A group of 12 right-handed students from the University of Aix-Marseille, eight men and four women with an average age of 19.6 ± 1.0 years (M ± SD), took part in the experiment. They all provided written consent before participating voluntarily in our study. The study was approved by the local institutional review board of the Institute of Movement Sciences (Comité Ethique de l’Institut des Sciences du Mouvement d’Aix-Marseille Université) and conducted according to University regulations and the Declaration of Helsinki.

The experiment consisted of three consecutive sessions in which participants were to manually intercept virtual balls moving downward across a screen. A ball could be intercepted by moving an on-screen paddle laterally over an invisible horizontal interception axis at the bottom of the screen. During the first experimental session participants intercepted balls individually (Figure 1A). This session served to familiarize participants with the experimental set-up. In addition, by counting the number of intercepted balls, we obtained a measure of how well individual participants performed the interception task. The second experimental session was, again, an individual-participant session. This time, however, participants were assisted by a static “partner” incorporated by a large stationary paddle located at the opposite side of the interception axis (Figure 1B). Balls arriving at the stationary paddle were returned upward and counted as a successful interception. Participants had to avoid touching the static paddle; on-screen contact immediately led both paddles to disintegrate and interception was no longer possible. In the third experimental session participants performed the interception task in teams (Figure 1C). We composed teams of two participants with similar interception scores on the first two sessions. Like in Sessions 1 and 2, participants were able to move all along the interception axis and, comparable with Session 2, they should avoid touching one another; both paddles would disintegrate if they did. No communication in any form was allowed.

The experiment took place in a darkened room without windows. Figure 2 present the experimental setting for the session in which two participants performed the task together. Participants were seated at one of the two possible seats on one end of a table. They were facing a large television screen (Samsung 55″ LED ED55C, with a 1920 × 1080 pixels resolution) that was positioned 2 m away at the other end of the table. When seated, the participants faced the screen at eye height. Six participants were always seated at the right side of the table during each of the three sessions and are referred to as Right-side Participants (RPs); the other six participants always sat left and are referred to as Left-side Participants (LPs).

Using their right hand, participants displaced the on-screen paddle by laterally displacing a handheld knob on top of an in-house-constructed linear positioning device placed on the table in front of them. The knob was firmly attached to a small (3 by 6 cm) aluminum cart that could slide along two (75-cm long) parallel iron bars. The cart’s position was sampled at a frequency of 100 Hz using a linear magnetic potentiometer (MP1-L-0750-203-5%-ST, Spectra Symbol, West Valley City, UT, USA) connected to the computer (HP ZBook 15) controlling the experiment. The digitally sampled electrical output of the potentiometer was converted by in-house developed ICE^® (ISM, Aix-Marseille Université, France) software into a paddle position using a constant gain, such that the two extreme knob positions corresponded to (virtual) screen positions slightly beyond the physical screen. This allowed participants to cover the full (121 cm) length of the interception axis on the screen without ever reaching the extremities of the 75-cm long positioning device. Unless specified otherwise, positions and distances reported from here on correspond to distances on the screen, with the origin corresponding to the horizontal center of the interception axis. The screen thus extended horizontally (X-axis) from -60.5 cm to +60.5 cm and vertically (Y-axis) from -2 cm to +66 cm.

Participants had to intercept virtual (2-cm diameter circles) white balls depicted against a black background, moving downward across the screen at various angles and speeds, by making them bounce back upward after contact with their white (3-cm wide and 0.8-cm high) paddle.

For a trial to start, participants moved the paddle to a designated start position (see Figure 1) positioned at ±21 cm from the center of the screen in Session 1 and at ±30.25 cm from the center of the screen in Sessions 2 and 3. Start positions were marked by a 3-cm wide translucent red rectangle that would turn green when the center of the paddle was located at a horizontal distance of less than 0.3 cm from the center of the rectangle. After the participant(s) had remained in place for 2 s, the rectangle disappeared and after another 2 s the appearance of a ball at the top of the screen marked the beginning of the trial. Balls immediately moved downward with vertical velocities of 0.40 or 0.64 m/s corresponding to movement durations until reaching the interception axis of 1.6 and 1.0 s, respectively.

Ball trajectories were constructed with the use of five standard ball departure positions (Y = 64 cm) and five standard arrival positions (Y = 0 cm), both at X = -42, -21, 0, +21 and +42 cm. Combining the five departure positions with the five arrival positions gave rise to a total of 25 standard rectilinear trajectories. To avoid participants becoming familiarized with the arrival positions of the ball, a random distance between -10.5 cm and +10.5 cm was added to both the standard departure and arrival positions of a trajectory. This way, balls could appear and arrive everywhere between X = -52.5 cm and X = +52.5 cm while trajectory angles were kept the same. In a single block, all 25 trajectories appeared with two different vertical ball velocities, for a total of 50 fully randomized trials per block. All participants performed four blocks per session, adding up to a total of 200 trials per participant in a 1-h session.

Successful interception required that the paddle touched the ball when it crossed the interception axis. After a successful interception, the paddle turned green and the ball moved back up. In an unsuccessful trial the ball continued moving downward and the paddle turned red. Three seconds after ball arrival at the interception axis, the paddle returned to its original white color and the translucent red triangle would appear again to indicate the start of a new trial.

All sessions started off with ten practice trials. During these practice trials participants were asked not only to intercept a number of balls but also to purposely miss a ball so they would have experienced all the possible actions and their outcomes. In Sessions 2 participants were also asked to touch the stationary paddle during a trial, so as to experience what would happen if they did during the experiment. For the proper experimental sessions participants were instructed to intercept as many balls as possible, without any further information being provided. To motivate the participants, the experiment was organized as a competition in which all participants competed anonymously.

In Session 3 participants were seated next to each other (see Figure 2). They were separated by a black cloth, hanging from the ceiling, that effectively prevented each participant from seeing (any part of) the other. Moreover, they wore headphones (3M Peltor Optime2) and earplugs (DEXTER Lm30215-10) so that they could not hear each other either. No communication in any form was allowed (both before and during the experiment). The participants were explicitly instructed that the number of interceptions per individual did not matter and that their performance as a team was the only thing that counted.

Kinematic data of the participants’ paddles and the ball was sampled at a frequency of 100 Hz and stored on an external disk. Along with the kinematic data, we registered trial characteristics including whether a participant intercepted the ball or not and, in Sessions 2 and 3, the time of a collision, if any. Before further analysis, the kinematic data was filtered with a second-order Butterworth filter with a cut-off frequency of 5 Hz run through twice in order to negate the phase shift (Ledouit et al., 2013).

Interception scores were calculated per block as the percentage of balls intercepted from the total number of 50 balls presented. The score used to assemble the teams was the mean value of interception scores obtained during the first and second individual sessions.

Movement initiation time was defined as the first moment a participant crossed a velocity threshold of 3.0 cm/s provided that the participant’s movement amplitude reached at least 1 cm. Based on this criterion we determined for each individual trial whether, and if so when, a participant initiated a movement. Velocity-time series were obtained using a three-point central difference method. Peak velocity was determined as the maximum velocity reached during a movement.

Defining angles β_LP and β_RP according the definition provided in Figure 3A, allowed deriving time-series of the rates of changes of these angles (i.e., angular velocities) for the LP and the RP. As demonstrated in Figures 3B–D, the manner in which a participant’s paddle movement affects the pattern of change of the angle β (i.e., the state of the angular velocity, AV) is lawfully related to the future outcome of the ongoing action (also see, for instance, Fajen and Warren, 2004). As we will detail later, this prospective character of the (visual) information provided by the LP’s and RP’s angular velocities may be used to develop an account of emergent decision making.

We begin by examining performance on the interception task, operationalized by the percentage of balls intercepted, in each of the three experimental sessions (see Table 1).

During the first session individual participants had to cover the full 105-cm range of potential ball arrival positions with their paddle initially positioned at an eccentricity of 21 cm (to the left for the LPs and to the right for the RPs) with respect to the center of the screen. With an average interception performance of 85.7 ± 5.4% for the total of 200 trials completed by each participant, performance was overall quite good. A repeated-measures one-way ANOVA on the evolution of performance over the four blocks of 50 trials revealed a significant effect of Block [F(3,33) = 18.51, p < 0.001, η² = 0.63], reflecting an initial increase from Block 1 (78.2 ± 8.9%) to Block 2 (88.8 ± 4.2%), followed by a leveling off of performance during Blocks 3 (87.2 ± 6.3%) and 4 (88.7 ± 5.6%). Post hoc Newman–Keuls analyses confirmed that performance in Block 1 was significantly different from performance in Blocks 2, 3, and 4 (p’s < 0.001), while no significant differences were observed among the latter.

During the second session the individual participant’s paddle was initially positioned at an eccentricity of 30.25 cm (to the left for the LPs and to the right for the RPs) with respect to the center of the screen. Participants were assisted by a static partner (32-cm wide stationary paddle) covering the final 24-cm range of potential ball arrival positions on the opposite side of the full 105-cm range. They therefore needed to cover an 81-cm range of potential ball arrival positions while avoiding contact with the static partner’s paddle. Collisions with the stationary paddle occurred only sporadically (on average on 0.5 ± 0.6% of the trials, see Table 1), with only three participants colliding once during the first block. Interception scores were stable over blocks (89.3 ± 4.5, 91.7 ± 5.2, 93.0 ± 5.9, and 92.0 ± 4.5%, for blocks 1, 2, 3, and 4, respectively); a repeated-measures ANOVA did not reveal significant differences in performance over the four blocks [F(3,33) = 1.61, p = 0.205, η² = 0.13]. These results indicate that participants performed well from the beginning of the session.

In order to examine potential differences between LPs and RPs in Sessions 1 and 2, we conducted a mixed two-way ANOVA on interception scores with Side (LP and RP) as a between-participant factor and Session (1 and 2) as a within-participant factor. This analysis did not reveal significant differences between LP and RP [F(1,10) = 1.22, p = 0.296, ηp2 = 0.11]. Inspection of individual means (cf. Table 1) confirmed that performance was comparable for left and right participants in both sessions.

Having thus characterized the performance of individual participants in Sessions 1 and 2, we now turn to the third session in which the 12 participants were combined into six teams, each consisting of an LP and an RP. Paddles were initially positioned 30.25 cm to the left (LP) and to the right (RP) with respect to the center of the screen. Together, the two participants needed to cover the full 105-cm range of potential ball arrival positions while avoiding contact between their paddles. As in Session 2, collisions were rare (6 out of the total of 1200 trials, see Table 1), with only two teams colliding once within the first block. Interception scores were quite high from the start and stable over blocks (90.7 ± 4.3, 92.3 ± 3.9, 92.3 ± 5.1, and 89.7 ± 7.0%, for blocks 1, 2, 3, and 4, respectively); a repeated-measures one-way ANOVA did not reveal significant differences in performance over the four blocks [F(3,15) = 0.50, p = 0.688, η² = 0.09]. Interestingly, team performance could not be predicted on the basis of its members’ scores observed in Session 2. Indeed in two cases team performance in Session 3 was better than the best team member’s score in Session 2 (teams 3 and 5, see Table 1). In two other cases the opposite pattern was observed (teams 1 and 4, see Table 1).

Figure 4 provides a graphical summary of the interception results as a function of the ball’s arrival position on the interception axis for all 200 trials of each team. Interceptions accomplished by the LP (dark blue circles) and by the RP (light blue circles) were plotted on two separate axes, so as to allow visual discrimination of who intercepted the balls where. These intercepted trials were completed with the trials in which both participants failed to intercept the ball (red circles, referred to as errors) and with the trials in which the LP and RP paddles made contact with one another (purple dots, referred to as collisions). The (rare) collisions occurred for balls arriving at locations near the center of the screen. Errors, on the other hand, were generally distributed over the full range of ball arrival positions. Indeed, errors for ball arrival positions located within the interval between both participants’ initial positions (n = 53) occurred as often as errors for ball arrival positions outside this interval (n = 52), indicating that the majority of errors seemed to result from individual mistakes. Together with the high interception scores (on average 91.3 ± 3.4%) and the low number of collisions (on average 0.5 ± 0.3%), these results demonstrate that participants succeeded remarkably well in coordinating their interceptive movements with one another.

Visual inspection of Figure 4 revealed that all six teams exhibited a quite well-defined distribution of who intercepted the ball where, with the LP intercepting the grand majority of balls arriving on the left half of the interception axis and the RP intercepting the grand majority of balls arriving on the right half. Interestingly, however, the interception performance of all teams also included an area where both participants could intercept balls. In order to quantify the separation of interception domains, for each team we computed a logistic regression equation with ball arrival position as the explanatory variable. Using a logit link function (Nelder and Wedderburn, 1972), logistic probability curves were derived for the balls intercepted by the LP (P = 1) and by the RP (P = 0) for all teams independently. The boundary between both interception domains was defined as the Median Effective Level (MEL), that is, the position on the interception axis where the probability of the LP intercepting the ball is equal to the probability of the RP intercepting the ball (i.e., P = 0.5). As can be seen from Table 2 (observed interception performance), teams 1–5 revealed MEL values close to zero with a maximum absolute deviation of 1.08 cm, indicating that in these teams the boundary between both interception domains laid close to the exact (and yet unmarked) middle of the interception axis. Team 6, on the other hand, was characterized by a MEL value of -4.66 cm, indicating that the boundary between both interception domains was shifted almost 5 cm to the left. Of potential interest here is the fact that team 6 was the team with the largest difference in individual performances, as observed in Sessions 1 and 2 (see Table 1). The boundary shifted toward the participant with the lowest interception score, resulting in a 19.5% difference in the ranges of both participants’ interception domains. Note, however, that even in the presence of a shift in the location of the boundary team 6 still demonstrated a rather well-defined separation of interception domains.

The degree of separation between both interception domains is reflected in the steepness of the slopes of the logistic curve and the amount of overlap may be calculated as the distance between the 5 and 95% points of the logistic curve (Cox and Snell, 1989). On average, overlap thus defined amounted to a non-negligible 14.6 ± 3.6 cm. Interestingly, the amount of overlap between interception domains was not related to a team’s performance [r = 0.13, t(4) = 0.263, p > 0.8]. While team 6 (characterized by the leftward boundary shift discussed above) demonstrated an above-average overlap (16.9 cm, see Table 2) as well as the lowest team performance (85.5% of all balls intercepted, see Table 1), team 3 not only revealed the largest overlap (19.3 cm) but also the highest team performance (95.5% of all balls intercepted).

We first examined initiation times for all interception movements in all three sessions. As can be seen from Table 3, whereas average initiation times were similar for Sessions 1 (428 ± 38 ms) and 2 (437 ± 44 ms), they appeared longer for Session 3 (534 ± 51 ms). However, this observation was difficult to interpret because the different sets of initiation times refer to different ranges of movement in the three sessions. For Sessions 2 and 3 we therefore calculated the initiation times for the subset of all interception movements that were directed to ball arrival positions between the initial paddle position and the middle of the screen (i.e., between -30.25 cm and 0 cm for the LPs and between 0 cm and +30.25 cm for the RPs). As can be seen from the last two columns of Table 3, even for these range-corrected interception movements a difference in initiation time occurred [paired t-test: t(11) = 3.56, p < 0.01] with movements being initiated later in the presence of a dynamic partner (Session 3: 518 ± 50 ms) than in the presence of a static partner (Session 2: 459 ± 61 ms).

In Session 3, interception on a given trial could in fine only be accomplished by a single participant but this did not necessarily imply that the other participant did not move at all. For every single trial and independent of the result, we therefore determined for both LP and RP whether they initiated a movement. Figure 5 summarizes the resulting frequency distribution of observed movement initiations for the LPs and RPs as a function of the arrival position of the ball, with the full 105-cm range of potential ball arrival positions divided into 20 (5.25-cm wide) bins. Each trial was classified into one of four categories: initiation LP only (dark blue), initiation RP only (light blue), initiation both LP and RP (green), and no initiation, that is, neither LP nor RP (red) initiated a movement. Of all 1200 trials, 436 (i.e., 36.3%) revealed LP initiation only, almost exclusively associated with balls arriving on the left side of the interception axis. Similarly, 421 (i.e., 35.1%) of all trials revealed RP initiation only, almost exclusively associated with balls arriving on the right side of the interception axis. Of the 279 (i.e., 23.3% of all trials) revealing both LP and RP initiations, 246 (i.e., 88.2%) resulted in successful interception, implying that one of the participants must have abandoned the launched interception attempt at some point so as to allow the other participant to intercept the ball. The prevalence of such double initiations appeared to follow a bell-shaped distribution over the interception axis, with its peak located in the vicinity of the center of the interception axis (i.e., the center of the screen). In 5.3% of the trials neither of the two participants initiated any movement. In 63 of these 64 trials without movement initiation, balls arrived at or close to one of the participants’ initial positions (i.e., ±30.25 cm). Note that in 59 (i.e., 93.7%) of those 63 trials the ball was in fact intercepted, making contact with one of the motionless (3-cm wide) paddles.

In order to obtain a grasp on when one of the participants abandoned the launched interception attempt, we examined the relation between the distance to be covered and the peak velocity reached during the movement on each trial. Figure 6 presents this relation for each successful (i.e., intercepted) trial in which at least one participant initiated a movement, for each team and each of the two vertical ball speeds separately. Successful interceptions by the LPs (dark blue dots) and the RPs (light blue dots) were characterized by proportional scaling relations between the distance covered (i.e., the distance between initial paddle position and ball arrival position) and the peak velocity reached during the movement (see Ledouit et al., 2013, for similar results). For each individual player we therefore performed a linear regression analysis of peak velocity onto distance covered for the balls intercepted by that participant. Results of these regression analyses are reported in Table 4 and shown graphically in Figure 6.

While the slope of the relation varied both as a function of participant characteristics and as a function of vertical ball speed, individual correlation coefficients were satisfactorily high to allow the definition, for each participant at each vertical ball speed, of a “standard” relation (operationally defined by a range of ±2 SDs around the mean, dashed parallel lines in the panels of Figure 6) between ball arrival position and peak velocity reached during an interception movement. Using this “standard” relation observed for successful interceptions, we could identify whether the 246 abandoned interception attempts (i.e., successful trials in which the participant that did not intercept the ball had nevertheless initiated a movement) occurred early or late during the trial. Late abandoning was characterized by the participant still reaching the standard peak velocity (green dots in Figure 6), whereas early abandoning was characterized by the participant reaching a lower-than-standard peak velocity (green crosses in Figure 6). Of the 246 successfully intercepted trials demonstrating both LP and RP initiation, 179 (i.e., 72.8%) were characterized by early abandoning, while 67 (i.e., 27.2%) were characterized by late abandoning.

Several of the results discussed in the previous sections suggest that team performance, as observed in Session 3, cannot be satisfactorily understood as resulting from a form of organization with pairs of independent players, each covering their own half of the interception space. First, while for five of the teams the boundary between interception domains laid close to the center of the screen (with differences in the sizes of individual participant interception domains being limited to 2.3 ± 1.4%), in team 6 this boundary was shifted by almost 5 cm, leading to a difference in domain sizes of 19.5%. Second, for all six teams the boundary between interception domains was fuzzy rather than sharp, with participants regularly entering their teammate’s domain to intercept balls there without such “intrusions” leading to collisions. The observed degree of overlap between interception domains was indeed quite substantial (14.6 ± 3.6 cm), amounting to 13.9 ± 3.4% of the full range of potential ball arrival positions. Third, balls arriving near the center of the screen (four center bins of Figure 5, with ball arrival positions ranging from -10.5 to +10.5 cm) more often evoked movement initiations of both participants than only initiations of the participant in whose interception domain the ball would in fact arrive. Yet, both collisions and errors were rare, as 87.9% of the trials on which both participants initiated a movement resulted in successful interception by one of the participants. Finally, while in 72.8% of the 246 double-initiation trials one of the participants abandoned the launched interception attempt early on, in the remaining 27.2% of the trials the interception attempt was abandoned after the participant had reached a peak velocity associated with an ongoing interception attempt. Together, these results suggest that participants took into account the ongoing actions of their partners.

Without going as far as suggesting that this is the information used by the participants (see Fajen and Warren, 2007; Bootsma et al., 2016, for further details), for the present purposes the state of the angle formed, for each participant, by the line connecting this participant’s paddle with the other participant’s paddle and the line connecting this participant’s paddle with the ball (see Figure 3) may well allow capturing the unfolding team interactions. Indeed, by physical law, a constant angle (i.e., a zero AV) indicates that the player’s current movement speed will lead the paddle to reach the interception point when the ball arrives there. Put differently, zero AV means that an interception will occur if both ball and paddle speed remain constant over the remainder of the trial. Given that in the present study ball speed was always constant over the course of a trial, from the foregoing it follows that a positive AV (i.e., an opening of the angle) implies that maintaining current paddle speed will lead to an early arrival at the interception location and, likewise, that a negative AV (i.e., a closing of the angle) implies that maintaining current paddle speed will lead to a late arrival at the interception location.

When neither of the two participants has begun to move their paddle (i.e., from the beginning of a trial up to the moment of first movement initiation), for both participants AV will be negative for balls arriving at a location between the two paddles. For balls arriving at locations to the left of the LP, AV will be positive for the stationary LP and negative for the stationary RP. Mutatis mutandis, AV will be positive for the stationary RP and negative for the stationary LP for balls arriving at locations to the right of the RP.

Each trial in which one or both participants initiated a movement is represented in Figure 7 as a point in space defined by the states of the AV-LP (abscissa) and the AV-RP (ordinate) at the moment of first movement initiation. Dark blue dots designate the 436 trials in which only the LP initiated a movement, light blue dots designate the 421 trials in which only the RP initiated a movement, and green dots designate the 279 trials in which both players initiated a movement. As was already visible in Figure 5, balls arriving to the left of the LP almost invariably evoked only movement from the LP. In Figure 7, these trials correspond to the (predominantly dark blue) dots in the lower right quadrant where AV-LP is positive and AV-RP is negative. Likewise, balls arriving to the right of the RP almost invariably evoked only movement from the RP. In Figure 7, these trials correspond to the (predominantly light blue) dots in the upper-left quadrant where AV-LP is negative and AV-RP is positive. As was also already visible in Figure 5, trials evoking initiation by both the LP and RP generally arrived between the initial positions of both paddles, close to the center of the screen. In Figure 7 these trials correspond to the green dots predominantly located in the lower-left quadrant where both AV-LP and AV-RP are negative.

The (AV-LP, AV-RP) state space allows us to scrutinize the evolution over time of the behavior of both participants with respect to the ball. The trials of interest for such scrutiny are of course the trials in which both participants initiated an interception movement (green dots in Figure 7). For these reasons, the subset of 246 successfully intercepted trials in which both participants initiated a movement is once again presented in Figure 8, but this time coded for the player who in the end intercepted the ball (LP interception: dark blue, RP interception: light blue). When participants start moving they actively change their relation to the ball, which is functionally captured by a change in their AV. The motion through the (AV-LP, AV-RP) state space thus captures the dynamic triangular relation between both players and the ball. As in Figure 7, Figure 8A depicts the situation at the time of first movement initiation. Figures 8B–D depict the situation, respectively, 100, 200, and 300 ms later.

Inspection of Figure 8 brings out that trials that eventually gave rise to LP-interception were characterized by a change in AV-LP from negative to positive (resulting from the LP’s sustained movement toward the future interception location), with dots moving from the lower-left quadrant either to the lower-right quadrant or, for a smaller proportion of trials, to the upper-right quadrant. A similar picture emerged for the trials that eventually gave rise to RP-interception. These trials were characterized by a change in AV-RP from negative to positive (resulting from the RP’s sustained movement toward the future interception location), with dots moving from the lower-left quadrant either to the upper-left quadrant or, for a smaller proportion of trials, to the upper-right quadrant. Figure 8 thus reveals the gradual separation in the two groups of trials based on who intercepted the ball in the end. This observation suggests that the decision of who intercepts the ball in fact emerges over the course of a trial, as a function of the expediency with which both participants engaged in their interception attempts. In fact, it appeared that the first participant to reach positive AV tended to be the one that ended up intercepting the ball. Recalling (cf. Figure 3) that negative AV implies that with the current movement speed the participant will be (too) late, positive AV implies that with the current movement speed the participant will in fact arrive at the interception location before the ball gets there. Even though all participants generally slowed down prior to interception (probably so as to minimize chances of colliding with the other participant), the occurrence of a positive AV for one participant may signal to the other that the interception attempt should be abandoned.

In order to test this idea, we examined the evolution over time of AV-LP and AV-RP for all 1095 trials on which the ball was intercepted. Starting from the situation at the onset of a trial, we classified the trial as LP-interception or RP-interception, as a function of the first participant to reach positive AV. Note that this rule led to correct (although immediate) classification of balls arriving to the left of the LP as LP-interception and of balls arriving to the right of the RP as RP-interception. The results of this on-the-fly decision formulation are presented in Figure 9 for all six teams separately.

As can be seen from Figure 9, attribution of interception to the LP (dark blue circles) or the RP (light blue circles) was correct in the overwhelming majority of cases. Overall, attribution errors occurred on only 2.0% of the trials, corresponding to a total number of errors of 2, 2, 6, 7, 3, and 2, for teams 1–6, respectively. The on-the-fly decision criterion of interception by the “first participant to reach positive AV” not only allowed to predict which participant would intercept the ball with more than satisfactory precision, but also reproduced the qualitative aspects of the distribution of interception domains observed in each team. Deriving logistic probability curves for the predicted performance (see Table 2, predicted interception performance) revealed that the locations of boundaries between interception domains were well predicted [r = 0.92, t(4) = 4.54, p = 0.010], laying close to the center of the screen (2.17 cm maximal absolute deviation) for teams 1–5 while being shifted 4.24 cm to the left for team 6. Similarly, even though somewhat overestimated, the amount of overlap between interception domains was fairly well predicted [r = 0.80, t(4) = 2.63, p = 0.059].

Finally, because the moment at which the first participant reached positive AV could be detected, we examined whether this criterion also correctly predicted when the non-intercepting participant abandoned the launched interception attempt in the trials in which both participants initiated an interception movement. In 209 (i.e., 85.0%) of the 246 double-initiation trials, the abandoning participant indeed reached peak velocity after the intercepting player had reached positive AV. Thus, the non-intercepting participant was already decelerating (that is, had already abandoned) before the intercepting player reached positive AV in only 15.0% of the cases. This first analysis suggests that our on-the-fly decision criterion also captures the timing of the decision rather well. We can take the analysis one step further by also considering the information with respect to the moment of abandoning contained in the magnitude of the peak velocity reached by the non-intercepting participant, as described in Section “Movement Kinematics.” If the peak velocity reached during an abandoned interception attempt corresponded to the “standard” peak velocity of a successful interception movement, the interception attempt was considered as still underway at the moment the non-intercepting participant reached this peak velocity. Abandoning was then classified as late. If, on the other hand, the peak velocity reached during an abandoned interception attempt was smaller than the standard peak velocity, the interception attempt was considered as already abandoned when the non-intercepting participant reached this lower-than-standard peak velocity. Abandoning was then classified as early. Table 5 presents the foregoing results in the form of a contingency table.

As can be seen from Table 5, of the 209 double-initiation trials in which the non-intercepting participant reached peak velocity after the intercepting participant had reached positive AV, 150 (i.e., 71.8%) had been characterized as early abandoning and 59 (i.e., 28.2%) as late abandoning. This repartition nicely mirrors the observed overall 72.8% (179 out of 246) early abandoning and 27.2% (67 out of 246) late abandoning. Of the 37 trials in which the non-intercepting participant had reached peak velocity before the intercepting participant reached positive AV, the grand majority (29 or 78.4%) had been characterized as early abandoning. We suggest that in many of these trials the non-intercepting participant produced only a small movement, characterized by a low peak velocity (i.e., the green points close to the zero velocity axis in Figure 6). Overall we conclude that the on-the-fly criterion that the ball will be intercepted by the “first participant to reach positive AV” allows the observed team interactions to be rather accurately captured.