Journal of Sports Sciences, 2012; 30(5): 459–469
Constraints on competitive performance of attacker–defender dyads in team sports
Luís Vilar, Duarte Araújo, Keith Davids & Bruno Travassos
Introduction
Performance analysis in team sports has emphasized use of notational analysis methods, which attempt to identify time-discrete parameters associated with key performance outcomes (e.g. Hughes & Bartlett, 2002; Hughes & Franks, 2005). While worthwhile, such general methods tend to provide performance information of a descriptive nature and have been criticized for lacking a theoretical focus to explain performance behaviours such as decision making for action (see Davids, Araújo, & Shuttleworth, 2005; Glazier, 2010). More recently, ideas from ecological dynamics have been advocated to explain individual/ team performance by identifying stability, variability, and transitions among coordinative states of beha- viour (Arau ́jo, Davids, & Hristovski, 2006; Davids, Handford, & Williams, 1994; Handford, Davids, Bennett, & Button, 1997).
Ecological dynamics suggests that functional performance behaviours (decisions and actions) emerge from the interactions of individuals under task and environmental constraints over time (Arau ́jo et al., 2006). Due to the complementary relations between players and their performance environment, the control of behaviour is located at the player–environment system level (Fajen, Riley, & Turvey, 2008).
Interpersonal interactions in team sports have been studied by analysing couplings in attacker–defender dyadic systems (McGarry, Anderson, Wallace, Hughes, & Franks, 2002). Although these studies have typically analysed performance during practice tasks, they have revealed spatial interpersonal patterns in team sports, such as basketball (Arau ́jo, Davids, Bennett, Button, & Chapman, 2004; Bourbousson, Seve, & McGarry, 2010a; Davids, Button, Arau ́jo, Renshaw, & Hristovski, 2006) and rugby union (Passos et al., 2008; Passos et al., 2009).
Sport performance constraints change over time, leading to instabilities in states of system coordination (Arau ́jo & Davids, 2009). When an attacker in team sports dribbles/runs past a defender with the ball, a system phase transition may occur, with another stable coordinated pattern of behaviour emerging (Arau ́jo et al., 2004). Phase transitions in dyadic systems, therefore, can lead to changes in spatial structural organization of team games cap- tured by the appearance and disappearance of offensive and defensive patterns of play.
A challenging issue for this area of work is that task constraints differ across team sports. For example, players may run with the ball in their hands (e.g. rugby union), dribble a ball with the hands (e.g. basketball) or with the feet (e.g. futsal, a 5-a-side indoor football game). Bourbousson and colleagues (2010a) used relative phase to examine coordination between displacement trajectories of attacker– defender dyads in basketball. These authors found that longitudinal (y) axis trajectory data demon- strated attractions to in-phase patterns or 08 (i.e. both players in a dyad moved closer/further from the same goal-line at the same time) and strong repulsions from anti-phase relations or 1808 (i.e. both players in a dyad moved in opposite directions at the same time). However, lateral displacement (side-to-side lines) data demonstrated a bi-stable distribution to in-phase and anti-phase mode. Their findings imply that key informational variables, such as the location of the goal and the ball, may be important constraints shaping the specific coordination dynamics that emerge between performers (Davids, Button, & Bennett, 2008).
Support for this view comes from other research on 1 vs. 1 sub-phases in team sports analysing the influence of a goal/target area’s location. For example, Arau ́ jo and colleagues (Araújo et al., 2004; Davids et al., 2006) analysed spatial measures, such as the distance to the basket of an attacker and defender, and found that a phase transition in that variable precipitated a scoring event. However, a goal could also be scored merely as a consequence of instabilities in a defender’s alignment between the goal and an attacker’s position. Thus, analysis of pattern-forming dynamics in team sports needs to consider both players’ relative distances and angles to a goal as informational constraints on attacker– defender dyads. Passos and colleagues (2009) observed the importance of attacker–defender angu- lar relations (i.e. spatial measures) relative to the try-line in rugby union. However, in many team sports, such as netball, lacrosse, and futsal, the goal area is not a perpendicular line running along the field, but a specific target area located in its middle, such as a bounded net.
Furthermore, there is a need to examine spatial relations that constrain pattern-forming dynamics in team sport players during competitive performance, such as in an international championship. In competitive performance, the existence of more than one defender is a distinct constraint that is likely to be a major influence on the coordination dynamics capturing the interpersonal interactions in attacker-defender dyadic systems. During competitive per- formance in team games, it is expected that more than one sub-system phase transition needs to occur in the displacement of an attacker and defender with respect to the location of the goal and ball, because defending teammates can forge new couplings when an attacker successfully breaks symmetry with an immediate defender.
The aim of this study was to advance existing knowledge by developing an understanding of how the specific location of the goal and ball during team game performance constrains the coordination dynamics of an attacker–defender dyad in a 5 vs. 5 futsal match. To achieve this, we analysed the spatial coupling of players in a dyad with respect to the relative distance and angle to the goal and ball during competitive performance. Instead of describing players’ actions using performance statistics, we attempted to explain players’ behaviours during successful performance by examining how they use critical sources of information from their perfor- mance environment, such as the locations of their opponents, the goal, and the ball. We also analysed one exemplar trial in which an attacker was responsible for scoring a goal. This approach not only allowed us to compare our data with previous research on 1 vs. 1 team games sub-phases, in which the sole attacker was responsible for the shot at goal, but also to illustrate how researchers and practitioners can examine phase relations in each dyadic system.
Methods
This study was conducted within the guidelines of the American Psychological Association and the protocol received approval from a local university ethics committee.
Data collection
Data were recorded from ten futsal games between five national teams in the 2009 Lusophony Games. A digital camera located above and behind the short axis of a futsal court was used to film each game. Thirteen sequences without transitions in ball possession were randomly selected for movement analysis from all the sequences that ended in a goal being scored (n 1⁄4 79). In futsal, the clock stops every time the ball goes out of the court or the referee identifies a foul. Therefore, the selected data sequences were timed from moment of the last clock interruption before a goal was scored to the moment the ball entered the goal. Within each randomly selected sequence of play, displacement trajectories of four attacker–defender dyads formed by outfield players were analysed, giving 52 trials in total. Each player was identified in all analyses as described in the caption to Figure 1.
Data analysis
Digital video footage was digitized at 25 Hz with TACTO software. This procedure consisted of following a selected working point with a mouse cursor in slow video motion analysis of performance. The working point selected was the middle point between the feet of each player, since this point represents the projection of the player’s centre of gravity on the ground (Duarte et al., 2010). This process allowed conversion of player displacement trajectories into pixel coordinates. Next, two-dimen- sional DLT (direct linear transformation) files were produced and used to convert pixel coordinates into actual coordinates (calibrated in metres). This method considered the z-coordinates always to be equal to zero and directly correlated an object point located in the object space/plane and a correspond- ing image point on the image plane. Finally, data were filtered using a Butterworth low-pass filter (6Hz) (Fernandes, Caixinha, & Malta, 2007). The bottom left corner of the futsal court was assigned zero coordinates, and the length of the field or longitudinal direction was assigned to the y-axis, while the x-axis represented the width or lateral direction of movement (Figure 1).
Time-series data were obtained for each player and ball position, according to the x- and y-coordinates on the field. The distance of all field defenders to all field attackers was then calculated, as well as the position of the closest defender to each attacker in each time frame (i.e. the attacker–defender dyads were established). Next, we computed the distance of each player to the ball and to the centre of the goal, and the angle of each player to the ball and the centre of the goal (see Figure 2).
These variables were chosen to determine the constraining influence of the ball and the goal, to reveal spatial measures (i.e. distances and angles) identified in previous research. While the distance variable captured the proximity between the players to the ball or the goal, the angle measure revealed the alignment/misalignment be- tween players to the ball or the goal during performance. The angle to the goal was defined by the angular relation that each player attained with the centre of the goal line. Therefore, we recorded the angle between the vectors: (i) player–centre of the bottom goal and (ii) centre of the bottom goal–left bottom corner. For example, the player closest to the bottom left corner of the field attained an angle near 08, and the player closest to the bottom right corner attained an angle near 1808. The angle to the ball was 08 when the player–ball line was parallel to the goal line. When the player–ball line was perpendicular to the goal line, and the player was further away from the goal than the ball, the angle was computed as 908. When the player–ball line was perpendicular to the goal line and the player was closer to the goal than the ball, the angle was designated as 7908.
Relative phase plots were used to capture stabilities and instabilities in attacker–defender phase relations as well as phase transitions in a given data sequence. Relative phase was calculated using the Hilbert transform (see Palut & Zanone, 2005) of perfor- mance data of an attacker and the closest defender, from each of four variables: distance to goal, angle to goal, distance to ball, and angle to ball. Given the circular (360º) nature of relative phase, values of -270º, 90º, 450º, and other 360º multiples all represented the same phase relation: a quarter-phase in this example. Frequency histograms were plotted using the same methods as Bourbousson et al. (2010b). By forcing the dynamics of relative phase into -180º and 180º limits, the frequency histograms represented the instantaneous phase relations between the defined variables. All data were computed in MATLAB R2008a.
Statistical procedures
The relative phase histogram data of each variable were subjected to repeated-measures analysis of variance (ANOVA), to compare the amount of time that an attacker and defender were coordinated in each phase range. The sphericity assumption of the variables was checked using Mauchly’s test of sphericity. When a violation of this assumption was apparent, the Greenhouse-Geisser correction proce- dure was used to adjust the degrees of freedom. Any significant effects were followed up using Bonferroni post-hoc tests. Statistical significance was set at p < 0.05. All statistical analyses were computed using SPSS v.16.0 software (SPSS Inc., Chicago, IL).
Intra- and inter-rater assessment
One of the 13 goal sequences subjected to data analysis was selected at random and the displace- ment trajectories of the ball and players (n=11) re-digitized by the same experimenter (intra-rater assessment) and by a different experimenter (inter- rater assessment). The data were then assessed for accuracy and reliability using the technical error of measurement (TEM) and coefficient of reliability (R) (Goto & Mascie-Taylor, 2007). The intra-TEM measure yielded values of 0.012 m (0.135%), 0.010 m (0.074%), and 0.024 m (0.095%) for data on positioning of attackers, defenders, and the ball, respectively. The coefficient of reliability for the intra-rater assessment showed high reliability of the data for the attackers (R > 0.999), defenders (R > 0.999), and ball (R > 0.999). The inter-TEM measure yielded values of 0.015 m (0.133%), 0.019 m (0.288%), and 0.006 m (0.103%) for data on positioning of attackers, defenders, and the ball, respectively. The coefficient of reliability showed high reliability of the data for the attackers (R > 0.999), defenders (R > 0.999) and ball (R > 0.999).
Results
In this section, for brevity, we present one figure for each of the four variables analysed. On the left-hand side of each figure we present a trial from one exemplar dyadic system, in which the attacker (#5) scored a goal. Following Bourbousson et al. (2010a, p. 7), our goal was to illustrate how researchers and practitioners might observe stabilities (maintenance of relative phase within a specific range of coordina- tion), instabilities (relative phase drifts into a wider range of coordination without acquiring new states of stability), and phase transitions (relative phase changes of a specific range of coordination) in an exemplar dyadic system. The right-hand side of each figure represents data from all attacker–defender dyadic systems (n-52). Moreover, we present a table for each of the four variables analysed, reporting the post-hoc statistical analysis for the preferred mode of coordination of attacker and defender.
Relative position to the goal
Analysis of players’ distances to the goal showed that the defender appeared always to be closer to the goal than attacker #5. As play evolved, the distance of both the attacker and defender to the goal decreased until, towards the end of the sequence of play, the values were very similar (see exemplar data in Figure 3A). Data show three stable temporal plateaux in an in-phase mode of coordination during the sequence (from the beginning to 24 s, from 24 s to 33 s, and from 34 s until the end) (see exemplar data in Figure 3B). For the 52 trials analysed, repeated-measures ANOVA reveals significant dif- ferences in the pattern of coordination of attacker and defender distances to the goal (F(2.07,105.49)=58.71, p < 0.001; see Figure 3C). Post-hoc testing revealed that the time spent between -30º and 29º modes of coordination was significantly higher than in any other coordination mode. Moreover, the time spent in the phase range of 30º through 59º was significantly higher than in the -180º through -61º and 60º through 180º ranges. Finally, the time spent in the phase range of -60º through -31º was significantly higher than in the -180º through -61º and 120º through 180º ranges (see Table AI).
Analysis showed the players’ angles to the goal to be similar during the sequence, suggesting that the defender tried to remain between attacker #5 and the centre of the goal. However, towards the end of the sequence, the angular differences of both players relative to the goal increased, suggesting that a misalignment of the defender’s position in between the attacker and the centre of the goal may have precipitated a successful shot on goal (see exemplar data in Figure 4A).
The coupling dynamics between variables showed two stable temporal plateaux of an in-phase mode of coordination (from the beginning to20 sandfrom21 suntil38 s).Near the end of the play we identified the presence of system fluctuations and an order–order transition (see exemplar data in Figure 4B). Repeated-measures ANOVA reveals significant differences in the pattern of coordination of attacker and defender angles to the goal (F(1.85,94.36)=50.91, p < 0.001; see Figure 4C). Post-hoc testing revealed that the time spent between 0º and 29º modes of coordination was significantly higher than in any other coordination mode. Moreover, the time spent in the phase range of -30º and -1º was significantly higher than in the phase ranges of -180º through -31º and 60º through 180º. Finally, the time spent in the phase range of 30º and 59º was significantly higher than in the phase ranges of -180º through -61º and 60º through 180º (see Table AII).
Relative position to the ball
During the exemplar sequence, the distance to the ball of attackers and defenders remained similar. However, when the distance of attacker #5 to the ball decreased to near 0m (at 4s, 10s, 14s, 28s, 36s, and 38s), the defender’s distance to the ball was never less than 3 m (see exemplar data in Figure 5A). Moreover, analysis of the coupling dynamics re- vealed the existence of three stable temporal plateaux of an in-phase mode of coordination (from the beginning until 19 s, from 23 s until 32 s, and from 34 s to 37 s). System fluctuations were also evident between 19s and 23s, between 32s and 34s, and at 38s (see exemplar data in Figure 5B). Repeated-measures ANOVA revealed significant differences in the pattern of coordination of attacker and defender distances to the ball (F(2.39,122.09)= 55.07, p < 0.001; see Figure 5C). Post-hoc testing revealed that the time spent between -30º and 29º modes of coordination was significantly higher than in any other coordination mode. Finally, the time spent in the phase ranges of -60º and -31º and of 30º and 59º was significantly higher than in the phase ranges of -180º through -61º and 60º through 180º (see Table AIII).
The defender’s angle to the ball was predominantly smaller than that of the attacker, suggesting that the defender was always further below the imaginary line of the ball than attacker #5 (see exemplar data in Figure 6A). More precisely, the angle relative to the ball of attacker #5 and defender exhibited similar values for some periods of time (e.g. between 17 s and 28 s), suggesting that the defender was in between the ball and attacker #5. However, there were other moments at which both players showed differing values (4s, 10s, 14 s, 28 s, 36 s, and 38 s). These might reveal the periods of time in which attacker #5 had possession of the ball, and the ball was in between attacker #5 and the defender. However, on attacker #5’s last ball possession (38 s), the defender was not in front of the ball carrier and a goal was scored. Coordination dynamics analysis showed stable phase relations in an in-phase mode of coordination (e.g. between 19 s and 28 s), and also some phase transitions to an anti- phase mode of coordination. The latter occurred at 4s to 180º, at 10s to -180º, at 14s to -540º, at 28s to -900º, and at 36s to -1260º (see exemplar data in Figure 6B). Repeated-measures ANOVA revealed significant differences in the pattern of coordination of attacker and defender angles to the ball (F(3.44,175.27)=40.67, p<0.001; see Figure 6C).
Post-hoc testing revealed that the time spent between 08 and 298 modes of coordination was significantly higher than in the phase ranges of -180º through -31º and 30º through 180º. Moreover, the time spent in the phase range of -30º and -1º was significantly higher than in the phase ranges of -180º through -31º and 60º through 180º. Finally, the time spent in the phase range of 30º and 59º was significantly higher than in the phase ranges of -180º through -61º and 60º through 180º (see Table AIV).
Discussion
The primary goal of this study was to determine how interpersonal coordination between an attacker and defender was constrained by the location of the ball and goal in the team sport of futsal. In addition, we identified phase transitions in dyadic systems when a goal was scored to enhance understanding of interpersonal coordination during competitive performance in team sports. Results showed that stable patterns of coordination emerged from changes to both the distances and angles of attackers and defenders to the goal (Araújo et al., 2006). Moreover, individual analysis of coordination patterns showed that, in the given example, while the attacker was in possession of the ball, and the defender was between the goal and attacker, symmetry between the players was maintained (Araújo et al., 2004). Under these task constraints, in order to break system symmetry and score a goal, attacker #5 used lateral displacement to increase the angle to the goal relative to the defender’s position, while decreasing the distance to the goal. In contrast, the defender tried to maintain a stable relation between the distance and angle to the goal relative to those of attacker #5, in order to intercept the ball and block shots. These findings extend the data of Passos and colleagues (2009) to task constraints where the aim was not to carry the ball in the hands towards a perpendicular area across the field (in rugby union), but instead to dribble and shoot the ball at a specific target. This example demonstrates that in the team sport of futsal, a defender might not always seek to coordinate the lateral displacement trajectory with the attacker, because of the constraint to remain between the attacker and the goal, and not just right in front of the attacker. Although this observation might be expected to be generalizable, it would be interesting to analyse this coordination process in other team sports with different task constraints, such as association football (11-a-side).
As the sequence of play evolved towards the goal, the defender’s efforts to maintain system stability were often insufficient and critical fluctuations precipitated more than one phase transition. States of system stability were shorter, providing attacker #5 with opportunities to score goals. These findings build on the work of Araújo and colleagues (Araújo et al., 2004; Davids et al., 2006) by showing that, in 1 vs. 1 sub-phases in futsal, order-order transitions need to emerge in more than one dyadic sub-system for a goal to be scored. This finding was related to the presence of more defenders in the competitive game phases we observed. Only when symmetry-breaking processes emerged near the goal, and the defenders did not have the collective ability to re-establish dyadic system stability, did a goal opportunity present itself. Results showed a goal was scored when the distances to the goal of attacker and defender were very similar but their relative angles to the goal were slightly different. Despite critical fluctuations being observed in the interpersonal coordination of the exemplar dyadic system agents, only the players’ angles to the goal tended to show a phase transition. The observation of this dyadic system extends understanding of the work of Araújo and colleagues (Araújo et al., 2004; Davids et al., 2006) in basketball, who proposed that a phase transition in the players’ relative distance to goal needs to occur for a basket to be scored. Our results suggest that analysing both the players’ relative distances and angles to the goal at the same time is a useful method to understand how goals are scored in team sports such as futsal.
Our results also suggest that the attacker’s and defender’s distances and angles to the ball were attracted to an in-phase mode of coordination. However, an anti-phase pattern of coordination between the players’ angles to the ball also emerged between them when the attacker received the ball. This might be because the ball was typically located between an attacker and defender. Moreover, the phase relation between the players’ distances to the goal showed a similar frequency in the -30º bin (29%), suggesting that the dyadic system coupling may have been led by the attacker’s distance to the ball by one-twelfth of a cycle (Palut & Zanone, 2005). This observation suggests that the attacker was being more proactive in attempting to destabilize the dyad, whereas the defender’s movements were more reactive in attempting to maintain system stability. In the exemplar data, when the attacker’s distance to the ball was near to 0 m (i.e. when dribbling the ball: 4s, 10s, 14s, 28s, 36s, and 38s), the defender maintained a critical distance to his opponent. This finding may illustrate the defender’s perception of his positional advan- tage relative to the goal, which he wished to preserve. This result supports Passos and colleagues’ (2008) conclusions on the importance of the defender remaining a critical interpersonal distance to a ball carrier to prevent dyadic system instabilities emerging and phase transitions in the sport of rugby union.
During performance in the exemplar trial, the defender’s angle relative to the ball was lower than that of the attacker. This observation may have been due to the goal constraint, i.e. due to the defender’s precise positioning between the attacker and the goal. As with the players’ interpersonal relations relative to the position of the goal, as the sequence evolved, the stable plateaux of phase relations decreased their duration, possibly reflecting an imminent opportunity for the attacking team to score. Towards the end of a sequence, the defender was not able to maintain the symmetry between his values for distance and angle to the ball with those of attacker #5. Because the coordination of dyadic systems became unstable near the goal, the system tended to transit to a different state of coordination (Araújo et al., 2006) where attacker #5 was able to shoot at goal without the defender blocking the shot, and increasing the likelihood that a goal would be scored.
Conclusions
This study has provided an alternative to traditional descriptive analysis of performance in team sports. Ecological dynamics allowed us to explain how players in futsal regulate their performance by using information about their relative positioning to the nearest opponent, goal, and the ball.
Our results show that the location of the ball did not appear to exert as much of an influence on coordination of players in dyadic systems as did location of the goal. This may be because the primary objective of attackers and defenders is to score and prevent goals respectively, and not just to maintain or regain ball possession. From individual analysis of the interactions in one exemplar dyadic system, we observed that a stable state of coordination emerged when the attacker’s distance to the ball was less than that of the defender, and the defender was closer to, and between, the attacker and the goal. One may argue whether, to score a goal in futsal, attackers need to induce a symmetry-breaking process with opponents by gaining positional advantage (i.e. changing the angular and distance relationship with defender relative to the goal), while maintaining ball possession. Because our goal was to study the importance of simultaneously considering the constraining influ- ences of distances and angles of the players to the ball/goal, it is possible that these variables contained some interdependence. Having established their importance in performance, further research is needed to examine the dependence between these variables during competitive performance.
This study has implications for applied practice/ coaching in team sports like futsal. Traditionally, practitioners have sometimes inadvertently removed from their practice task designs critical sources of information that players use to control their actions, such as the opponents (e.g. in static shooting drills), the goal (e.g. in keep ball possession drills), and the ball (e.g. in some conditioning exercises). Instead, we propose that the coach should carefully manipulate these constraints (e.g. number of opponents, locations of the ball and goal) not only to facilitate the appropriate detection and use of information by the players, but also to increase opportunities for transfer of functional behaviours to the competitive performance environment.
Acknowledgements
The first author was supported financially by a grant from the Portuguese Foundation for Science and Technology (SFRH/BD/43251/2008).
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