Informational constraints on the emergence of passing direction in the team sport of futsal

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Informational constraints on the emergence of passing direction in the team sport of futsal

Umberto Cesar Corrêa^a, Luís Vilar^b, Keith Davids^c & Ian Renshaw^c

a School of Physical Education and Sport, University of São Paulo, São Paulo, Brazil

b Faculty of Physical Education and Sports, Lusófona University of Humanities and Technologies, Lisbon, Portugal

c School of Human Movement Studies, Queensland University of Technology, Brisbane, QLD, Australia

Published online: 16 Oct 2012.

To cite this article: Umberto Cesar Corrêa, Luís Vilar, Keith Davids & Ian Renshaw (2014) Informational constraints on the emergence of passing direction in the team sport of futsal, European Journal of Sport Science, 14:2, 169-176, DOI:

10.1080/17461391.2012.730063

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ORIGINAL ARTICLE

Informational constraints on the emergence of passing direction in the team sport of futsal

UMBERTO CESAR CORREˆ A¹, LUI´S VILAR², KEITH DAVIDS³, & IAN RENSHAW³

1School of Physical Education and Sport, University of Sa˜o Paulo, Sa˜o Paulo, Brazil,²Faculty of Physical Education and Sports, Luso´fona University of Humanities and Technologies, Lisbon, Portugal, and³School of Human Movement Studies, Queensland University of Technology, Brisbane, QLD, Australia

Abstract

This study investigated compound spatial and temporal measures of interpersonal interactions purported to constrain the emergence of affordances for passing direction in the team sport of futsal. For this purpose, attackerdefender interactions in 37 sequences of play from a futsal competition in which 24 male professional players participated (M30.04 years,SD 4.10) were filmed and analysed using TACTO software. Relative angle data were used as measures to study coordination tendencies that emerged between players during performance. Results showed that the direction for a pass emerged from relative angles between: (1) the vector from a ball carrier to ball receiver and the vector from the ball carrier to the nearest defender (708) (pB0.01) and (2) the vector from a ball carrier to ball receiver and the vector from the ball carrier to a ball receiver’s nearest defender (318) (pB0.01). Furthermore, passing direction was also constrained by temporal information from the emergence of both angles, since the pass was performed to attackerdefender dyads with the highest velocities of these angles (pB0.05). Results suggested that decisions on selecting the direction of a pass in the team sport of futsal emerged at critical values of these key compound motion measures.

Keywords:Spatiotemporal constraints, passing direction, team sport of futsal, attackerdefender dyads, dynamic pattern formation, emergence

1. Introduction

The understanding of how players make decision in order to act as a team has become the central concern in sport sciences in recent years. As a complex phenomenon, team sports have been ap- proached in different perspectives, for example team cognition (Bourbousson, Poizat, Saury, & Se`ve, 2010,2012; Eccles & Tenenbaum,2004; Lecouteur

& Feo, 2010) and, of further interest, ecological dynamics (Arau´ jo, Davids, Bennett, Button, &

Chapman, 2004; Arau´ jo, Davids, & Hristovski, 2006; Davids, Arau´ jo, & Shuttleworth, 2005;

McGarry,2005).

A principal pillar of the ecological dynamics approach is the inseparability of the performer and the performance environment in the study of human behaviour. The performerenvironment relationship

is predicated on two main assumptions. One is the characterisation of humans as open systems in nature, which interact continually with their environment, exchanging energy and information (von Bertalanffy,1952). Uncertainty in the performance environment is reduced as actions are coupled to perceptual information available to regulate behaviours. A second assumption is that during their interactions with the environment, individuals control their actions through the perception of what the environment offers, provides or furnishes in terms of opportunities for action, i.e. affordances (Gibson, 1986).

From this perspective, recently developments in ecological dynamics have been introduced into studies of sport performance having as main task to understand the sources of information that may constrain the actions of individuals in specific sport

Correspondence: U. C. Correâ, School of Physical Education and Sport, University of Saõ Paulo, Saõ Paulo 05508-030, Brazil.

E-mail:[email protected]

Vol. 14, No. 2, 169176, http://dx.doi.org/10.1080/17461391.2012.730063

#2012 European College of Sport Science

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contexts. Sport teams can be characterised as social systems with many interacting agents, whose actions are constrained by the tendencies for competition and cooperation between them (Correˆa, Alegre, Freudenheim, Santos, & Tani, 2012). Previous research has attempted to identify the spatial and temporal variables that can constrain these competing and cooperating tendencies between performers during their interactions (e.g. see Bourbousson, Se`ve, & McGarry, 2010a, 2010b; Correia, Arau´ jo, Craig, & Passos, 2011; Duarte et al.,2010; Passos, Arau´jo, Davids, Gouveia, Milho, et al.,2009; Passos et al., 2008; Travassos et al., 2012; Vilar, Arau´ jo, Davids, & Button,2012; Watson et al., 2011).

The results of this body of work have led to two main conclusions on the performance of individuals in team sports. First, it is apparent that dynamic patterns of behaviour emerge from critical values of key spatio-temporal variables in performance regions of self-organised criticality (Passos, Arau´ jo, Davids, Gouveia, Serpa, et al., 2009). What this means is that the system formed by interacting players in a sub-phase of play reaches critical states of organisa- tion when the value of a key performance variable (a potential system control parameter) changes (Bak &

Chen, 1991; Bak, Chen, & Creutz, 1989). For example, Passos et al. (2008) investigated the effects of changes in variables like interpersonal distance and relative velocity between attackers and defenders on success of tackles in rugby union. They showed that between interpersonal distances of 42 m, relative velocity increased and changed the coordination patterns emerging between an attacker and defender. Second, it has been shown that, together, spatial and temporal variables provide the necessary sources of information for performers to adapt their behaviours in advance of a key event occurring.

From this perspective, it is clear that prospective control of movement behaviour through perception of compound motion measures is a sine qua non for success in team sports performance because of their highly dynamic characteristic (Bastin, Craig, &

Montagne,2006; Fajen, Riley, & Turvey,2009).

What these ideas signify is that perceptual attunement to the dynamic flux of information emerging from the continuous interactions between players in team sports implies the perception of key variables for actions, such as gaps for completing successful passes (Fajen et al.,2009). As highlighted by Arau´ jo et al. (2006), when a performer perceives an opportunity for action, this process is not indepen- dent of the affordances offered by the actions of other players in a specific performance sub-phase.

For example, it has been shown that the decision- making of attacking players in the team sport of rugby union is emergent and predicated on the movements of immediate defenders (Passos, Arau´ jo,

Davids, Gouveia, Milho, et al., 2009; Passos et al., 2008). In the present study, we aimed to extend current understanding of the key variables that constrain the emergence of successful actions in team sports by investigating how spatio-temporal variables influence the emergence of the direction of a pass in futsal. It is important to understand how key spatio-temporal variables emerge from and constrain the ongoing competing and cooperating tendencies of attackerdefender dyads (sub-systems of competing individuals) that are continually formed throughout performance in team sports (McGarry, Anderson, Wallace, Hughes, & Franks, 2002; Arau´ jo et al., 2004; Passos, Arau´jo, Davids, Gouveia, Milho, et al.,2009).

During successful passing performance, the actions of a player in possession of the ball (the ball carrier) require the perception of the dynamic interactions between him/her and the nearest defender (forming a dyad). Successful passing also re- quires the need to perceive the interactions between other attackerdefender dyadic systems during team sport performance. This is because ball carriers and teammates continually move in order to create gaps between defenders for passing the balls, while defenders move to eliminate or reduce the extent of these gaps (Correˆa et al.,2012). In order to study the decision-making of players in possession of the ball concerning where to pass, it was decided to investigate the interacting possibilities for passing and intercepting the ball in players functioning as a dyadic (attackerdefender) system in team sports.

Here we defined a pass as the act of kicking the ball to another player on the same team. Thus, the opportunity to complete a successful pass in this study was designated by an imaginary line (vector) connecting a ball carrier and a teammate. Possibi- lities to intercept a pass involved three specific vectors linking: (1) the ball carrier and the closest defender, (2) the ball carrier and a teammate’s nearest defender, and (3) a teammate and the closest defender. The interaction of each interception vector with the passing vector resulted in three informational variables capturing the inter-personal relationships between the futsal players, which we termed of relative angles. Therefore, we sought to understand the nature of the angular gap that a ball carrier looks for in the team sport of futsal, and how the spatio- temporal changes of an angular gap afford passing direction for the player with the ball.

2. Method

Participants were 24 male professional players (M 30.04 years, SD4.10) who played in the final of the UEFA Futsal Cup 2010 held in Lisbon. All procedures were performed in compliance with the 170 U. C. Correˆa et al.

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guidelines of the American Psychological Associa- tion, and the protocol was approved by the local university ethics committee.

The game was recorded using a digital camera (frequency25 Hz) located above and behind the short axis of a futsal court to capture the displace- ments of all players and the ball. Sequences of play in which passes were performed between outfield players were randomly selected from the beginning to the end of the game, resulting in 37 sequences of play with an average length of 1.56 seconds (SD 1.04). The sequences of play were edited from the moment the ball carrier received the ball until the moment a teammate received his pass (successful passes, n27) or a defender intercepted the in- tended pass to the teammate (unsuccessful passes, n10).

2.1. Data analysis

The selected sequences of play were digitised using TACTO software. This procedure consisted of following with a computer mouse in a slow motion video image (frequency2 Hz) the player’s working point on the futsal court. The working point was an equidistant point between the feet of each player considered as a projection of the centre of gravity of each individual player on the floor (Duarte et al., 2010). These digitalisation procedures allowed ex- tracting virtual coordinates of players’ 2D movement displacement trajectories (Fernandes, Folgado, Duarte, & Malta,2010). Each working point allowed us to identify and track the x and y coordinates of each player’s positions on court. Next the bi-dimen- sional coordinates (also referred to as the ‘virtual’

coordinates) were transformed into ‘real-world’ coordinates using direct linear transformation (DLT2D) software and filtered with a low-pass filter (6 Hz) (Winter,2005). This method considers thez- coordinates to always be equal to zero and directly correlates an object point located in the object space/

plane and a corresponding image point on the image plane (Duarte et al., 2010). After one month, data were re-digitised by the same experimenter to verify intra-analyser reliability. Spearman’s correlation test found high reliability for x and y coordinates (r0.98, andr0.97, respectively).

The players’ displacement trajectories in the sequences of play above mentioned were obtained considering the players as a dyadic sub-system. The proximity of attackers and defenders allowed us to identify four different attacker and defender dyadic sub-systems: dyad 1the ball carrier and the nearest marking defender; dyad 2the ball receiver and the nearest marking defender; dyad 3 the closest teammate who did not receive the pass and the nearest marking defender; and dyad 4 furthest

teammate who did not receive the pass and the nearest marking defender.

Relative angles were calculated for inter-personal relations (IPR) within and between dyads (intra- and inter-dyads) for the ball carrier’s dyad and the remaining three dyads formed on court. Relative angles involving the dyads, including the ball carrier and the ball receiver, were considered as inter-dyads 12 (or passing dyads) and angles involving the ball carrier’s dyad and the remaining dyads were considered as inter-dyads 13 and inter-dyads 14 (or non-passing dyads formed by players who did not receive the pass).

In order to verify which angles may have acted as inter-personal relationship measures that constrained the emergence of passing direction, three relative angles were analysed as a compound dependent variable in each one of the these inter-dyadic relationships (Figure 1). These comprised: the passing vector (imaginary line from the ball carrier to his teammate) and the following ball interception vectors: (1) ball carriernearest defender, (2) ball carrierteammate’s nearest defender, and (3) teammatenearest defender. Each vector was obtained through the equation:

a¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P2xP1x

ð Þ²þðP2yP1yÞ²

2

q

, where ‘a’ refers to the distance between player 1 (P1) and player 2 (P2). Similar procedures were conducted for the other two vectors, resulting in two other distance values being obtained (b and c). The angles denoting the interactions between players were computed according to the equation: Cosua²(b²c²)/

2×b×c, and resulted from the interactions of the passing vector and each of the three interception vectors, such as:

1. Passing vector angle to the ball carriernearest defender’s vector;

2. Passing vector angle to the ball carrierteammate’s nearest defender’s vector;

3. Passing vector angle to the teammatenearest defender’s vector.

All relative angles were recorded from the moment the ball carrier received the ball (initial angle) to the moment he performed the pass (final angle). More- over, we also analysed how relative angles were formed from the initial time of ball reception to the moment of pass initiation. First, we sought to identify the angular temporal constraints on passing direction. Angular velocity (vu) was calculated by vu(uF uI)/t,whereFwas the final angle (when ball carrier performed the pass), I was the initial angle (when ball carrier received the ball), and t referred to the time between both initial and final angles. Second, angular variability analysis considered the values of each angle in each frame from the

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moment the ball carrier received the ball, to the moment that he passed it. Angular variability refers to the variation in the values of each angle, computed by calculating the coefficient of variation (CVs/m), where CV is the ratio of variability, srefers to the standard deviation, andmis the arithmetic mean.

2.2. Statistical procedures

To consider the interactions between players in the performance of successful passes, 32 mixed-model ANOVAs were conducted on data from the A, B and C relative angles to identify main effects of IPR Initial and Final Angles. We also conducted a 33 mixed-model ANOVA for IPRA, B and C relative angle velocities, and for IPRA, B and C relative angle variabilities. In addition, the angles found to be significant in statistical analyses were analysed in relation to passing outcomes (successful and unsuccessful passes) also by a mixed-model ANOVA 22 (AnglesPassing Outcomes). Observed significant effects were followed up using Tukey_HSD post hoc tests. Finally, to identify if there was a critical value for the emergence of passing direction we analysed those angles based on the ball carrier’s time of ball possession. This analysis was made through a KruskalWallis test, and the Bonferroni procedure was used as a follow-up test. All analyses were preceded by ShapiroWilk’s W and Bartlett’s tests of normality and homogeneity of variance. For all analyses the level of significance was set atpB0.05, using STATISTICA^† 9.0 software (Stat Soft Inc., Tulsa, USA).

3. Results 3.1. Relative angles

For angle A, a 32 mixed-model ANOVA (IPR Initial and Final Angles) revealed effects for IPR [F(2, 52)7.43, pB0.01,h²0.22] and for angles [F(1, 26)5.46, pB0.05, h²0.17]. It was observed that this angle increased from time of ball reception to pass initiation (pB0.02), and that passing dyads displayed a greater angle value than the non-passing dyads (pB0.01) (Figure 2a).

Concerning angle B, a 32 mixed-model ANO- VA (IPRInitial and Final Angles) revealed the following significant effects: IPR [F(2, 52)5.24, pB0.01, h²0.17], angles [F(1, 26)8.55, pB 0.01, h²0.24] and interaction [F(2, 52)3.93, pB0.02,h²0.13]. Post hoc testing showed that the passing dyads displayed a greater initial angle than non-passing dyads 13 and, a greater final angle than the other non-passing dyads (pB0.01). It was also observed that there was an increase in the value of angle B only for passing dyads (pB0.01).

Finally, for angle C no statistically significant differences were found.

The 33 mixed-model ANOVA (IPRA, B and C Velocities) found significant differences only for IPR, F(2, 50)3.94, pB0.05, h²0.13. Post hoc testing showed that the angular velocity was greater in inter-dyads 12 than in inter-dyads 13 (pB0.05) (seeFigure 2b).

Finally, 33 mixed-model ANOVA (IPRA, B and C’ Variabilities) found effects for IPR, F(2, 50)3.79,pB0.03,h²0.13, and for relative angle

Attack

Dyad ball carrier

Dyad ball receiver

Attack

Dyad ball carrier

Dyad ball receiver

Attack

Dyad ball carrier

Dyad ball receiver

C

a b c

A

B

Non-passing dyad

Figure 1. Illustration of the angles analysed: (a) Passing vector angle to the ball carriernearest defender’s vector; (b) passing vector angle to the ball carrierteammate’s nearest defender’s vector; and (c) passing vector angle to the teammatenearest defender’s vector.

172 U. C. Correˆa et al.

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variabilities, F(2, 50)5.39, pB0.01, h²0.17.

Post hoc analysis showed that the angles A and B were more variable than angle C (pB0.05). Post hoc analysis also showed that the inter-dyads 12 varied less than inter-dyads 13 (pB0.05) (Figure 2c).

3.2. Passing outcomes

Since previous results showed that pass direction was constrained by the final angles A and B and their velocities and variabilities ratio, these two angles were analysed investigating passing outcomes (i.e.

successful or unsuccessful). Therefore, 10 successful passes were randomly selected from the 27 passes to compare them with the 10 unsuccessful passes.

The 22 mixed-model ANOVA (Passing Out- comesAngles) revealed effects for passing outcomes [F(1, 18)8.48, pB0.01, h²0.32], angles [F(1, 18)11.96, pB0.01, h²0.39] and interaction [F(1, 18)6.48, pB0.05,h²0.26]. Post hoc tests showed that in successful passes, angle A was greater than angle B (pB0.01). Moreover, in successful passes angle A was greater than in unsuccessful passes (pB0.01) (Figure 3a).

Concerning the angular velocity, no significant differences were found. Finally, mixed-model 22 ANOVA (Passing OutcomesVariabilities) found

main effects for angular variability [F(1, 13) 6.47, pB0.05, h²0.33] and passing outcomes [F(1, 13)0.43, pB0.05, h²0.36]. Post hoc testing showed that the successful passing angles were less variable than unsuccessful passing angles (pB0.05), and that A angles were less variable than B angles (pB0.05) (Figure 3b).

3.3. Time of ball possession and angular measures In order to investigate the constraint of time of ball possession on the emergence of passing direction, we analysed the dynamics of A and B angles from the time of ball reception until the pass was initiated.

Trials ranged from 0.08 to 4.12 seconds and were divided into four groups (G1, G2, G3 and G4), ordering data from lowest to highest values, and adopting quartiles as the cut-off points (Altman &

Bland,1994).

KruskallWallis ANOVA showed no significant differences in A and B angles between the different subgroups analysed. Similarly, no statistically significant differences were found for angular velocities of A and B. Differences were revealed in the variability of A [H(3, N26)12.07, pB0.01]

and B [H(3, N26)10.66, pB0.05]. Post hoc tests showed that angle A was less variable in G1

Inter-Dyads 1-2

Inter-Dyads 1-3

Inter-Dyads 1-4 -20

-15 -10 -5 0 5 10 15

Angular Velocity (o/s)

A B C

Angles 0,0

0,1 0,2 0,3 0,4 0,5

Coefficient of Variation

Inter-Dyads 1-2 Inter-Dyads 1-3 Inter-Dyads 1-4

(b) (c)

Initial Angles

A B C

0 10 20 30 40 50 60 70 80 90 100

Angle (o)

Final Angles

A B C

Inter-Dyads 1-2 Inter-Dyads 1-3 Inter-Dyads 1-4

(a)

Figure 2. (a) Means of A, B and C angles of inter-dyads 12, 13 and 14; (b) means of angular velocities of inter-dyads 12, 13, and 1 4; (c) means of variability of A, B and C angles of the inter-dyads 12, 13 and 14.

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than in G4 (pB0.05). Bonferroni’s procedures also showed that angle B was less variable in G1 than in group G4 (pB0.05).

4. Discussion

This study aimed to investigate how physical variables capturing the players’ inter-personal coordination tendencies in the team sport of futsal constrained the emergence of passing direction.

Specifically, we aimed to investigate how spatial and temporal variables related to the angular dynamics of a ball carrier positioning relative to other players on court (both teammates and opponents) constrained the emergence of passing direction in futsal.

Passing vector angles for the ball carriernearest defender’s vector (A) and passing vector angles for the ball carrierteammate’s nearest defender’s vector (B) seemed to act as angular spatial information that constrained the emergence of passing direction.

Results showed that at the instant of pass initiation, passing dyads (12) displayed higher values of A and B than the remaining dyadic relations (13 and 14).

This result implies that the ball carrier was attuned to the angular relations (A and B) that were established with each dyad, and decided to pass the ball in the direction of the relative angle with a higher value (a mean value of 708for A and 318for B).

Moreover, temporal information of A and B angles seemed to have also constrained passing direction emergence. More precisely, the ball carrier seemed to pass the ball towards dyads which had higher velocities of these angles, that is, positive rates of change. This finding implies that the supporting teammates should continuously move in order to increase the passing vector angles to (1) the ball carriernearest defender vector and (2), the ball carrierteammate’s nearest defender vector, and afford a passing opportunity. This temporal variable

appeared to have provided information to the ball carrier about the difficulties that both defenders were experiencing in attempting to intercept the ball, affording him the possibility to pass the ball.

Lower levels of variability observed in A and B angles for dyadic system relations 12 (the ball carrier and the ball receiver dyads) compared to dyadic system relations 13 and 14 (non-passing dyads) suggest that this information acts as a constraint on the ball carrier’s decision-making when passing the ball. The variabilities in these relative angles may have implied in a high level of uncertainty, and hence in the perceived risk of an interception of a pass, constraining the ball carrier to maintain ball possession and/or searching for more safe options for passing the ball.

Analyses of passes suggested that although players used information from the A and B angles (that they established with different dyads on court) to decide where to pass the ball, A was the specifying variable for successful or unsuccessful passes. This finding suggests that attackers and defenders should re- attune their perceptual systems (Fajen et al., 2009) towards the information from the passing vector angle to the ball carriernearest defender’s vector, to pass or to intercept the ball, respectively.

Since passes were performed after different times of ball possession and no differences were found between them in both angles of inter-personal relationships (passing vector angles to (A) the ball carriernearest defender vector and (B) the ball carrierteammate’s nearest defender vector), it could be suggested that the ball carrier needs to seek specific values of angles A (708) and B (318). Like previous studies (e.g., Duarte et al., 2010; Passos, Arau´ jo, Davids, Gouveia, Milho, et al.,2009; Passos et al.,2008), the existence of critical values for the emergence of passing direction could be interpreted as a region of self-organised criticality. In such a region of team game performance as a complex

Unsuccessful Successful -10

0 10 20 30 40 50 60 70 80 90 100

Angle (o)

A Angle B Angle

(a)

Sucessful Unsuccessful -0,1

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Coefficient of Variation

A Angle B Angle

(b)

Figure 3. (a) Means of A and B angles of successful and unsuccessful passes; (b) mean of variability of A and B angles of the successful and unsuccessful passes.

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system, it becomes located at the border or edge of chaos prompting creation, innovation and evolution in the actions of system agents (Kauffman, 1993;

Langton,1992; Packard,1988).

Results suggested that to maintain ball possession, attackers should be synchronised in both spatial and temporal dimensions of their interpersonal cooperation tendencies. Ball carriers should not only perceive spatial relations that are established with teammates and opponents, but also the temporal changes in these measures, acting as informational constraints that support prospective control of affordances in passing direction. In fact, recently studies have highlighted the constrain influence of spatio- temporal variables on the performance and decision- making in the game of futsal (Travassos, Arau´ jo, Vilar, & McGarry,2011; Travassos et al.,2012; Vilar et al., 2012). For instance, Travassos et al. (2012) showed evidences that the defender’s velocity relative to the ball’s trajectory constrains the interception of passing ball in the game of futsal. This view supports the assumptions of ecological dynamics that inter- player coordination is regulated by spatio-temporal information available from the performance environment through a process of perceptual attunement (Correia et al., 2011; Fajen et al., 2009; Jacobs &

Michaels,2007).

In summary, the findings of this research study allowed us to conclude that passing direction in the team game of futsal emerged from interpersonal interactions of performers, specifically related to two angles involving: (1) the passing vector and ball carriernearest defender’s vector (708) and (2) the passing vector and ball carrierteammate’s nearest defender’s vector (318). And that the emergence of both relative angles involved a greater positive angular velocity and a lower angular variability.

These findings allowed us to conclude that passing direction emerged from critical values of these key compound motion measures of performer interactions in the team sport of futsal. In terms of practical implications, they point to how to develop the ability of futsal players to make decisions regarding where to pass based on information from the inter-personal angular interactions. For example, small-sided practice games could be used in order to provide an opportunity for futsal players to pick up information such as rates of change in angles between teammates and opponents.

Concerning the study’s limitations three aspects warrant further investigations: (1) the angular constraints on the emergence of passing direction in the team sport of futsal should also be analysed considering the goalkeeper as an attacker. For example, it is common in decisive moments of a futsal game the goalkeeper to play outside of goal area, as an

outfield player. In such a situation the goalkeeper provides an additional possibility for passing; (2) the angular constraints on the kind of passing emergence should be investigated in order to identify key spatio-temporal variables that act as informational constraints on action in team games. Our methodo- logical procedures were delimited to a bi-dimen- sional analysis. However, in a game of futsal the passes might also be performed involving thez axis (e.g. passes with parabolic ball trajectory); and (3) the angular relationship should be focused from perspective of the other players. In the present study, three specific angular relations were investigated based on the interaction of passing and intercepting possibilities from the perspective of who decide for where to pass the ball carrier. However, because both of these possibilities were formed considering the attackers and defenders as dyadic sub-systems, other angular relations than those A, B and C could provide an additional understanding of the passing in the game of futsal. As previously described, ball carrier’s teammates also continually move in order to create passing possibilities. In this case, how they would deal with the angular relations with the aim of facilitate the pass? On the other hand, what and how angular relations would constrain the defenders to eliminate or reduce the passing possibilities?

Acknowledgements

This research was supported by the Capes Foundation, Ministry of Education of Brazil (BEX 3243/10-9), awarded to the first author. The authors wish to thank Prof. Ms. Se´rgio Aparecido dos Santos for his mathematic support.

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