Improving interpersonal coordination skills is a key issue for tactical performance in team sports (Menuchi et al., 2018; Passos et al., 2016). However, it has not received enough attention in the sports science literature (Sarmento et al. 2017; 2018). This indicates that its practice is not guided by scientific knowledge but is mainly based on the preferences of coaches.
Team sport competitions have been conceptualized as complex dynamical systems composed of many interacting parts (e.g., Davids et al., 2005). A dynamical systems approach to sport performance describes how patterns of coordinated movement form, emerge, persist, and change. It builds on the insight that teams, as social systems, consist of many interacting parts, endowing them with a capacity for spontaneous pattern formation or selforganization. The spontaneous creation of coherent macroscopic patterns (e.g., group or team coordination) is important scientifically, and the resulting macroscopic patterns of the dynamics of one or a few collective variables or order parameters can be studied carefully (e.g., dyadic relative phase, Travassos et al., 2011; or cluster phase, Duarte et al., 2013), without needing to record all of the microscopic states of the individual parts (e.g., the movement of each player; see Araujo and Davids, 2016).
Beyond the focus on operational measures and performance descriptors, interpersonal coordination benefits from theoretical guidance for the generation of hypotheses, interpretation of data, and design of interventions, including the design of learning equipment. The theoretical framework of ecological dynamics (Araujo and Davids, 2016) recognizes the "flexibility" of social systems (i.e., teams), and its principles can explain how the same performance outcomes can emerge from different behavioral patterns. Namely, the framework hypothesizes that team behavior, as a social synergy, emerges by means of self-organization, as a consequence of players' perceptual attunement to shared affordances (Silva et al., 2016).
However, it is interesting to note that research has focused mainly on dyads (e.g., McGarry et al., 2002; Travassos et al., 2011) or, more sporadically, on clusters of entire teams (Duarte et al., 2012; Lopez-Felip et al., 2018). The processes of interpersonal coordination for dyads and team clusters have commonalities, as well as distinctive characteristics. These distinctions led to a research program specifically focused on interpersonal coordination in small groups, namely groups of three players or triads. Specifically, triadic coordination patterns are a key component in the understanding of complex collective behavior in soccer games (Ramos et al., 2017; Yamamoto and Yokoyama, 2011). Research shows that these are among the most common coordination patterns during a soccer match. In rapidly changing game situations, players need to maintain different types of dyadic and triadic coordination (Ramos et al., 2017). From the perspective of a player, triadic coordination is the maintenance of two types of dyad coordination (Yokoyama and Yamamoto, 2011), and it is a key coordination pattern during a match.
Based on coupled oscillators as complex dynamical systems, Yokoyama and Yamamoto (2011) predict the synchronization patterns of rings of three coupled players during a three-versus-one ball possession task. The players' synchronization was given by the three angles of the triangle made by the three players' positions. The authors found that two types of synchronized patterns conformed to two of the three patterns predicted by the symmetric Hopf bifurcation theory. In a dynamical system, a Hopf bifurcation is a critical point where a system's stability switches and a periodic solution arises (Stewart and Golubitsky, 1992; Strogatz, 1994). One of these patterns was a rotation pattern (R) in which the phase differences among the three angles (adjacent oscillators) were almost equal to 2[pi]/3. This means that one of the angles of the triangle constructed by three players was larger than the other two angles, with a constant interval. The other pattern was a partial anti-phase pattern (PA) in which two of the angles were in anti-phase and the third angle frequency was null. The typical situation in this null frequency pattern is that the distance between two players (e.g. Player A and Player B) is kept constant, and the other player (Player C) moves on the arc line between two players (Players A and B).
Skill level in interpersonal coordination has also been found to play the role of a bifurcation parameter. Specifically, expert players tend to show R patterns more often than novice players did. In a follow-up study, Yokoyama et al. (2018) use mathematical simulations to examine how different expressions of interpersonal coordination, based on players' social synchronization skills, influence how they perform the same three-versus-one soccer task. The authors postulate three kinds of "forces" that underlie these social synchronization skills: spatial, avoiding, and cooperative forces. From their simulation data, they find that the so-called "cooperative social force" has a very important role in the interpersonal coordination of experienced players, though the specifics of this role are not addressed. Building on these results, Yokoyama et al. (2018) further develop a prototype three-elastic-bands tool that physically (haptically) facilitates players' perceptions of interpersonal coordination. Experimental results show that the threeelastic-bands tool influences novice players' relative positions, namely, the inner angles of the triangle formed by the three players. This same tendency is found among the expert players who master the "cooperative social force" skill.
However, it is not clear if and how these changes improve interpersonal coordination, leaving the effectiveness of this three-elastic-bands tool in question. The results of the simulations by Yokoyama et al. (2018) indicate that the use of this tool may increase the frequency of the R synchronization pattern and may decrease the frequency of the PA synchronization pattern. Specifically, if the strength of cooperative forces is larger, the frequency of PA patterns decreases, and the frequency of R patterns increases. Moreover, we can also predict that an increase in the symmetrical coupling of the players would cause a higher frequency of R patterns. With these two theoretical predictions, we develop a new one-elastic-band tool, connecting the three players simultaneously. Contrary to the three-elastic-bands tool, with the one-band-elastic tool, each player could haptically perceive the resultant force simultaneously generated by movements of the two other players.
Therefore, it is hypothesized for the study that players 1) will improve their triadic coordination skills with the help of a band tool, either with a one elastic band or with three elastic bands; and 2) the one-elastic-band tool will facilitate the R pattern more than the three-elastic-bands tool.
Sixteen male Japanese junior handball players participated in this study (mean age: 10.81 [+ or -] 1.16 yrs. old; max. age: 12 yrs. old; min. age: 9 yrs. old). Their experience in handball ranged from about four to six years, but they were novices in soccer. Their handball experience facilitated their involvement in team coordination tasks, even though they had not practiced them before in soccer. The participants were split into four groups composed of four players each, balanced by age and motor ability in team sports to enhance the internal validity of the experiment. The difference in average age between each group was within one year. The motor ability was assessed by their handball coach; the groups were adjusted so that these values would be as close as possible between each group.
We obtained informed consent from the participants and their parents. The experimental procedures conformed to the principles in the Declaration of Helsinki and were approved by the Ethics Committee of Kogakuin University.
Task design and tool conditions
The experimental task was a three-versus-one ball-possession task in soccer. In this task, three attacking players were instructed to exchange a ball with one another as many times as possible in 60 seconds without going out of the 7-square-meter area marked by tape on the floor. The defensive player was instructed to take the ball away from the attacking players as quickly as possible. The role of each participant (as attacker or defender) was decided before the experiment, and it remained the same in all trials. The defenders were selected based on their greater endurance ability than the other members in each group, as assessed by their coach, because defenders must move harder than attackers.
Three experimental conditions were presented: (1) the one-elastic-band condition; (2) the three-elastic-bands condition; and (3) the control condition. In the one-elastic-band and three-elastic-bands conditions, three attacking players performed the experimental task using the one-elastic-band and three-elastic-bands tools, respectively. In the control condition, players performed the experimental task without any tool.
As shown in Figure 1a, both tools were comprised of...