# Perceiving the affordance of interceptability for multiple others

Samruddhi Damle, Reinoud J Bootsma, Frank T J M Zaal

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Samruddhi Damle, Reinoud J Bootsma, Frank T J M Zaal. Perceiving the affordance of interceptability for multiple others. Human Movement Science, 2026, 106, 10.1016/j.humov.2026.103469. hal-05532403

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Human Movement Science

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# Perceiving the affordance of interceptability for multiple others

Samruddhi Damle<sup>a,1</sup>, Reinoud J. Bootsma<sup>b,2</sup>, Frank T.J.M. Zaal<sup>a,*,3</sup>

## ARTICLE INFO

Keywords:

Perception-action

Interception

Affordance perception

Affordances for others

Manual lateral interception

Action boundaries

Perceptual judgments

## ABSTRACT

Previous research has demonstrated that people can perceive the affordance of interceptability not only for themselves but also for another person. In the present study we explored whether they could do so for multiple others. To this end, we asked one group of 12 participants (the “actors”) to attempt to intercept balls moving along various trajectories downwards across a large screen by moving an on-screen paddle along a horizontal interception axis. By manipulating the paddle's maximum reachable distance, we introduced an action boundary beyond which balls could not be intercepted. A selection of each actor's recorded interception attempts, sampled around this action boundary, was subsequently played back to another group of 12 participants (the “observers”), half of which had previously participated in an actor-type session themselves. On each trial, observers thus viewed the temporal unfolding of some actor's ball-and-paddle kinematics, with the last 25% of the trial being occluded to make the trial outcome unavailable to them. At the end of each trial, observers judged whether an actor would have been able to intercept the ball or not using the 2AFC method. Observers demonstrated an overall 72% accuracy in their judgments, indicating that they could reliably perceive the affordance of interceptability for the twelve actors. We conclude that in our task information about the interceptability for another individual resides in the unfolding ball-and-paddle kinematics. This information appears to be quite salient, as observer accuracy was not affected by whether they had previously performed the constrained interception task themselves or not.

## 1. Introduction

In dynamic, fast-paced sports settings, athletes must be capable of perceiving not only their own affordances but also those of teammates and opponents (Araujo & Davids, 2009; Fajen et al., 2009; Passos et al., 2012). Similarly, parents must be aware of the actions afforded to their children, especially in high-risk situations (Cordovil et al., 2012; Cordovil et al., 2013; Cordovil et al., 2015). To coordinate successfully with others, whether in sports or everyday life, it is essential to accurately perceive affordances for others, just as we do for ourselves. There is ample evidence that people can perceive the action opportunities available to another in various contexts. For example, observers can judge, for somebody else, maximum reaching height while jumping (Ramenzoni et al., 2008; Ramenzoni et al., 2010; Weast et al., 2011, 2014; Weast-Knapp et al., 2019), maximal support height for sitting (Stoffregen et al.,

<footnote><sup>a</sup> Department of Human Movement Sciences, University Medical Center Groningen, Groningen, the Netherlands</footnote>

<footnote><sup>b</sup> Institut des Sciences du Mouvement, Aix-Marseille Université, CNRS, Marseille, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: f.t.j.m.zaal@umcg.nl (F.T.J.M. Zaal).</footnote>

<footnote n="1">¹ https://orcid.org/0000-0002-8103-4557</footnote>

<footnote n="2">² https://orcid.org/0000-0002-3719-7586</footnote>

<footnote n="3">³ https://orcid.org/0000-0003-2697-3612</footnote>
1999), minimal aperture size for passing (Chang et al., 2009), or whether a ball is interceptable (Damle et al., 2025). Such findings suggest that people are well adept at perceiving affordances for another.

Previous work has also shown that these perceptual judgments remain accurate even when using point-light displays (Stoffregen et al., 1999; Weast et al., 2011, 2014), which show the actor in reduced form, as opposed to live in full view. Pioneered by Johansson (1973), this method uses strategically placed points (landmarks) on the body to represent biological motion. Point-light displays have been found to reveal action type, gender, and even identity (Cutting & Kozlowski, 1977; Kozlowski & Cutting, 1977; Mather & Murdoch, 1994). Runeson and Frykholm (1981, 1983) further demonstrated that such displays can also convey the actor's intention of action. Building on this, Weast et al. (2011, 2014) showed that point-light kinematics contain information sufficient to specify action-scaled affordances for others. The present study considers the affordance of interceptability for others, using played-back ball-and-paddle kinematics from a manual lateral-interception task (e.g., Damle et al., 2024, 2025; Ledouit et al., 2013; Ledouit et al., 2024; Montagne et al., 1999; Peper et al., 1994).

In manual lateral interception, an agent is allowed to move in one dimension (usually sideways) to manually intercept an approaching object (often a ball; e.g., see Montagne et al., 1999; Peper et al., 1994). We used the version of the task in which virtual balls move downwards under an angle with the vertical from the top to the bottom of a large screen (cf. Damle et al., 2024, 2025; Ledouit et al., 2013; Ledouit et al., 2024). Participants control a paddle that can move laterally along an invisible interception axis near the bottom of the screen to intercept the ball. In our previous studies (Damle et al., 2024, 2025), we considered also balls that were uninterceptable. We demonstrated that people are able to perceive the affordance of interceptability (i.e., whether or not a ball would be interceptable) for themselves (Damle et al., 2024) and for another individual (Damle et al., 2025). In the former situation, the participants were controlling the paddle themselves through a hand-held slider while verbally indicating that balls would be uninterceptable for them. However, in the latter situation of judging affordances for another, participants made their calls on the basis of played-back ball-and-paddle kinematics, which implies that this kinematics contain the information for perceiving the affordance of interceptability.

If the information about the affordance of interceptability is indeed present in the ball-and-paddle kinematics of our manual lateral-interception task, it should not matter if the played-back ball-and-paddle kinematics were compiled from the actions of a single actor (cf. Damle et al., 2025) or from the actions of multiple actors. Interestingly, most prior research on affordances for others has in fact considered a single actor whose affordances had to be judged by a group of observers. In the present study, we deployed the manual-lateral-interception task that we used before (Damle et al., 2024, 2025) but now created a set of animations with ball-and-paddle kinematics from multiple actors. A fresh set of observers were presented these played-back ball-and-paddle kinematics and asked to judge (un)interceptability for each occasion.

In lateral interception, whether or not a ball is interceptable is a function of when and where the ball will pass the interception axis and of how much time an agent needs to cover the distance to the interception location. The latter is affected, for instance, by the maximum speed that the agent can reach. Interestingly, also the time that the agent takes to start moving determines interceptability. Obviously, with the same distance to the interception location, starting later may require moving faster. However, sometimes, the required speed is beyond one's action capabilities. In the limit case, even when a ball is initially clearly within reach of an agent, if they do not start moving, at some point the ball will become uninterceptable. In effect, differences within and between individuals in the initiation of their movement, the speed of their movement and so on, will affect the interceptability of balls that follow the exact same trajectory. For instance, the individual differences in success rates within and between participants in the Damle et al. (2024) study might stem from this. Having more variation in paddle kinematics because they came from multiple actors will allow for a more convincing test that the information about interceptability is really about the relative movement of ball and paddle. For this reason, we used ball-and-paddle kinematics from multiple actors to create the materials to be presented to the observers in the present study.

We also implemented a number of methodological improvements over the design in Damle et al. (2025), the study in which we used the ball-and-paddle kinematics of a single actor to be judged by observers. Ball arrival positions (the locations where the ball passed the interception axis), for the actors, covered the entire width of the screen. Damle et al. (2024) showed that balls uninterceptable to the actors mostly passed the interception axis at the longest distance from the actors' movement initiation position, although an independent effect of ball speed across the full range of distances was also seen. The latter effect would be alleviated by having a wider paddle. To be able to compile a balanced set of interceptable and uninterceptable balls to present to the observers, we needed to increase the number of uninterceptable balls as compared to our previous study (Damle et al., 2024). For this reason, we introduced a limit in distance over which the actors could move their paddle.<fnref n="4" /> This caused balls with ball arrival positions beyond this limit to be uninterceptable by definition. Note that this only applied to a small fraction of the full set of trials performed by the actors (we aimed for about 10% of the total number). Next, we sampled around this boundary (i.e., the limit of paddle distance) to arrive at a set of trials for the observers with a 50–50 distribution of interceptable and uninterceptable balls. Finally, different from what we did in our previous study on the perception of affordances for another (Damle et al., 2025), in which we had the observers call “no” when they felt that a ball would be uninterceptable for the actor, we now used a 2-alternatives forced-choice (2AFC) method, which is a more powerful method to examine the observers' ability to judge interceptability.

In sum, we aimed to devise a stronger test of observers' ability to judge interceptability for others than in our previous work (Damle

<footnote n="4">⁴ Alternatives to this manipulation, for instance, would be the increasing of ball speed (i.e., decreasing the time that actors had for their interceptive action) or the decreasing of paddle width. Unfortunately, pilot testing had indicated that faster ball speeds than used in the Damle et al. (2024) study would result in on-screen smearing effects. Furthermore, the use of a smaller rather than a wider paddle would introduce more misses in general, across the full screen width, not only around the boundary of interest, which would hamper the analyses.</footnote>
et al., 2025). To this end, we used played-back ball-and-paddle kinematics from multiple actors and took measures to increase the number of trials with balls uninterceptable for the actors, with the latter allowing us to use a more powerful method to test the observers' performance.

## 2. Materials and methods

### 2.1. Participants

We recruited 24 right-handed young adults (12 females, 12 males) from the University of Groningen, whose average age was 21.38 ± 2.23 years (M ± SD). Half of them (6 females, 6 males) were assigned to the group of actors, and the other half (6 females, 6 males)

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Visual representation of the screen and task dimensions in centimeters (not to scale). Top panel: The paddle starting position is designated by the red rectangle at the bottom right position on the interception axis centered on the adopted origin (0,0), with horizontal distance X increasing leftward and vertical distance Y upward. Generic ball arrival positions are indicated below the interception axis. The green bar depicts the possible range of paddle center motion resulting from the asymmetric mapping of the slider-paddle system. Bottom: Schematic top view of the slider and TV screen. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
were assigned to the group of observers. All of them provided written consent before participating in our study. The inclusion criteria for participants were normal or corrected-to-normal vision and no reported or apparent physical injuries or disabilities. The Ethics Board of the UMCG (University Medical Center Groningen, University of Groningen, Netherlands) approved the experimental protocol, which was in accordance with the Declaration of Helsinki.

## 2.2. Experimental set-up

In line with our previous work (Damle et al., 2024, 2025), in this study we used a manual lateral interception paradigm. The experiment was conducted in a darkened room without windows. Participants were seated on a chair at the center of a table, facing a large TV screen of dimensions 120 × 67.5 cm (Samsung 55" QLED QN95A, with a resolution of 1920 × 1080 pixels). We used a HP computer (Windows 11) to run the experiment. An open access python-based software, PsychoPy®, was used for designing and conducting the experiment (Peirce et al., 2019). Participants sat at a distance of 2 m and viewed the center of the screen at eye height (Fig. 1).

In the manual lateral interception task, participants used their right hand to laterally move a knob mounted on a slider-device. The slider-device was constructed in-house using a linear potentiometer and worked like a linear-positioning device, operating at a sample frequency of 100 Hz. The slider could be smoothly displaced laterally over a 1-m long rail. The (lateral) slider position was coupled to the (lateral) position of an on-screen paddle (6.75 cm wide, 0.8 cm high white rectangle) that moved along an invisible horizontal interception axis, located 2 cm from the bottom of the screen (see Fig. 1). Note that the width of the paddle in the present study is larger than in our previous studies (6.75 vs. 4.5 cm in Damle et al., 2024, 2025). Participants used this paddle to attempt to intercept virtual balls (2-cm diameter white circles) which moved downwards across the black-background screen. Unless otherwise specified, the positions and distances reported from here on correspond to distances on the screen, with the origin (located 18 cm to the left and 2 cm above the lower right screen corner) corresponding to the midpoint of the designated paddle starting position on the interception axis, marked by the red box in Fig. 1. For practical purposes lateral distance was defined as increasing to the left of the origin.

In our previous studies (Damle et al., 2024, 2025) the symmetric constant-gain slider-paddle mapping allowed moving the paddle beyond both edges of the screen, with the midpoint of the slider device corresponding to the midpoint of the screen. For the purposes of the present study, the slider-paddle mapping was modified. The mapping was made asymmetric (as indicated by the green bar in Fig. 1) with the maximal leftward on-screen position that could be reached by the (center of the) paddle at 80.9 cm and the maximal right-most position at -19.2 cm, with the 6.75-cm wide paddle thus being partially off-screen. This mapping led to the constitution of a physical action boundary on the left side of the screen, with the objective of introducing truly uninterceptable balls on the left side of the screen only; balls arriving on the right side of the screen would theoretically be interceptable. This modified mapping will be referred hereafter to as the asymmetric mapping, as opposed to the original (symmetric) mapping used in our previous studies (Damle et al., 2024, 2025).

A Movo M1 USB Lavalier microphone was used to record the actors' verbal judgments ("no"-calls, details below). An HP keyboard was used to acquire the judgments of the observers in the two-alternative forced-choice (2AFC) task. The virtual positions of the paddle and ball were sampled at a frequency of 100 Hz using the PsychoPy® software. The recorded data was stored on a secured research drive within the environment of the UMCG network.

## 2.3. Design and procedure

We recall that the major goal of the present study was to evaluate observers' ability to judge whether a ball was interceptable for others on the basis of pre-recorded ball-and-paddle kinematics of others ("actors") performing the interception task that were played back to the observers. For each trial, the recorded kinematics (position time series) of the ball and actor's paddle movement was taken to recreate the corresponding paddle and ball images (i.e., draw the paddle and the ball). Using the same PsychoPy® setup in which the screen was updated with the moving ball and paddle for the actors, these images were shown frame-by-frame to present the recorded motions to the observers. Because the stimuli for the observers came from the actors' interception attempts, we first describe the procedure followed for the actors and subsequently describe the procedure followed for the observers.

### 2.3.1. Actors' experimental sessions

Each of the 12 actors performed three experimental sessions, labeled *training*, *action* and *judging*. The order of the latter two sessions was counterbalanced across the actors. The *training* session served to familiarize and train the actors on the interception task. The task was to intercept as many virtual balls as possible using the virtual paddle. The *training* trials only comprised balls designed to be interceptable (i.e., arriving at reachable positions on the interception axis). On every trial in the *training* session, the actors were presented with a ball moving downwards at constant speed along a rectilinear trajectory towards the interception axis. Individual ball trajectories were determined by first selecting a combination of one of five generic ball departure positions (BDP at Y = 64 cm, X = 69.50, 55.75, 42, 28.25, or 14.50 cm) and one of five generic ball arrival positions (BAP at Y = 0 cm, X = 69.50, 55.75, 42, 28.25, or
14.50 cm). Next, a random offset of half the distance between neighboring generic BDPs and BAPs (in the training session, this amounted to random offsets between -6.875 and + 6.875 cm) were applied to the selected generic ball departure and arrival positions separately.<fnref n="5" /> The reason for this was to have the ball trajectories fill the entire range continuously rather than in a discrete fashion. The ball trajectory was subsequently extrapolated upwards, such that the ball would start invisibly and appeared to move down entering from the top of the screen. Finally, on each trial the time taken by the ball to move from the generic ball departure position to the generic ball arrival position, defined as ball flight time (T), could be 1.6 or 1.2 s. This resulted in blocks of 50 trials (5 generic ball departure positions x 5 generic ball arrival positions x 2 ball flight times).<fnref n="6" /> The actors performed three blocks of such trials, leading to a total of 150 *training* trials.

The next two sessions for the actors were the *action* and *judging* sessions. The order of these sessions was counterbalanced across the group of actors. In the *action* session, the actors were required to make as many interceptions as possible using the paddle. However, the trials were now designed to include both interceptable and uninterceptable (arriving at positions within and beyond paddle reach). This was achieved by expanding the range of generic ball arrival positions and reducing the ball flight times. In the *action* session, the ball trajectories were determined, again, by combining five generic ball departure positions (BDP at Y = 64 cm, X = 84, 63, 42, 21, or 0 cm) with five generic ball arrival positions (BAP at Y = 0 cm, X = 84, 63, 42, 21, or 0 cm, see Fig. 1). On each trial, random offsets, now between -10.5 and + 10.5 cm (half the distance between neighboring BDPs and BAPs), were applied to the selected generic ball departure and arrival positions separately. Given that the center of the paddle could be moved leftward to a maximal distance of 80.9 cm and that the paddle was 6.75 cm wide, the left edge of the paddle could end up at a maximal distance of at 84.3 cm. With the random offsets applied to the generic ball trajectories, this meant that about 50% of the balls with a generic ball arrival position of 84 cm could not be reached with the left side of the paddle. Finally, the ball flight times on each trial could be 1.2, 1.0 or 0.8 s. Combining the 5 generic ball departure positions with the 5 generic ball arrival positions and the 3 ball flight times gave rise to 75 trials. The actors performed two blocks of such trials, leading to a total of 150 *action* trials.

In the actors' *judging* session, they were presented with generically identical trials (same generic ball departure and arrival positions, but slightly different because the random offsets played out differently on each trial) as above described for the *action* session. However, the actors' task was now to verbally call “no” when they perceived a ball to be uninterceptable for themselves, while attempting to make the interception. After giving a “no”-call, the actors were free to abandon their interception attempt on that trial (cf. Damle et al., 2024). All other details of the *judging* session were identical to those of the *action* session. The actors also performed two blocks of 75 trials, leading to a total of 150 *judging* trials.

Each trial commenced with the actors moving their paddle to the designated starting position on the interception axis, depicted by a red rectangle (7.5 cm wide, 1 cm high), on the right side of the interception axis (X = 0 cm, see Fig. 1). The trial began after the paddle had stayed inside the rectangle for 1 s, after which the red rectangle disappeared, and the ball started moving down the screen. If the ball was intercepted by the paddle by bouncing it back upwards, the trial was classified as a hit (paddle turned green). If the trial was unsuccessful, the ball would move downward beyond the interception axis and was classified as a miss (paddle turned red). Actors received short breaks between every session and an optional break within sessions.

### 2.3.2. Observers' experimental sessions

Like the actors, each of the 12 observers also performed three experimental sessions, labeled *training*, *action* and *judging*. The order of the latter two sessions was counterbalanced across the observers. The *training* session of the observers was identical to the *training* session of the actors. Thus, the observers were to intercept as many virtual balls as possible using the virtual paddle, and the *training* trials only comprised balls which were designed to be interceptable (arriving at reachable positions on the interception axis). Combining the 5 generic ball departure positions with the 5 generic ball arrival positions and the 2 ball flight times (1.6 or 1.2 s), again, gave rise to 50 trials. The observers performed three blocks of such trials, leading to 150 *training* trials.

The next two sessions for the observers were the *action* and *judging* sessions. The observers' *action* session was also identical to the actors' *action* session. Thus, the observers were required to intercept as many balls as possible using the paddle and the trials comprised both interceptable and uninterceptable balls (arriving at positions within and beyond reach). Identical to the actors' *action* session, the 25 combinations of generic ball departure and arrival positions were combined with the 3 ball flight times (1.2, 1.0 or 0.8 s), which gave rise to 75 trials. The observers also performed two blocks of such trials, leading to 150 *action* trials.

For the *judging* session, there were three crucial differences between the actors and the observers. First, in the actors' *judging* session, actors made judgments about interceptability for themselves (self-judgments), whereas the observers made judgments about interceptability for the actors (others-judgments). Second, the actors' judgments entailed verbal “no”-calls when they perceived a ball to be uninterceptable while trying to make interceptions. On the other hand, the observers' judgments comprised keypresses in a 2-Alternative Forced-Choice (2AFC) task while they observed the actors' played-back interception attempts. Third, while the actors' *judging*

<footnote n="5">⁵ Throughout the present study, on each trial different random offsets were added to the generic ball departure and arrival positions. This implied that the resulting trajectory incidence angles with respect to the interception axis also differed over trials with identical generic combinations of ball departure and arrival position. Unlike our previous studies (Damle et al., 2024, 2025), in this study the angle of approach was thus truly a continuous variable.</footnote>

<footnote n="6">⁶ Balls did not stop at *ball arrival positions*: When intercepted, they bounced back up near this position and when missed, they passed through the interception axis at this position, continuing their motion. Also, balls started at an invisible (off-screen) position that was different from the *ball departure position*. Obviously, what was relevant for the participants was the linear ball trajectory that we constructed to pass through these two points, not the positions per se. For ease of presentation, we chose to label the two points by referring to ball departure and arrival.</footnote>
session involved balls arriving at positions covering the entire interception axis, the observers' *judging* session involved only a selection of balls arriving towards the left side of the interception axis. The rationale for this is explained below.

The selected trials were displayed to the observers in a randomized order on the screen. The observers were informed that trials from a previous experiment would be presented in which participants (actors) performed a similar interception task as the observers had experienced in their *training* session. The fact that the paddle movement was limited on the left side of the screen was not mentioned to the observers. In this *judging* session, when the ball had reached the bottom 25% of the screen, this bottom 25% of the screen was occluded, such that both the ball and the paddle were made invisible. This ensured that the observers could not know the outcome of the trial, and thus they received no feedback on their judgments. The observers viewed the unfolding ball-and-paddle kinematics and were required to make a 2AFC keypress on a keyboard to indicate whether they perceived that the ball could still be intercepted by the actor ("interceptable": right arrow key) or not ("uninterceptable": left arrow key) on each trial.

For the set of trials to be presented to the observers, we selected 12 trials from each actor, making a pool of 144 *judging* trials. The rationale for selecting the trials was to achieve a 50-50 distribution between two trial types: "uninterceptable" and "interceptable". In prior experiments (Damle et al., 2024, 2025), achieving such an even split had proved to be difficult. Thus, to achieve this even distribution, in the present study we sampled around the enforced action boundary, near the left side of the screen. We curated criteria for the selection of trials for the "uninterceptable" pool (72) and the "interceptable" pool (72) as follows.

First, the criteria for selecting trials that we labeled "uninterceptable" were retaining only those trials wherein: (i) the actor had made a "no"-call, (ii) the actor had not intercepted the ball (a miss),<fnref n="7" /> and (iii) the generic ball arrival position was the leftmost of the five (84 cm, i.e., farthest away from the starting position). This led to a pool of 187 trials that fit these criteria. Out of these 187 trials, we randomly selected 2 trials per ball flight time (1.2, 1.0, 0.8 s) for each actor. This resulted in 6 trials per actor which fit the criterion of "uninterceptability". The random selection also ensured a balance across ball departure positions. Thus, there were 2 trials per ball flight time (1.2, 1.0 or 0.8 s) per actor (12), creating the pool of 72 "uninterceptable" trials.

Second, the criteria for selecting "interceptable" trials were retaining trials wherein: (i) the actor had not made a "no"-call, (ii) the actor had intercepted the ball (a hit),<fnref n="8" /> and (iii) the generic ball arrival position, again, was the leftmost (84 cm, i.e., farthest away from the starting position). These criteria led to a pool of 104 trials. We attempted to include 2 trials per ball flight time (1.2, 1.0, 0.8 s) per actor, as was done for the "uninterceptable" trials. However, there were 10 instances wherein these criteria were not fulfilled for some actors. Thus, we expanded the selection to the adjacent generic ball arrival position (63 cm, i.e., second to leftmost BAP) to make up for the 10 missing trials. Again, the random selection also ensured a balance across ball departure positions. Thus, there were 2 trials per ball flight time (1.2, 1.0 or 0.8 s) per actor (12), creating a pool of 72 "interceptable" trials.

Two blocks of the 144 *judging* trials of the (12) actors' ball-and-paddle kinematics were presented to the observers in a randomized order, making a total of 288 *judging* trials. On each trial, observers judged the ball's interceptability for the actor controlling the paddle by pressing one of two keys (right arrow key: interceptable, left arrow key: uninterceptable). Observers received short breaks between every session and an optional break within sessions.

## 2.4. Data analysis

For each trial of the sessions requiring participants to attempt to intercept the ball (i.e., actors' *training*, *action* and *judging* sessions and observers *training* and *action* sessions), the time series of ball and paddle position were saved in a separate file. Verbal judgments ("no"-calls) made by the actors in their *judging* session were recorded using a microphone. Each trial was saved as a separate wav file. In the observers' 2AFC *judging* session, their keypress judgments were recorded and saved.

Success rate of interception was calculated per session as the total percentage of balls intercepted. A trial was classified as a successful interception (or hit) if the ball bounced back up after making contact with the paddle. We computed positions and velocities of ball and paddle using a horizontal x-axis pointing from right to left and a vertical y-axis pointing upwards, with the origin at the average starting position of the paddle (see Fig. 1).

Generalized linear mixed effects regression (GLMER) models were developed for analyzing the actors' and observers' data. This analysis was appropriate since it accounts for the nested dependencies which often occur in repeated measures designs, such as the present study. We derived separate GLMER models for the actors' *action* (hit or miss) and *judging* (presence or absence of verbal "no"-call) sessions respectively. We also derived separate GLMER models for the observers' *action* (hit or miss) and *judging* (interceptable or uninterceptable keypress judgment) sessions, respectively. Further, to compute the accuracy of the observers' judgments, a confusion matrix was created based on the presented trial types and the observers' judgments.

For the GLMER models on the *action* sessions of both actors and observers as well as the actor's *judgment* session, we computed the continuous variables of distance from start (D) and the angle of approach (AoA). Distance from start (D) was calculated as the distance from the paddle starting position to the ball arrival position on the interception axis. Angle of approach (AoA) was operationalized as the angle (in degrees) with the vertical under which the ball approached the horizontal interception axis (i.e., the trajectory incidence angle), with a positive angle for balls with a leftward horizontal velocity component. These continuous variables were converted to Z-scores for the purpose of the analyses (Harrison et al., 2018; Schielzeth, 2010). Ball flight time (T) was considered as a factor with three

<footnote n="7">⁷ There were some trials wherein a "no"-call was made, yet the ball was still intercepted in the end making it a misjudged trial. These trials were not included in the pool shown to the observers.</footnote>

<footnote n="8">⁸ There were also trials on which a "no"-call was not made, and still the ball was not intercepted, thus also making it a misjudged trial. These trials were not included in the pool shown to the observers.</footnote>
levels, using *T* = 0.8 s as the reference. Session order (O: *action*-first or *judging*-first) was also considered as a factor in the models.<fnref n="9" /> In each model, participant (*P*<sub>a</sub> for actors and *P*<sub>o</sub> for observers respectively) was considered as random intercept.

For the GLMER models on the observers' *judging* session, we also considered the factors of distance from start (D), ball flight time (T), angle of approach (AoA), session order (O). In addition, we examined the position and velocity of the paddle and the ball at the moment of occlusion (i.e., when the ball had traveled 75% of its trajectory). Because the paddle only moved in the horizontal direction, we only computed its position (*p*<sub>x,paddle</sub>) and velocity (*v*<sub>x,paddle</sub>) in the x-direction. Also, the position of the ball at the moment of occlusion was only computed in the x-direction (*p*<sub>x,ball</sub>) because the y-position of the ball at the moment of occlusion did not vary, as it was always at 25% of the screen height from the bottom of the screen. The velocity of the ball was computed along both dimensions (*v*<sub>x,ball</sub> and *v*<sub>y,ball</sub>). These continuous variables were also converted into Z-scores for the GLMER analyses. In all models, we included participant (*P*<sub>a</sub> and *P*<sub>o</sub>) as random intercepts.

We consistently used the logit link function for the GLMER models because the distributions were binomial (dichotomous outcome variables). To assess the influence of the above-mentioned factors, we started off with an intercept-only model (i.e., a model with only *P* as random effect). Using a stepwise forward approach, we added other variables as predictors to the model and retained only those which led to a decrease of the Akaike Information Criterion (AIC) by 2 or more. We considered the VIF (variance inflation factor) for all variables and interactions to check for multicollinearity. After entering the main effects, we tested the various one-way interactions between the variables for a significant improvement of the model fit. We performed this procedure until the model could not be significantly improved any further.

## 3. Results

Before addressing the major goal of the present study of evaluating observers' ability to judge whether a ball was interceptable for others, we first briefly present the results of the actors' sessions, for two reasons. First, the materials collected from the actors were used to create the materials for the observers. Second, although not the main objective in our study, the design of the study allowed a direct comparison with our previous work (Damle et al., 2024). Details can be found in the supplementary materials.

### 3.1. Actors results

As stipulated before, the 12 actors performed three experimental sessions: *training*, *action* and *judging* for oneself. The order of the latter two sessions was counterbalanced across the actors. In the *training* session, all trials were designed to be interceptable; all balls arrived after ball flight durations of 1.6 or 1.2 s at positions on the interception axis between 76.375 and 7.625 cm, that is, within the range that the paddle could reach. The actors were highly successful in this session (overall success rate, on average, 98.3%, ranging from 93.3 to 100%).

#### 3.1.1. Actors' action session

In the *action* session, the actors were to intercept as many balls as possible. This session included a range of interceptable and uninterceptable balls, with balls arriving after ball flight durations of 1.2, 1.0 or 0.8 s at distances between 94.5 and – 10.5 cm. The actors' average overall success rate in the *action* session was 80.3% (ranging from 74.0 to 87.3%). Importantly, the realized random offsets to the ball arrival and ball departure positions played out such that 184 out of the total of 1800 trials (10.2%) and out of the 360 trials (51.1%), with the generic ball arrival position at 84 cm, were physically uninterceptable (i.e., beyond the paddle limit) for the actors.

The Generalized Linear Mixed Effects Regression (GLMER) analysis that we performed to establish the significant predictors of interceptability considered the following variables for inclusion in the model: task variables *D* (distance from start), *T* (ball flight time), AoA (angle of approach) as fixed effects, and participant (*P*<sub>a</sub>) as random intercept. These variables were previously found to predict interceptability for oneself (Damle et al., 2024). Additionally, the session order (O: *action*-first or *judging*-first) was also considered as a factor in the model.

As can be seen from the second column of Table 1 (Actors' Action) most of the abovementioned variables turned out to be significant predictors of the actors' interception success in the present study (for details, see supplementary material: Table S1). Importantly, session order did not emerge as a predictor, demonstrating that having done the *action* session before the *judging* session or not did not significantly affect the success rates. When we consider the task variables, increased distance from the start (D) as well as decreased ball flight time (T) resulted in decreased success rates. The interaction effect of *D* and *T* indicated that success rates deteriorated at longer distances for shorter ball flight times. Finally, the angle of approach (AoA) also affected the success rates, also in interaction with the distance from the starting position.

#### 3.1.2. Actors' judging session

In the *judging* session, actors were tasked with attempting to intercept the ball on each trial, while calling “no” as soon as they judged the ball to be uninterceptable for themselves. After calling “no” they could abandon their interceptive action. As in the actors'

<footnote n="9">⁹ Although our study did not have the objective of testing for gender differences on the (perception of the) affordance of interceptability, our design did allow this. Given the gender bias in science in general (cf. Perez, 2019), we did consider the factor of gender in our GLMER analyses. In none of these analyses, this factor turned out to be a significant predictor.</footnote>
<caption>**Table 1**</caption>

Summary table of final GLMER models with b-parameter estimates and standard errors for each factor (column 1) included in the model (column 2: Actors' *action* session, column 3: Actors' *judging* session, column 4: Observers' *action* session). For the action sessions, an interception was coded as 1 and a miss was coded as 0; for the *judging* sessions, a "no"-call was coded as 1 and the absence of a "no"-call was coded as 0. An 'X' denotes the absence of a significant predictor in the respective model. D: distance from start; T: ball flight time comparisons at two contrasts (T1: 1.0 s – 0.8 s and T2: 1.2 s – 0.8 s) and AoA: angle of approach. Participant is included as random intercept (P<sub>a</sub>: for actors, P<sub>o</sub>: observers).

<table><thead><tr><th rowspan="2"></th><th colspan="1">Actors' Action</th><th colspan="1">Actors' Judging</th><th colspan="1">Observers' Action</th></tr><tr><th>β ± SE</th><th>β ± SE</th><th>β ± SE</th></tr></thead><tbody><tr><td>Intercept</td><td>2.659 ± 0.15</td><td>-5.496 ± 0.49</td><td>0.258 ± 0.14</td></tr><tr><td>D</td><td>-1.868 ± 0.13</td><td>3.939 ± 0.40</td><td>-1.683 ± 0.12</td></tr><tr><td>T1 (1.0-0.8)</td><td>1.296 ± 0.22</td><td>-0.871 ± 0.23</td><td>1.128 ± 0.17</td></tr><tr><td>T2 (1.2-0.8)</td><td>1.726 ± 0.27</td><td>-1.363 ± 0.24</td><td>1.490 ± 0.18</td></tr><tr><td>AoA</td><td>0.552 ± 0.12</td><td>1.179 ± 0.45</td><td>0.412 ± 0.11</td></tr><tr><td>D x T1</td><td>-0.385 ± 0.20</td><td>X</td><td>X</td></tr><tr><td>D x T2</td><td>-0.675 ± 0.24</td><td>X</td><td>X</td></tr><tr><td>D x AoA</td><td>-0.626 ± 0.09</td><td>-0.948 ± 0.36</td><td>-0.677 ± 0.09</td></tr><tr><td>Equation</td><td>Actor Int. ~ D + T1 + T2 + AoA + D x T1 + D x T2 + D x AoA + (1 | P<sub>a</sub>)</td><td>Actor Judg. ~ D + T1 + T2 + AoA + D x AoA + (1 | P<sub>a</sub>)</td><td>Obs. Int. ~ D + T1 + T2 + AoA + D x AoA + (1 | P<sub>o</sub>)</td></tr></tbody></table>

*action* session, this session again included a range of interceptable and uninterceptable balls, with balls arriving after flight durations of 1.2, 1.0 or 0.8 s at positions on the interception axis between 94.5 and – 10.5 cm. The average rate of successful interception by the actors in this session was 78.8% (ranging from 65.3 to 86.0%). On average, the "no"-calls were given 0.83 s (average SD = 0.22 s) after the ball had started moving.

The actors made a cumulative 218 verbal "no"-calls on a total of 1800 trials, which amounts to 12.1% of all *judging* trials. The frequency varied per actor and ranged from a minimum of 11 to a maximum of 32 "no"-calls. Fig. 2 presents the frequency of "no"-calls (%) as a function of generic ball arrival position (BAP) and ball flight time (T). Clearly, hardly any "no"-calls were given until a distance from the start (D) of 63 cm and the frequency of "no"-calls at the generic distance from the start of 84 cm seemed affected by ball flight time (T). To scrutinize these effects, we performed a GLMER analysis on the presence of "no"-calls (for details, see supplementary material: Table S2). The third column of Table 1 (Actors' Judging) presents the final model. The analysis confirmed these observations, showing the effects of distance from the start (D) and ball flight time (T). Furthermore, also the angle-of-approach (AoA) affected the frequency of the "no"-calls, also in interaction with distance from the start (D). Finally, the absence of session order as significant predictor of the frequency of the "no"-calls indicated that there is no reason to consider an effect of having had the additional experience of doing the task oneself (in the *action* session) on the *judging*.

## 3.2. Observers results

The observers also performed three experimental sessions: *training*, *action* and *judging*, with the first two being identical to those of the actors and the latter now concerning judgments for others. The order of *action* and *judging* sessions was counterbalanced across the observers. On average, the observers were highly (97.9%, ranging from 96.0 to 100%) successful in the *training* session, in which all trials were designed to be interceptable.

### 3.2.1. Observers' action session

As mentioned before, half of the observers had their action session before the *judging* session and the other half of the observers the other way around. On average, the observers' success rate in the *action* session was 76.7%, ranging from 69.3 to 86.7%. As can be seen in the fourth column of Table 1 (Observers' Action), the GLMER analysis indicated significant effects of distance from starting position (D), ball flight time (T), angle-of-approach (AoA), as well as a D x AoA interaction effect (for details, see supplementary material: Table S3).

### 3.2.2. Observers' judging session

In the observers' *judging* session, observers did not manipulate the paddle themselves but watched (played-back recordings of) on-screen ball and paddle motions produced by the 12 actors in 144 selected trials from their *judging* session. Observers only saw the ball and paddle motions during the first 75% of the trial duration, after which the ball and paddle were occluded. Videos 1 through 4 present exemplar animations of the material presented to the observers, with trials with an interceptable ball (Videos 1 and 3) and trials with an uninterceptable ball (Videos 2 and 4). The animations in Videos 1 and 2 came from the same actor with the ball trajectory of the same generic ball departure positions, ball arrival position, and ball flight time (however, due to the random offsets that we applied, the ball trajectories were not identical). The animations in Videos 3 and 4 are from another actor, also with the same generic ball departure position and ball arrival position but different ball flight times. On each of the 144 selected trials (see Method section 2.3.2 for trial selection criteria), observers were required to indicate (un)interceptability for the actors using the 2AFC keypress method. Each observer viewed two blocks of the 144 selected trials for a total of 288 *judging* trials.

Out of a total of 3456 *judging* trials, in 27 trials (between 2 and 3 per observer), no keypress response was recorded. These trials
were excluded in the analyses of the observers' *judging* session, which thus pertained to the remaining 3429 trials. The observers gave 1921 judgments of interceptability (56.0%). The frequency of each individual observer's judgments of interceptability and uninterceptability can be found in the supplementary material (Table S4). On average, the judgment came 2.12 s (average *SD* = 0.43 s) after the ball had started moving down.

Table 2 gives the confusion matrix with the observers' judgments (interceptable or uninterceptable for the actor) as a function of the trial type (interceptable or uninterceptable). To reiterate, a trial was labeled to contain an interceptable ball if the actor had successfully intercepted the ball and had not given a “no”-call; a trial was labeled uninterceptable if the actor had given a “no”-call and had not intercepted the ball. The congruency of the observers' judgments with the trial type resulted in 2476 correctly judged trials (1347 + 1129) out of 3429 total trials, implying that the accuracy of the observers' judgments was 72.2%. Additionally, the measures of precision (or positive predictive value) and sensitivity (recall or true positive rate) were found to be 70.1% and 78.0% respectively. The model's performance was also evaluated by the Area Under the Curve (AUC) yielding a value of 0.72. Taken together, these measures indicated that the observers performed well above chance level and were moderately accurate in making their judgments about interceptability for the multiple actors.

Next, we performed a series of GLMER analyses to assess which variables turned out to be significant predictors of the judgments. We started with a set of potential predictors that we had considered before: Distance from the starting position (D), ball flight time (T), and the angle of approach (AoA). In this first model, we considered these three candidate variables as potential predictors as well as the order (O) in which the observers had performed the *action* and *judging* sessions. The second column of Table 3 (Model 1) shows that all these variables except the order of the sessions significantly contributed to predicting the judgments (for details, see supplementary material: Table S5). Apparently, experiencing the action-session task (with the physical boundary) oneself did not lead to significantly better performance in judging. As can be seen in the table, balls that would intersect the interception axis at larger distances from the start (D) and balls that would take less time to reach the interception axis (T) would have a higher probability to be judged as uninterceptable.

The predictors in the first model all referred to (experimenter-controlled) ball kinematics: the position where it crossed the interception axis, the duration of its flight, and the angle under which the ball approached the interception axis. The (actor-produced) paddle motion was not included in the analyses that led to this first model. Given that an affordance is relationally defined, the kinematics of the paddle, most probably, will also be a factor in judging if a ball will be interceptable or not. For instance, the same ball (i. e., same arrival position, speed, and approach angle) might be interceptable when the paddle started moving early on and at high speed but not when the paddle's movement was initiated later on or when it moved at a lower speed. At the moment of occlusion (at 75% of ball flight duration), the paddle would be closer to the ball in the former situation than in the latter situation, and perhaps also still be closing the paddle-ball gap at a faster pace. In a second model, in addition to the distance from the starting position, ball flight time and angle of approach as the predictors, we also considered the position and the speed of the paddle at the moment of occlusion (for full model output, see supplementary material: Table S6). As can be seen in the third column of Table 3 (Model 2), adding the position of the paddle at the moment of occlusion to the set of predictors significantly improved the model of the observers' judgments whereas the

<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Frequency of “no”-calls (%) as a function of generic ball arrival position (BAP) and ball flight time (T) in the *actors’ judging* session. The ball flight times are represented as follows: 1.2 s: blue, 1.0 s: orange, 0.8 s: green. The paddle starting position was at the right-most BAP (0 cm). The error bars depict the standard deviation across participants. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
<caption>**Table 2**</caption>

Classification table for the observers' judging session with respect to the trial type (interceptable or uninterceptable) and observers' 2AFC judgments (judged interceptable or judged uninterceptable).

<table><thead><tr><th rowspan="2"></th><th colspan="2">Trial Type</th><th rowspan="2">Total</th></tr><tr><th>Interceptable</th><th>Uninterceptable</th></tr></thead><tbody><tr><th>Judgment</th><td></td><td></td><td></td></tr><tr><th>Judged Interceptable</th><td>1347</td><td>574</td><td>1921</td></tr><tr><th>Judged Uninterceptable</th><td>379</td><td>1129</td><td>1508</td></tr><tr><th>Total</th><td>1726</td><td>1703</td><td>3429</td></tr></tbody></table>

speed of the paddle at that moment did not. The probability of the observers indicating that a ball would be uninterceptable for the actor controlling the paddle increased when the paddle, at the moment of occlusion, was positioned more to the right, farther from where the ball was destined to pass the interception axis. Clearly, this second model demonstrates that the affordance of (un)interceptability is contingent upon the relation of ball and paddle movement, and that the observers' judgments reflect this.

Up to the moment of occlusion, the position and speed of the paddle are visible<fnref n="10" /> to the observers. The same is not true for the ball flight time. However, ball flight time is one-to-one related to ball speed, and ball speed is visible to the observers. Also, the angle of approach (given that in the present experiment and its predecessors, balls followed straight trajectories, which makes that the angle of approach does not change during ball flight) is visible to the observers. However, the position where the ball will pass the interception axis is not. There is optical information in the unfolding of the ball trajectory that specifies this position (e.g., see Ledouit et al., 2013) but the position per se lies in the future and will be occluded. In contrast, for the observers, at the moment of occlusion, the paddle's position and speed are optically available, just as the ball's position and velocity (because the ball travels under an angle with the vertical, not only its speed but also the direction of motion differs from trial to trial). Therefore, in a third model, we considered paddle position and speed as well as ball position and its horizontal and vertical speeds, all at the moment of occlusion (i.e., when the ball had traveled 75% of its downward path). All these variables turned out to be significant predictors in the resulting model, presented in Table 4 (for full model output, see supplementary material: Table S7). Moreover, this third model possesses significantly better predictive power than the previous two models.

An inspection of Table 4 indicates that the probability for balls to be judged as uninterceptable increased when, at the moment of occlusion, the ball was positioned more to the left and the paddle was positioned more to the right. Furthermore, the higher the horizontal ball speed (leftward speed was defined as positive) the higher the probability of judging the balls as uninterceptable. The same holds for the paddle, although the effect of paddle speed was slightly smaller than that of horizontal ball speed. The interaction effects are much harder to interpret. However it may be, the mix of effects demonstrates that the probability for balls to be judged as uninterceptable is related to a set of kinematic variables in a complex fashion. A logical next step seems to be to inspect the angle $\beta$, formed by the interception axis and the (invisible) line connecting the ball and paddle, and its temporal derivatives (cf. Benerink et al., 2016, 2018; Damle et al., 2025; Van Opstal et al., 2018). This angle and its temporal derivatives are defined over exactly the variables that we considered in this final model. A GLMER model with $\beta$ and its first temporal derivative as candidate variables did show significant effects of both as well as a significant interaction effect. The predictive value of this model (i.e., the AIC value) was better than all GLMER models except the final one with the kinematic variables at the moment of occlusion. We left the endeavor with a more principled consideration of these angular variables for future studies.

## 4. Discussion

In the present study, we used a manual lateral interception task to investigate whether individuals could accurately perceive the affordance of interceptability for others. In the interception paradigm that we adopted, a virtual ball moved down under an angle with the vertical from the top to the bottom of a screen. A paddle could be moved along an invisible (horizontal) interception axis near the bottom of the screen. What we presented to the observers in this study were ball-and-paddle motions recreated from the kinematics of successful and unsuccessful interception attempts by the group of actors. These actors controlled a paddle through a hand-held slider (using the “asymmetric” slider-paddle mapping). A successful interception meant that the paddle was moved such that it ended up at the right position in the right time to contact the ball (after which the ball would bounce up).

Earlier (Damle et al., 2024), we demonstrated that people are quite accurate in perceiving the affordance of interceptability for themselves. In a next study, we used the on-screen ball-and-paddle kinematics of a single actor from the Damle et al. (2024) study and played these back to a fresh group of participants. The judgments of these participants (the observers in Damle et al., 2025) resembled the original (single) actor's judgments, which we took as a first indication that people are quite well able to perceive the affordance of interceptability for another. This would imply that information about the interceptability for another individual resides in the

<footnote n="10">¹⁰ An issue that we will not be able to resolve in the present contribution is what the information is that observers use to make their judgments. Or more in general, what informs people about (un)interceptability in the manual lateral interception task. The informational variable will, mathematically, be a complex combination of the variables that we included in our analyses, probably in the form of an angle (e.g., between the line connecting the paddle and the ball and the horizontal interception axis) or one of its derivatives (e.g., see Benerink et al., 2016, 2018; Van Opstal et al., 2018).</footnote>
<caption>**Table 3**</caption>

Summary table of the GLMER Models 1 and 2 of the Observers' *judging* session (2AFC). An uninterceptability judgment was coded as 1 and an interceptability judgment was coded as 0. Model 1 includes the predictors of D, T, AoA and D x T interactions. Model 2 additionally includes the predictor of *p*<sub>x,paddle</sub>. D: distance from start; T: ball flight time comparisons at two contrasts (T1: 1.0 s – 0.8 s and T2: 1.2 s – 0.8 s), AoA: angle of approach and *p*<sub>x,paddle</sub>: paddle X-position at the moment of occlusion. Participant is included as random intercept (*P*<sub>a</sub>: for actors, *P*<sub>o</sub>: observers). The AIC (Akaike information criterion) is noted at the top of each model.

<table><thead><tr><th rowspan="2"></th><th>Model 1 (AIC = 3964)</th><th>Model 2 (AIC = 3506)</th></tr><tr><th>β ± SE</th><th>β ± SE</th></tr></thead><tbody><tr><td>Intercept</td><td>-0.240 ± 0.23</td><td>-0.213 ± 0.21</td></tr><tr><td>D</td><td>0.253 ± 0.04</td><td>0.249 ± 0.04</td></tr><tr><td>T1 (1.0–0.8)</td><td>-1.560 ± 0.10</td><td>-0.622 ± 0.11</td></tr><tr><td>T2 (1.2–0.8)</td><td>-1.922 ± 0.10</td><td>-1.103 ± 0.12</td></tr><tr><td>AoA</td><td>-0.240 ± 0.04</td><td>-0.129 ± 0.04</td></tr><tr><td><i>p</i><sub>x,paddle</sub></td><td></td><td>-1.239 ± 0.06</td></tr><tr><td>D x T1 (1.0–0.8)</td><td>-0.650 ± 0.09</td><td>-0.447 ± 0.09</td></tr><tr><td>D x T2 (1.2–0.8)</td><td>-0.794 ± 0.11</td><td>-0.678 ± 0.12</td></tr><tr><td>Equation</td><td>Obs. Judg. ~ 1 + D + T + AoA<br/>+ D x T + (1 | Po) + (1 | Pa)</td><td>Obs. Judg. ~ 1 + D + T + AoA + <i>p</i><sub>x,paddle</sub><br/>+ D x T + (1 | Po) + (1 | Pa)</td></tr></tbody></table>

unfolding ball-and-paddle kinematics. Importantly, in (lateral) interception, it is not only the ball kinematics (nor its place and time of crossing the interception axis) in relation to the actor's interception ability (e.g., their maximally attainable speed) that determine whether a ball is interceptable. Indeed, the actor will also show inherent variability in their movements (for instance, in their initiation time). Even a ball that will pass the interception axis close enough to be easily reached by an actor will become uninterceptable when the actor starts moving too late (or not at all). The trial-by-trial variations in the kinematics are an integral part in determining whether a ball will be interceptable. The Damle et al. (2025) study suggests that information is available to observers that accommodates all this variability. Stronger evidence for this would be the demonstration of the ability to perceive the affordance of interceptability for others, now using ball-and-paddle kinematics from multiple actors. This is what the present study aimed to contribute.

Rather than using the ball-and-paddle kinematics from the complete set of participants of the Damle et al. (2024), from which we had selected the single actor in Damle et al. (2025), we decided to collect ball-and-paddle kinematics anew, allowing us to introduce a number of differences in the design that would be beneficial for putting together a set of animations (i.e., played back ball-and-paddle kinematics for the observers). One of the differences was in the mapping between the slider and paddle. Whereas the previous studies had used a symmetric mapping between the slider and paddle, such that the full range of slider movement allowed moving the paddle across the full width of the screen (and even beyond), the slider-paddle mapping used in the present study made it impossible for the paddle to move completely to the extreme left of the interception axis. A check of this effective boundary indicated that this manipulation was successful. For the actors' trials that were within the leftmost ball-arrival-position bin (i.e., the spread in ball arrival positions around the distance of 84 cm), about half of the trials were beyond the reach of the paddle. Next, this manipulation enabled us to sample around the boundary for trials to be presented to the observers, thus producing a balanced set of interceptable and uninterceptable trials from the actors' session. Subtly different from our previous studies (Damle et al., 2024, 2025) was also the criterion that we used to label balls interceptable or not. The previous studies compared the judgments (i.e., the “no”-calls) with the success of interception attempts, ignoring the situations in which balls that were judged to be uninterceptable were still intercepted and unintercepted balls were not accompanied by an uninterceptability judgment. Here, we only presented balls to our observers in which the actors' judgment and action outcome were congruent. Now, having a balanced set of interceptable and uninterceptable trials allowed us to test the observers' perception of interceptability using a 2-Alternative Forced-Choice (2AFC) design (Fechner, 1966; Hautus et al., 2009; Wixted, 2020). Rather than indicating that a ball was deemed to be uninterceptable by calling “no” (cf. Damle et al., 2024, 2025, and the actors in the present study), in the present study we had observers push different buttons for trials judged to show interceptability or uninterceptability, respectively. This inspired another difference relative to the earlier studies, the occlusion of the final part of the actors' ball-and-paddle kinematics. In the Damle et al. (2025) study, we tested the effect of this occlusion and found no significant effects on the judgments. Here, we needed this manipulation to obscure the actors' interceptability outcome success. Finally, we used a wider paddle than in the Damle et al. (2024, 2025) studies. This made that the unsuccessful interceptions by the actors were less affected by ball speed per se. In these earlier studies, interception success rate was affected by ball speeds even for balls clearly within reach, such as balls passing the interception axis on the right half of the screen. Interceptability, under these conditions, was a function of how much time ball speed allowed actors to move to the interception location but also of ball speed in and of itself. A wider paddle mitigates the latter effect and aligns interception success rates more with the former effect.

The design differences as compared to the one used in Damle et al. (2024, 2025) had the effects that we intended. We were able to create a (nearly) 50–50 distribution of trials with interceptable and uninterceptable balls while considering mostly trials with ball arrival positions of the most leftward bin (at 84 cm). The number of trials with balls that turned out uninterceptable for the actors was larger than in our previous study and concentrated more towards the longer distances (e.g., compare Fig. 2 of this study with Fig. 3 in Damle et al., 2024). Furthermore, our analyses indicated that the same task variables were at play in affecting the interception success rates in both studies, be it slightly different, in line with the intended effects of the differences between the studies.

As for the main objective of the present contribution, we found, as hypothesized, that observers were moderately accurate in judging interceptability for the different actors from viewing the actors' ball-and-paddle kinematics. Despite presenting only the end-
<caption>**Table 4**</caption>

Summary table of GLMER Model 3 of the Observers' *judging* session (2AFC). An uninterceptability judgment was coded as 1 and an interceptability judgment was coded as 0. Model 3 includes the predictors of paddle X-position, paddle speed, ball position, horizontal and vertical ball speeds, all at the moment of occlusion. *p*<sub>x,paddle</sub>: paddle X-position, *v*<sub>x,paddle</sub>: paddle speed, *p*<sub>x,ball</sub>: ball X-position, *v*<sub>x,ball</sub>: ball horizontal speed and *v*<sub>y,ball</sub>: ball vertical speed. Participant is included as random intercept (*P*<sub>a</sub>: for actors, *P*<sub>a</sub>: observers). The AIC (Akaike information criterion) is noted between brackets.

<table><thead><tr><th></th><th>Model 3<br>(AIC = 2878)<br>β ± SE</th></tr></thead><tbody><tr><td>Intercept</td><td>-0.197 ± 0.25</td></tr><tr><td>p<sub>x,paddle</sub></td><td>-1.932 ± 0.09</td></tr><tr><td>v<sub>x,paddle</sub></td><td>0.316 ± 0.08</td></tr><tr><td>p<sub>x,ball</sub></td><td>1.549 ± 0.06</td></tr><tr><td>v<sub>x,ball</sub></td><td>0.928 ± 0.05</td></tr><tr><td>v<sub>y,ball</sub></td><td>0.168 ± 0.08</td></tr><tr><td>p<sub>x,paddle</sub> X v<sub>x,paddle</sub></td><td>-0.481 ± 0.08</td></tr><tr><td>p<sub>x,paddle</sub> X p<sub>x,ball</sub></td><td>0.385 ± 0.06</td></tr><tr><td>Equation</td><td>Obs. Judg. ~ 1 + p<sub>x,paddle</sub><br>+ v<sub>x,paddle</sub> + p<sub>x,ball</sub> + v<sub>x,ball</sub><br>+ v<sub>y,ball</sub> + p<sub>x,paddle</sub> X v<sub>x,paddle</sub><br>+ p<sub>x,paddle</sub> X p<sub>x,ball</sub> + (1 | Po) + (1 | Pa)</td></tr></tbody></table>

effector plus ball kinematics of 12 actors in a randomized order, the accuracy of the observers' judgments was 72%. When one has to judge if a ball is interceptable or not, this will be obvious for some balls (clearly within or without reach) and more difficult for the balls that will land close to the boundary of interceptability, the location that can just be reached in the time that the balls need to move there. The present experiment sampled around this boundary. Thus, we cannot expect the observers to be fully correct (neither would they need to be) and their better-than-chance performance indicates an ability to judge the affordance of interceptability in the present paradigm.

The GLMER analyses indicated that the judgments were best predicted by the combined ball-and-paddle motion right before we occluded this. Thus, the information for knowing if a ball will still be interceptable for someone else must be present in the evolving structure of the ball and paddle positions. Although prior research showed that people could perceive the actions afforded to another person (e.g., Ramenzoni et al., 2008, 2010; Weast et al., 2011, 2014, Weast-Knapp et al., 2019; Davis et al., 2010), these studies, as far as we are aware of, never used the results of multiple actors. With the information residing in the ball-and-paddle kinematics, it should not matter how many individuals contributed to the set of trials offered to the observers. Indeed, regardless of whether one or twelve people contributed their ball-and-paddle kinematics, observers were still able to judge (un)interceptability for them.

Before performing their judging task, all of the observers received the same training as the actors had had. However, half of the observers also first had an action session. In contrast to the training session, the action session included balls passing the interception axis beyond the limit in allowed paddle movement. If having had experience with this limit would have helped the observers in their judgments, this would have resulted in the analyses indicating a significant order effect. No such effect emerged from the analyses. Of course, caution is called for in interpreting the absence of significant effects, but it seems fair to conclude that we have no reason to expect a consequential influence of this experience on the observers' judgments. In the present study, we applied a manual lateral interception task with virtual balls that followed downward linear trajectories at a constant velocity. A valid point of critique might be that real balls never follow such trajectories (in Earth's atmosphere, that is), which begs the question whether results from such a task generalize to the real-world affordances. Would it not be better to study a task that involves interception of real balls (e.g., Postma et al., 2018, 2022)? The main reason to resort to a ball-and-paddle-on-a-screen task, obviously, was the much higher control over ball motion than in real-ball interception. Furthermore, the task that we adopted has a long history in our field, and important critical effects known from real-ball interception have been replicated in the present task (e.g., the angle-of-approach effect and movement reversals; compare Peper et al., 1994 and Montagne et al., 1999 to Ledouit et al., 2013, Ledouit et al., 2024). Still, more follow-up studies with balls following natural trajectories would be welcome also in terms of the affordance of interceptability. Given how challenging it can be to manipulate, control, and measure free-flying balls, a middle ground could be to apply VR, with balls and the rest of the environment being presented through head-mounted displays (HMDs), which then might make that one would prefer to study locomotor rather than manual lateral interception (e.g., Bootsma et al., 2016) and the interception of other targets than balls (e. g., Steinmetz et al., 2020).

In summary, in the manual lateral-interception task that we adopted, by sampling around the action boundaries of multiple actors and only displaying their ball-and-paddle kinematics with late-occlusion, we found that observers were able to perceive the affordance of interceptability for (the) actors. This underwrites that information about interceptability for others is present in these ball-and-paddle kinematics (i.e., agent-ball relations). The candidate informational variable, we posit, may reside in the rate of change of the angle $\beta$, formed by the interception axis and the (invisible) line connecting the ball and paddle (cf. Benerink et al., 2016, 2018; Damle et al., 2025; Van Opstal et al., 2018). Future research is however necessary to identify whether change in angle $\beta$ is indeed the informational variable that specifies the affordance perception of interceptability for oneself and for others.

Supplementary data to this article can be found online at https://doi.org/10.1016/j.humov.2026.103469.
CRediT authorship contribution statement

**Samruddhi Damle:** Writing – review & editing, Writing – original draft, Visualization, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Reinoud J. Bootsma:** Writing – review & editing, Validation, Supervision, Project administration, Methodology, Funding acquisition, Conceptualization. **Frank T.J.M. Zaal:** Writing – review & editing, Validation, Supervision, Software, Project administration, Methodology, Funding acquisition, Data curation, Conceptualization.

Funding

This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 956003.

Declaration of competing interest

None.

Acknowledgements

We thank Ylse Dantuma and Michel Timmer for their assistance in data collection. We also thank Emyl Smid for his help with building the slider-device.

Data availability

Data will be made available on request.

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