Search Strategy

The systematic review was prepared in accordance with the Preferred Reporting Items for Systematic Reviews and Meta Analyses (PRISMA) guidelines (Moher et al., 2009). The protocol was not registered prior to initiation of the project and did not require Institutional Review Board approval. A systematic search of four databases (i.e. SPORTDiscus, PubMed, ProQuest and Web of Science) was performed by three authors (MRG, ALA, JPO) to identify articles published before the 13^th of November, 2018. The authors were not blinded to journal names or manuscript authors. To provide an explicit statement of question, the PICO (Moher et al., 2009) design was used. The search was carried out using two filters when the database allowed it: journal article; and title (TI)/abstract. This was possible in all databases except for Web of Science, which was searched through the text. In addition, in the final database, the sports sciences branch was selected. Database search strategy considered three main groups: 1) population, team sports (at least two players per team and, in which the use of the mobile object was simultaneous), 2) intervention, the assessment tools were included, and 3) outcomes, the results that the authors hoped to find. The keywords were connected with “AND” to combine the three groups and using “OR” to link the words of each group (Table 1).Screening Strategy and Study Selection

When the authors had completed the search, they compared their results to ensure that the same number of articles were found. Then, one of the authors (MR) downloaded the main data from the articles (title, authors, date, and database) to an Excel spreadsheet (Microsoft Excel, Microsoft, Redmond, USA) and removed the duplicate records. Subsequently, the same authors screened the remaining records to verify the inclusion-exclusion criteria using a hierarchical approach (Table 2) in two phases: 1) Phase 1, where possible, titles and abstracts were screened and excluded by two authors (MR, ALA) and 2) Phase 2, full texts of the remaining papers were then accessed and screened by the same two authors (MR, ALA).

In comparison to Low et al. (2019), we did not include several tactical variables as the stretch index (Yue et al., 2008) and the team spread (Yue et al., 2008). As those authors themselves pointed out, these variables may not be computations of the area per se (Low et al., 2019). In the same way, we did not consider tactical variables that assessed the numerical relations of players within pre-established sub-areas (Clemente et al., 2015; Low et al., 2019; Vilar et al., 2013) because this space was not calculated through the data position of players. Moreover, we did not consider variables that analysed the use of space for players in isolation (e.g., players´ mayor range, spatial index exploration [SEI]) because these variables were not “collective” tactical behaviours (Table 2, 5^th inclusion/exclusion criteria).

Any disagreements on the final inclusion-exclusion status were resolved through discussion in both the screening and excluding phases. Moreover, relevant articles not previously identified were also screened in an identical manner and the studies that complied with the inclusion-exclusion criteria were included and labelled as ‘not identified from search strategy’.

Occupied space

Gréhaigne (1992) suggested the effective playing-area (EPS), the polygonal area (i.e. occupied play-space) obtained by a line that linked all players of both teams, except the goalkeepers, positioned at the periphery of the play (Gréhaigne, 1992) in order to assess the use of space in soccer. Since then, several new variables and modifications have been applied to analyse the space occupied by players in team sports. Despite previous studies, it seems that using a simple tool that technical staffs and researchers understand in a similar way is most recommended, although there have been several differences regarding to its conceptualization and computation.

Okihara et al. (2004) measured the team area, the quadrilateral formed by the four outfielders of each team, during a futsal match. In addition, they measured the team area by multiplying the length (i.e., between the front and the tale) by the width (i.e. between the left-edge player and the right-edge player) during a soccer match. Five years later, Frencken and Lemmink (2009) suggested that the surface area represents the overall team ‘position’ and a complement of the geometrical centre to measure the “pressure”. Specifically, they measured the total field coverage of one team, excluding goalkeepers, to describe goal-scoring opportunities in soccer. The mathematical methods to compute the quadrilateral formed by the four outfielders and the surface area were not provided by Okihara et al. (2004) nor Frencken et al. (2009), respectively. Later, Frencken et al. (2011) defined the surface area as the total space covered by the outfield players, referred to as the area within the convex hull, in a new study carried out in soccer during a SSG. They computed the convex hull for both teams using a modified Graham algorithm (1972) and the convex hull area (CA) by summing the triangles formed from the geometrical centre to each of the consecutive points of the convex hull. Following studies applied different concepts and methods to compute the occupied space in team sports (Bueno et al., 2018; Clemente et al., 2013; Duarte et al., 2012; Frencken et al., 2011; Moura et al., 2012). Duarte et al. (2012) calculated the surface area of each team as the area of a triangle with a formula for Cartesian coordinates (Table 3) in a (3+GK) vs. (3+Gk) soccer SSG. Moura et al. (2012) used the Quickhull technique (Barber et al., 1996) to compute the convex hull during a soccer match and, unlike Frencken et al. (2011), showed the division of the convex hull into triangles formed between the closest players to propose the computation of the CA at each instant of time (CA(t)) by summing the areas of all of these triangles (Moura et al., 2012).

All studies mentioned above did not consider GKs to measure the occupied space (i.e. EPS). This match space reference has been habitually used to design training strategies in team sports. However, the actual effective playing-area is all of the playing space which is used according to the rules of each team sport (e.g., offside rule). In addition to considering GKs to measure the EPS at the initial time, Clemente et al. (2013) suggested several practical applications to assess the use of the space based on the EPS and their corresponding computation methods. They focused on the effective free-space (i.e. the real area that a team covers without intercepting the effective area of the opposing team) instead of the original EPS per se. Specifically, they calculated (1) all of the non-overlapping area (i.e. triangles) formed by the players of the same team and (2) the area (i.e. triangles) of each team without interception. In the same line, Bueno et al. (2018) suggested and measured the surface area that a team could present on the court in futsal normalized by the maximum possible value. In a complementary manner, Gonçalves et al. (2018) suggested the measurement of the EPS for subgroups of 3-10 players to assess the use of space for sub-systems in a soccer match. They used the smallest inter-player distance to identify the subgroups. The EPS presented an increase with a higher number of players, especially considering the transition from 3 to 4 players. At a practical level, the match EPS values according to the number of players can be used as a reference to design training tasks.

Practical implications

At a practical level, caution is necessary when the occupied space area is used as a reference to limit the playing space in training tasks. The measurement of the occupied space should consider GKs and the total playing space because these constraints determine the use of the space. In this line of thought, several occupied space variables have been suggested and could be used in future works: effective free-space (Clemente et al., 2013), and the surface area that a team can present on the court normalized by the maximum possible value (Bueno et al., 2018). Moreover, the aforementioned studies used different mathematical methods to calculate EPS, making it difficult to compare them. In future, it would be interesting to compare the impact of the different concepts and computational methods in the measurement of the EPS.

Exploration space

Major ranges (MRs) were proposed in order to assess the mean position of each player during the game (Yue et al., 2008). The MR was defined by an ellipse centred at the 2D mean location of the player, with semi-axes being the standard deviations in x – and y-directions. Similarly, Gonçalves et al. (2017) suggested a novel variable to explain the covering space by each player: the Spatial Exploration Index (SEI). It was obtained for each player by calculating his mean pitch position, computing the distance from each positioning time-series to the mean position and, finally, computing the mean value from all the obtained distances (Gonçalves et al., 2017). Based on the fifth exclusion/inclusion criterion, these variables cannot be considered as a collective tactical variable. However, the major range concept was applied to assess the exploration space of the team by the measurement of the major range of the GC (i.e., the relative positioning of the team) (Yue et al., 2008).

Practical implications

The MR could be applied to assess collective exploration space variables at a subsystem level (i.e. pairs of players, intra-line, and inter-line). At a practical level, this variable should be measured differentiating between possession and no-possession playing phases to assess the explored space according to the playing style of each team.

Dominant space

In addition to the occupied and exploration spaces, dominant space variables have been applied to evaluate the use of the space in team sports. These variables have been based on the Voronoi region (Okabe et al., 1992). This allows expression of the spatial territory of each point (e.g., player) in relation with the remaining points (e.g. players) in a space (Okabe et al., 1992). Thus, it has been considered as a collective tactical behaviour. It is calculated by applying the concept of nearest-neighbour rule, which is associated to all parts of the pitch that are nearer to that particular player compared to any other (Clemente et al., 2018; Okabe et al., 1992).

Taki et al. (1996) suggested, for the first time, the dominant region to assess space management and cooperative movement in team sports. They defined the dominant region as a region where the player can arrive earlier than all of the others (Taki et al., 1996). In comparison to the Voronoi region, they replaced the distance d by time ts (i.e. minimum moving time pattern [MMT]) to assess dominant space in `dynamic environments´ like team sports (Taki and Hasegawa, 2000). In order to calculate the shortest time of an individual to each point x, they suggested considering: a) the position, b) the speed, and c) the accelerating ability of the player at the moment that is needed (Taki et al., 1996). The first two were estimated from images and the accelerating ability was modelled as a set of acceleration patterns based on the physical ability of an average player (Taki et al., 1996). This suggestion was applied for the first time in a team sport (i.e. soccer) by Taki and Hasegawa (2000).

Based on the dominant region (Taki et al., 1996), Taki and Hasegawa (2000) measured the dominant region to assess the sphere of influence in soccer and handball. Similarly, they considered the shortest time of an individual to each point x (Taki and Hasegawa, 2000) instead of the distance d. They also assessed the sphere of influence based on each individual’s movement and physical ability (Taki and Hasegawa, 2000). Later, Fujimura and Sugihara (2005) measured the dominant region in field hockey using a different motion model to measure players´ acceleration. In comparison to Taki and Hasegawa (2000), they did not assume that each player’s acceleration was constant and considered a resistive force that decreased the velocity. In comparison to the original Voronoi region, the three aforementioned studies and the k-region (Filetti et al., 2017) measured the dominant region in a different way. They considered time t instead of distance d to measure this tactical variable. This suggestion is interesting because it considers the parameter time, due to the fact that time is “managed” in team sports (i.e., `arrive a time´ does not depend solely on the physical fitness). However, dominant region values measured based on the time (t) should be assessed with caution.

In order to go into detail in the assessment of players’ contributions to teamwork, there has been a proposal of weighted dominant areas (Fujimura and Sugihara, 2005). Authors have suggested the measurement of the dominant area according to the location of each player with respect to the goal and the ball: the dominant area weighted by the goal and the dominant area weighted by the ball (Fujimura and Sugihara, 2005). The player’s weighted dominant area was measured, giving higher scores to points nearer to the goal, and giving higher scores to points nearer the ball (Fujimura and Sugihara, 2005). As this and other studies (Fonseca et al., 2012) found, the structural traits (Newell, 1986; Parlebas, 2002) of each team sport determine the use of space. In this case, the location of the player with respect to the target (i.e. the orientation of the space) determines the dominant region of the player.

Based on the original Voronoi region (i.e., the distance between players to measure the dominant region), Fonseca et al. (2012) measured the dominant region during the 5 vs. 4 phase in futsal. They defined the Voronoi cells by dividing the plane by mean values of the assignment of the points of the field of each player which is closer to other players versus any other. The key findings in this study were that the dominant regions could be dependent on the role that each team was performing at a given time. As Fonseca et al. (2012) noted, the distance values are used to compute dominant regions (i.e. Voronoi cells) in team sport (Baptista et al., 2018; Clemente et al., 2015; Fonseca et al., 2013; Lopes et al., 2015). At a practical level, Voronoi cells have been used to assess passing effectiveness (Filetti et al., 2017; Rein et al., 2017).

As Taki et al. (1996) suggested, the “team dominant region” can be measured considering the dominant regions of all players of the same team. This single region represents the dominant area of the team. In this line, based on the original Voronoi region (i.e. the distance), Fonseca et al. (2013) suggested the Superimposed Voronoi Diagram (SVD) for describing inter-team spatial interaction patterns of behaviour in futsal. They superimposed the Voronoi diagrams of the two competing teams and measured the maximum percentage of the overlapping area (Max%OA) and the percentage of the free area (%FA) (Fonseca et al., 2013) to describe the spatial interaction behaviour at an individual and collective level. The Max%OA was the maximum percentage of that player’s Voronoi region covered by the Voronoi region of an opponent, while %FA was the remaining space (Fonseca et al., 2013). The authors postulated that these spatial variables allow description of the interaction between two teams by comparing the spatial pattern formed by their respective players. This is largely dependent on the interaction established among pairs of opponents (i.e. man-to-man vs. zonal).

Practical implications

The percentage of the free area and the maximum percentage of the overlapped area provide more complete information about the dominant space of several players than the simple Voronoi diagrams or dominant regions. Thus, future studies could use these two variables to assess dominant space considering the relation between two teams.

Nonlinear analysis of the use of space

Nonlinear analysis techniques have been suggested to assess uncertainty due to the social interaction between teammates and opponents (Araújo and Davids, 2016; Newell, 1986; Parlebas, 2002). In comparison to linear techniques, they allow the assessment of team sports as a complex systems (Stergiou et al., 2004). One of these is entropy, which assesses the regularity of time series, and obviates the predictability of a system. Entropy was suggested by Pincus (1991) as a preliminary mathematical development of this family of formulas and statistics. The author emphasised the application of the Approximate Entropy (ApEn) in a variety of contexts (Pincus, 1991). One of these contexts was team sports, where the entropy technique has been applied to assess the predictability of the occupied space and the dominant area (Table 4a).

The measurement of the complexity and conditional irregularity of the surface area was suggested in team sports by Barnabé et al. (2016). They used two different techniques: the Sample Entropy (SampEn) and the cross-SampEn. In addition, the measurement of the regularity pattern of Voronoi cells was measured using the ApEn and ApEn^RatioRandom (Baptista et al., 2018; Fonseca et al., 2012). Initially, Shannon´s entropy and ApEn were applied to assess the predictability in complex systems such as team sports (Silva et al., 2016). However, Richman and Moorman (2000) suggested the use of the SampEn instead of ApEn for two main reasons: (1) ApEn was heavily dependent on the record length and was uniformly lower than expected for short records, and (2) it lacked relative consistency. In addition, Richman and Moorman (2000) developed cross-SampEn because while Cross-ApEn presented the necessity for each template to generate a defined nonzero probability, cross-SampEn remained relatively consistent for conditions where cross-ApEn did not.

Barnabé et al. (2016) assessed two teams with different maturity and experience levels and compared the irregularity and predictability among them with respect to surface area values. They found greater synchronisation between offensive and defensive surface areas in older age groups. Fonseca et al. (2012) assessed the regularity of time series data from the area of the dominant region (i.e. Voronoi cells) during 5 vs. 4+Gk phase in futsal using the ApEn^RatioRandom. They suggested that greater unpredictability (i.e., variability) of the use of space was played to generate uncertainty in the opposing team, while the defending team tended to be more stable in the use of the space to counter the opposing team. In addition, Baptista et al. (2018) found that predictability was dependent on the team´s formation.

Finally, Low et al. (2018) suggested the assessment of the synchronisation patterns between teams’ EPS signals and the length per width (LPW) ratio (Folgado et al., 2014) using the the relative phase (Low et al., 2018). The computation was performed using Hilbert Transformation (Palut and Zanone, 2005). They compared the EPS-LPW synchronisation between deep-defending vs. high-press defending strategies. For the first time, they suggested the analysis of synchronisation on the use of space (Table 4b). In addition, they combined a spatial tactical variable and a distance variable. The combination of the GC or distance variables with space variables to assess the synchronisation in team sports could provide a more complete picture of the use of space in team sports.

Practical implications

Since there is a lack of consensus on the technique that should be used to measure the predictability of the use of space in team sports, it will be necessary to compare the impact of each entropy technique on the measurement of the spatial tactical variables to assess the comparison among studies. Future studies could assess the synchronisation patterns among different collective tactical behavior variables (Low et al., 2018).