction case-by-case of the relationship between density and total passes, for SOP and UOP predicted outcomes, according to the second-block logistic regression model.

Frequencies of density values, according to the category of offensive play's successfulness.

Network characteristics such as density, clustering coefficient and centralization have been reported as good descriptors of game style in soccer teams, as they can be associated with metrics of success such as goals scored, shots, shots on goal, and competition stage reached by teams. However, since network analysis describes events occurring during entire matches, performance outputs and network properties metrics cannot be measured simultaneously. In this study, we attempted to clarify the association between specific network properties and successful (or unsuccessful) team behavior.

Our model was able to classify 58.7% of the events correctly, however, it performed better at identifying UOPs (69.5%) than SOPs (47.5%). These results suggest that these network metrics (density, clustering coefficient and centralization) can more accurately describe the team behaviors associated with UOPs (i.e., losing ball possession) than the behaviors leading to SOPs (i.e., moving into the finishing zone or shooting on goal). Thus, despite the limited predictive power, the model seems to better pinpoint the collective behaviors that the teams should avoid rather than the ones that they should perform in order to ensure success.

The total number of passes and density were the most relevant variables in our model. Total passes was introduced in the first block of regression model to assess the specific influence of the network metrics on team performance. The improvement in the model obtained by adding the second block confirmed the metrics' specific influence. We observed a positive association between total passes and team performance. Each new pass in a set of offensive plays occurring within a 15 min-period resulted in the teams being 8.2% more likely to move into the finishing zone or to shoot on goal. These findings corroborated the studies that showed that long passing sequences are more efficient than short passing sequences (Hughes and Franks,

It has been shown that strong cooperation between teammates makes teams stronger and more successful (Balkundi and Harrison,

We found that the clustering coefficient is not a significant predictor of the successfulness of offensive plays, thus corroborating previous research (Peña and Touchette,

In summary, our results suggest that network density contributes to the prediction of a team's ability to enter in the finishing zone or to shoot at the goal in elite football matches. Furthermore, this study gives new insights into the association between network density and team performance (Balkundi and Harrison,

Some practical implications can be drawn from the present findings. Teams that express high densities in their offensive process may lose possession of the ball in the advanced zones, This facilitates, for example, more space on the back of the defensive line and the need to control this space by efficient pressing in zones of loss. Furthermore, the establishment of varied links by a team is eventually dependent on the creation of numerous lines of pass to the player with the ball. In light with ecological dynamics (Araujo et al.,

We tested a model that analyzes the specific associations between the characteristics of a team's ball-passing network and the outcome of its offensive plays (entering the finishing zone and shot on goal vs. losing ball possession). Previous studies had not differentiated these different outcomes, which may explain our results revealing a negative relation between density and team performance. Additionally the limited predictive power of the model may be associated with some limitations of the study such as the reduced number of teams and games analyzed, which may influence the findings due to the specific style of play of the four teams and eventually by the intra- and inter-team synergies created in the matches among them. Finally, we demonstrated that neither clustering coefficient nor centralization are significant predictors of team performance successfulness, possibly indicating that diverse offensive styles can be equally effective for a team to succeed.

TP had a major contribution to study conception and design, acquisition of data and analysis and interpretation of data. AP had a major contribution to analysis and interpretation of data. DA had a major contribution to study conception and design and analysis and interpretation of data.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The authors would like to thank to José Pedro Silva, Rui Lopes, Micael Couceiro and João Ramos for their assistance in the data analysis. This work was partly supported by the Fundação para a Ciência e Tecnologia, under Grant UID/DTP/UI447/2013 to CIPER – Centro Interdisciplinar para o Estudo da Performance Humana (unit 447).