Social forces for team coordination in ball possession game

Team coordination is a basic human behavioral trait observed in many real-life communities. To promote teamwork, it is important to cultivate social skills that elicit team coordination. In the present work, we consider which social skills are indispensable for individuals performing a ball possession game in soccer. We develop a simple social force model that describes the synchronized motion of offensive players. Comparing the simulation results with experimental observations, we uncovered that the cooperative social force, a measure of perception skill, has the most important role in reproducing the harmonized collective motion of experienced players in the task. We further developed an experimental tool that facilitates real players' perceptions of interpersonal distance, revealing that the tool improves novice players' motions as if the cooperative social force were imposed.

Figure 1

Empirical data of the three versus one ball possession task [14]. (a) Snapshot of four players during the task. The definitions of the angle parameters (${\theta }_1$, ${\theta }_2$, and ${\theta }_3$) are illustrated in the image. (b) Time evolution in the three inner angles of the team composed of experienced and novice players. The blank periods in the time series indicate a pause resulting from ball interceptions by the Defender. (c) Schematic diagram of the two specific synchronized patterns: the rotation ($R$) and the partial antiphase ($PA$) pattern.

Figure 2

(a) Schematic definitions of position vectors and unit vectors used in the simulation. (b–d, top) Diagram of three social forces acting on player $i$. (b) The spatial force is depicted by red arrows. This force acts only when the offensive agent is outside the circle with a radius of the spatial range parameter, $L_s$ (shown by a red dashed circle). (c) The avoiding force is depicted by blue arrows. This force acts only when the offensive agent is inside the Defender-centered circle with a radius of the avoiding range parameter, $L_a$ (shown by the blue dashed circle). (d) The cooperative force acting on the pairs of offensive agents. When the distance is larger (or smaller) than the cooperative range parameter, $L_c$, it exerts an attractive (repulsive) force on the pair. (b–d, middle and bottom) Spatial profiles of the social forces and associated potential fields. $f_i^s$, $f_i^a$, and $f_i^c$ indicate the respective projections of the force vectors $F_i^s$, $F_i^a$, and $F_i^c$. See the main text for the precise mathematical definitions of the three social forces.

Figure 3

Occurrence frequency of the two synchronized patterns (red: rotation pattern, blue: partial antiphase pattern) as a function of the force parameters: (a) all the three force parameters ($k_s$, $k_a$, and $k_c$) were equalized and changed, collectively; (b) only the cooperative force parameter $k_c$ was changed, while $k_s$ and $k_a$ were fixed at $120\mathrm{N}/\mathrm{m}$. Dots and error bar indicate the mean and standard deviation of 50 simulation trials, respectively. Asterisks represent the significant difference between the frequency of $R$ and $PA$ pattern ($p<$ 0.01).

Figure 4

(Left) Time series of the three inner angles. The model used in the simulation involves: (a) all three social forces ($k_s=k_a=k_c=120\mathrm{N}/\mathrm{m}$), (b) two social forces excluding the cooperative force ($k_c=0$, $k_s=k_a=120\mathrm{N}/\mathrm{m}$), (c) two forces without the avoiding force ($k_a=0$, $k_s=k_c=120\mathrm{N}/\mathrm{m}$), and (d) two without the spatial force ($k_s=0$, $k_a=k_c=120\mathrm{N}/\mathrm{m}$). (Right) Frequency of the three inner angles for 50 trials. The red and green curves represent the inner angle distribution associated with experienced and novice players, respectively, deduced from empirical data.

Figure 5

(a) Snapshot of guidance tool-based experiment performed by novice players. (b) Schematic diagram of physical guidance tool. (c) Frequency of the three inner angles across four trials of 60 seconds, without (upper) and with (lower) the use of the elastic band. The red curves demonstrate the distribution pattern exhibited by experienced players, duplicated from Fig. 4.

Figure 6

(a) Diagram of Receiver's position and movement. (b) Diagram of the Defender's position and movement relative to the ball's trajectory.

Figure 7

(a) Schematic definition of the cooperative range parameter $L_c$. (b) Definition of the avoiding range parameter $L_a$ and spatial range parameter $L_s$.