Human Movement Science xxx (2010) xxx–xxx

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Human Movement Science journal homepage: www.elsevier.com/locate/humov

Judging the ‘passability’ of dynamic gaps in a virtual rugby environment Gareth Watson a,b,⇑, Sebastien Brault c, Richard Kulpa c, Benoit Bideau c, Joe Butterfield a, Cathy Craig b a School of Mechanical and Aeronautical Engineering, School of Psychology (Interdisciplinary Project), David Keir Building, 18-30 Malone Road, UK b School of Psychology, Queens University Belfast, David Kier Building, 18-30 Malone Road, BT7 1NN, UK c M2S Laboratory, UFR APS, University of Rennes 2 – ENS Cachan, Avenue Charles Tillon, 35044 Rennes, France

a r t i c l e

i n f o

Article history: Available online xxxx PsycINFO classification: 2323 Keywords: Affordances Perception–action

a b s t r a c t Affordances have recently been proposed as a guiding principle in perception–action research in sport (Fajen, Riley, & Turvey, 2009). In the present study, perception of the ’passability’ affordance of a gap between two approaching defenders in rugby is explored. A simplified rugby gap closure scenario was created using immersive, interactive virtual reality technology where 14 novice participants (attacker) judged the passability of the gap between two virtual defenders via a perceptual judgment (button press) task. The scenario was modeled according to tau theory (Lee, 1976) and a psychophysical function was fitted to the response data. Results revealed that a tau-based informational quantity could account for 82% of the variance in the data. Findings suggest that the passability affordance in this case, is defined by this variable and participants were able to use it in order to inform prospective judgments as to passability. These findings contribute to our understanding of affordances and how they may be defined in this particular sporting scenario; however, some limitations regarding methodology, such as decoupling perception and action are also acknowledged. Ó 2010 Elsevier B.V. All rights reserved.

⇑ Corresponding author at: School of Psychology, Queens University Belfast, David Kier Building, 18-30 Malone Road, BT7 1NN, UK. Tel.: +44 (0)28 9097 4686. E-mail address: [email protected] (G. Watson). 0167-9457/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.humov.2010.08.004

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1. Introduction Daily life presents many situations that require us to perform an action sufficiently ahead of time. This relies on successful perception of what the environment affords. Such situations may include crossing roads, pulling out of junctions, braking, or negotiating gaps between obstacles. Successful action in any of these circumstances is as a result of prospective control, i.e., adapting behavior in advance to what the environment affords. Opportunities for action within an environment are known as affordances and are a conceptual pillar of ecological psychology (Gibson, 1979). Such opportunities for action are often fleeting and can come and go in an instance, as is often the case in sport due to the fast paced nature of many sporting activities. As Fajen, Riley, and Turvey (2009) state, ‘‘A gap between opposing players can open to afford passing through at one moment and then collapse into an impenetrable barrier at the next moment” (p. 80). It is precisely this affordance, that of passibility (or passthrough-ability), that the present work investigates. This affordance has been studied in previous work investigating visually guided walking through apertures (Warren & Whang, 1987; Wraga, 1999). The present work sits in line with this by investigating the optical information specifying passability, albeit in a different setting where the aperture is not static, i.e., in the form of obstacles when walking, but dynamic, in the form of other players approaching. Fajen et al. (2009) identify an analog of this situation in American Football, where running backs must perceive whether constantly changing, dynamic gaps in the line of defenders afford passing or not. They point out that no research has investigated affordances in such a scenario. The present work aims to investigate the perception of affordances in exactly this scenario, but using Rugby Union as the sport setting, not American Football. Rugby Union, like American Football, is a fast, dynamic contact sport that is governed by linear defensive systems. The exploitation of gaps between defenders in the opposing defensive line is what often underlies successful attack. The ability to perceive passibility of a defensive gap ahead of time, in this instance, will determine what actions are possible with respect to that gap. This work therefore has relevance to decision making literature in the wider sense, in that optical information specifying passibility may determine the course of action that a player takes. For example, if an attacker with the ball approaches a defensive line where a gap is deemed passable, then he is likely to run through that gap, thus ‘breaking the line’. If it is not perceived as being passable, then that player is likely to pass or kick the ball.

1.1. Perceiving affordances Much research provides support for the notion that within an Environment-Agent System (EAS), affordances are grounded in the geometric properties of that system (pass-through-ability: Warren & Whang, 1987; step-onto-ability: Warren, 1984; walking-up-ability: Kinsella-Shaw, Shaw, & Turvey, 1992; sit-on-ability: Mark, 1987; step-across-ability: Cornus, Montagne, & Laurent, 1999; pass-underability: White & Shockley, 2005). These affordances are known as body-scaled affordances, where a measureable dimension of the actor’s body in relation to a property of the environment determines the possibility of an action (e.g., eye-height scaled information). However, Pepping and Li (2000) pointed out that the specific set of relevant properties that define an affordance are not solely defined by geometric variables, and that action capabilities are important in assessing what an environment affords at any given time. This leads onto the second broad category of affordances – action-scaled affordances, where how the actor can behave relative to the environment determines the possibility of an action. Perception of action-scaled affordances is likely to be prevalent in sport. For instance, in rugby, a player can implement techniques in order to aid gap crossing. If the gap is perceived to be on the boundary of passability, the attacker may perform an action such as pushing the defender away in order to still make it through the gap. Therefore, affordances may be body and/or action scaled. Oudejans, Michaels, Bakker, and Dolné (1996) explored the affordance of catchableness of fly balls. Participants were instructed to either judge the catchableness or actually attempt to catch the ball. Results showed that participants could perceive affordances in both cases, i.e., where affordances were body scaled and action scaled.

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1.2. Optical specification of information While it has been shown that affordances are directly perceivable, what relevant properties of the EAS define affordances for certain actions? That is, what information is used? The ecological approach challenges researchers to identify the informational variables that specify action-relevant properties of the environment. This approach also suggests that expert-novice differences can be, at least in part, explained by differences in perceptual attunement to these variables. This information-based approach has given rise to extensive research in perception–action and in particular, perception–action in sport. David Lee’s General tau theory (1976) underpinned much of this work as it provides a formal description of optical information available to the actor in a given situation. Tau theory is a theory of prospective motor control where changes in an organism’s optic array reveal potentially important sources of action-relevant information. At its most basic, tau is a variable that describes the time to closure of a motion gap between a current state and a goal state at its current rate of change. Time to contact (TTC) has been identified as being an action-relevant informational quantity in the timing of actions in various sporting instances, mostly involving interceptive action (e.g., catching and hitting: Bootsma & Peper, 1992; Gray & Sieffert, 2005; Lee, Young, Reddish, Lough, & Clayton, 1983; Regan & Gray, 2000; Savelsbergh, Whiting, & Bootsma, 1991). Outside of sport applications, this has been explored in collision detection in driving/braking (Bootsma & Craig, 2003; Bootsma & Oudejans, 1993; Gray, 2005; Gray & Regan, 2000) and road crossing (Demetre et al., 1992; Hancock & Manser, 1997; Lee, Young, & McLaughlin, 1984; Young & Lee, 1987). Road crossing is another situation where prospective gap possibility judgments (or gap acceptance judgments) have to be made. Much of the work in this domain, has identified ‘time-to-contact (TTC)’ or time-to-arrival variables as being important in judgments. Tau is specific to TTC and can therefore allow an agent to perceive TTC directly. The present work investigates tau theory applied to the dynamic gap passability context. A simplified dynamic gap scenario is created in a virtual rugby environment and modeled according to tau theory. This provides a parsimonious explanation for defining which conditions would afford passing in terms of information available to the participant, if velocities were to remain constant (i.e., first-order extrapolations). 1.3. Virtual reality methodology Simulated situations provide a way of presenting scenarios while maintaining complete control of visual information. Simulations have been used in sport science and psychophysics research, with immersive interactive virtual environments recently becoming more utilized. This study, beyond the theoretical position, aims to demonstrate the use of immersive interactive environments, in this case fully immersive interactive virtual reality (VR), as a useful methodological tool to carry out this type of work. Previous studies have used computer simulation for sport in order to present stimuli and evaluate behavioral responses to different sporting situations where the visual information presented to the participants is carefully controlled (Araújo, Davids, & Serpa, 2005; Bideau et al., 2003, 2004; Craig, Berton, Rao, Fernandez, & Bootsma, 2005). Being able to precisely control what the observer sees is a major methodological advantage when using virtual reality to simulate events, especially sporting situations that are highly dynamic in their natural setting. Creating immersive interactive environments allows the experimental control to be maintained while allowing accurate manipulation of all other variables, in this case, the visual information and the dynamics of the gap closure. This technology also allows replication of identical trials and the maintenance of highly temporally constrained judgment ‘windows’. For a review of advantages of VR in analyzing sports performance, and recent studies, see Bideau et al. (2010). 1.4. Aims and research questions The aim of the present work is to first demonstrate how tau theory can define a ‘passibility’ affordance in a simplified gap closure scenario and second, to see if novices (non-rugby players) use this information when making passibility judgments ahead of time. Please cite this article in press as: Watson, G., et al. Judging the ‘passability’ of dynamic gaps in a virtual rugby environment. Human Movement Science (2010), doi:10.1016/j.humov.2010.08.004

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2. Method 2.1. Design 2.1.1. Task The participant acted as the attacking player in an immersive attacking situation. He/she was faced by two approaching virtual defenders a certain distance away (from the attacker) and a certain distance apart (from each other). Although the attacker’s motion towards the defensive line was simulated in the virtual environment, the participant was stationary in the real world. The visual information regarding the dynamics of the closing gap between the defenders was controlled by systematically manipulating the conditions (i.e., the start gap and the end gap). A temporal occlusion paradigm was also integrated where the display was cut-off 8 and 12 m from the end gap (see Fig. 2a). At the cut-off point, the players in the display disappeared. Participants judged whether they would make it through the gap or not, had the situation have run on. Button press responses were recorded.

Fig. 1. Photograph of participant wearing the Head Mounted Display (HMD) and holding the ‘Sidewinder’ control pad used to record responses. Participants saw the image in the stereoscopic HMD display and recorded responses by pressing one of two trigger buttons assigned for ‘pass’ and ‘not pass’ judgments.

Fig. 2. (a) Bird’s eye schematic of experimental setup. Defenders are shown in blue and attacker in green. Feint figures at the 0m line represent where the attacker would or would not pass at the end gap. Attacker’s approach is simulated in a straight line up to this point. (b) Screenshot from the attacker’s perspective of the defenders’ approach within the virtual environment. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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2.2. Apparatus/materials 2.2.1. Hardware setup The Intersense IS-900 Precision Motion Tracking system was used to add interactivity to the virtual environment by creating a real time link between the participant’s head movements and the viewpoint being displayed in the virtual world. The wireless head tracker that was attached to the Head Mounted Display (HMD) sensed head orientation (200 Hz). The HMD used was a Vissette Pro (Cybermind) with a 45° field of view. Images were sent to two screens – one for each eye – allowing stereoscopic vision (see Fig. 1). 2.2.2. Animation process and software The virtual rugby environment was created through collaboration with Université Rennes 2 and Queens University Belfast. The environment consisted of two avatars standing facing the participant on a pitch that had the regulation line markings and posts, within a seated stadium with advertizing boards (see Fig. 2b). Motion capture technology was used to capture real motion for the avatars. Using MKM (Manageable Kinematic Motion); developed at M2S lab in Rennes (Multon, Kulpa, & Bideau, 2008), realistic foot-floor contact was refined and finally, the avatars were imported into the virtual rugby pitch. The pitch, avatars, and motions were all imported into ‘Virtools’ (Version 4.0; Dassault Systemes) software where velocities, motion paths, trajectories, and the appearance of the avatars were all controlled. 2.3. Participants Participants were 14 non-rugby playing adults consisting of eight males and six females selected from an undergraduate and postgraduate student population with an age range of 18–28 years (M = 22, SD = 3.1). Some participated to gain course credit. Full ethical approval was granted for the study and all participants gave written informed consent. 2.4. Experimental conditions Experimental trials varied as a result of systematic manipulations of several variables. Fig. 2 shows a schematic diagram of the experimental setup. Thirty-two separate experimental conditions were produced as a result of combining two start gaps, eight end gaps, and two cut-offs. Start gap refers to the initial distances between the defenders and was either 5 or 7 m. End gap is the distance between the defenders at the 0-m point; i.e., the gap that the attacker would have to get through. Eight values were chosen; 0.25 m (defenders would pass in front of the attacker), 0.05, 0.35, 0.65, 0.95, 1.25, 1.55, and 1.85 m. These values were evenly distributed about a critical value that was assigned at 0.8 m. This value was chosen to separate ‘passable’ and ‘not passable’ gaps following pilot testing. During pilot testing (n = 3), 0.8 emerged as the mean 50% value when ‘% judged as yes’ responses were plotted as a function of end gap. A range of end gaps is required from those that participants should perceive as passable to those not passable. Increments of 0.3 m gave rise to an adequate range. As mentioned previously a temporal occlusion paradigm was incorporated into the design, meaning that judgments regarding the passability of the end gap were prospective, as the information was cut-off ahead of the participants reaching the end gap. Two cut-offs were chosen: 8 and 12 m. These distances refer to the distance between the attacker and defenders, the point at which the defenders were removed from the scene (see Fig. 2a). The duration of stimulus display before cut-off was 0.8 s (12 m cut-off) and 1.2 s (8 m cut-off). 2.5. Procedure Participants put on the HMD and sat on a chair within the tracked space of the lab. First, a familiarization period allowed the participants to explore the virtual rugby environment by turning their head to look around and get used to both the HMD and the feeling of being immersed in the environment. Second, participants were given a short training period which consisted of 21 experimental trials, including each end gap at least once resulting in 11 not passable gaps and 10 passable gaps. Participants Please cite this article in press as: Watson, G., et al. Judging the ‘passability’ of dynamic gaps in a virtual rugby environment. Human Movement Science (2010), doi:10.1016/j.humov.2010.08.004

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were instructed to make a judgment as to whether they would pass or not pass the gap between the defenders, should they continue at their current velocities. In the training period, visual feedback was provided. When the response was ‘correct’, (e.g., they responded with ‘yes’ for an end gap size of 0.95 m or greater) a green square appeared in the visual field of the HMD and when the response was ‘incorrect’, a red square appeared. This was in order to show participants what a passable and not passable gap was for the critical value of 0.8 m and allowed them to get used to scaling within the virtual environment. No response window was defined, i.e., participants could respond as the defenders were running or after the cut-off. Finally, after the training period, the experimental trials were presented in four randomized blocks of 80 giving rise to a total of 320 trials (2 (start gap)  8 (end gap)  2 (cut-off)  10 (repetitions)). Trials ran consecutively and participants were given breaks to remove the headset both between the blocks of trials but also on request if so desired. 3. Results This section begins with a description of how the situation was modeled according to tau theory. 3.1. Modeling the scenario as closing gaps Tau theory is based on the concept of rate of closure of motion gaps. A tau value (or ‘time to contact’) is negative and approaches 0 as a gap closes. Tau allows for prospective judgments and guidance of action by encapsulating the dynamics of situation in terms of changes over time, irrespective of absolute values, and specific to the optic information available to the actor in the optic flow-field at the eye, at any time. We analyze this by considering the projection of the optic flow-field onto a flat projection plane, perpendicular to their direction of running (see Fig. 3). Using this model, we consider the current situation as the simultaneous closing of two gaps: one gap closes between the defenders and another gap closes between the attacker and the line of the defenders. Considering Fig. 3; Let kW be the critical distance of the defender’s near shoulder from the attacker’s line of running, such that the attacker could just avoid interception (k is a constant). Noting that the following is based on first-order extrapolations of the attacker and defender movement, i.e., their velocity does not change, then: If |s(X  kW)| > |s(Z)|; i.e., the value of the tau of the gap (X  kW; or the gap between the defenders near shoulder and the attackers outside shoulder) is greater than the value of the tau of the gap Z, then the attacker will pass (i.e., Z is closed, X (gap between defenders) is still open). If |s(X  kW)| < |s(Z)|; i.e., the value of the tau of the gap (X  kW; or the gap between the defenders’ near shoulder and the attacker’s outside shoulder) is less than the value of the tau of the gap Z, then the attacker will not pass (i.e., X (gap between defenders) is closed, Z is still open).

Fig. 3. Schematic diagram of the optical specification of the dynamic gaps. Physical dimensions are designated by uppercase letters, optical dimensions by lowercase letters. The defenders width (W) is assumed to stay constant. X and Z represent the distances in the X and Z axes. 0 represents the optic flow-field at the attacker’s eye.

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Herein the (X  kW) gap is referred to simply as X gap. For simplicity, physical dimensions are used throughout. These are, however, lawfully related to the optic variables available to the attacker. These equations are included in the Appendix of the current article. 3.1.1. Difference in tau values as an explanation for expected response The difference in the two tau values when one is taken away from the other can therefore provide a continuous scale by which to separate all of the 24 conditions. It is important to note that because this is a simplified scenario where first-order extrapolations are considered, the difference in tau values will not change within a trial due to the defenders and attacker moving at constant velocity. The different cut-off values mean that the visual information is available to the attacker for a longer duration. The table below summarizes how the difference in tau values can explain the expected responses for each experimental condition. Gap size at cut-off is included to show that similar gap sizes at this point can yield different expected responses, i.e., conditions were designed to ensure that responses could not be predicted based on a ‘freeze-frame’ image of gap size at the point of cut-off (see Table 1). When the two tau values are the same and the difference is 0, this will correspond to an end gap of 0.8 m as both gaps will close to the same point at the same time, i.e., a collision will occur. Note that this value does not correspond to 0 m as the gap is considered closed when it is 0.8 m or less (0.8 m that represents a body width). A zero value for the tau difference therefore separates the pass and not pass conditions. Using Tau Z  Tau X to calculate the difference in the two values, outcomes will either be negative (where time to gap closure for Z (Tau Z) is greater than time to gap closure of gap X (Tau X)) or positive (where time to gap closure of gap X (Tau X) is greater than time to gap closure of gap Z (Tau Z)). Note that a negative value means that gap X (the gap between the defenders) will close before gap Z (the gap between the attacker and the defenders) and hence the attacker will not pass. If however the value is positive, then gap Z will close before gap X and the attacker will be able to pass between the defenders. 3.1.2. Summary By considering the situation as the simultaneous closure of two motion gaps, tau theory can provide a model where, potentially, the attacker could pickup optical information regarding the difference in rate of closure of the two gaps, and use this information to inform prospective judgments as to the passability of the gap. This model is however, based on first-order extrapolations, i.e., defenders and the attacker maintain the same motion path, at the same velocity for the duration of each trial. Also, although modeling this simplified scenario according to tau can provide an elegant, parsimonious

Table 1 Table displaying the start gap, end gap, difference in taus, greater tau, expected result and cut-off gap values for each trial. Start gap (m)

End gap (m)

Tau Z  Tau X

Greater tau value

Cross

Gap size at cut off 1 (m)

Gap size at cut off 2 (m)

5 5 7 7 5 7 5 7 7 5 7 5 7 7 5 5

0.25 0.05 0.25 0.05 0.35 0.35 0.65 0.65 0.95 0.95 1.25 1.25 1.55 1.85 1.55 1.85

0.400 0.303 0.290 0.216 0.194 0.135 0.069 0.047 0.050 0.074 0.157 0.240 0.275 0.408 0.435 0.667

Z Z Z Z Z Z Z Z X X X X X X X X

No No No No No No No No Yes Yes Yes Yes Yes Yes Yes Yes

2.99 3.10 4.32 4.42 3.20 4.52 3.31 4.61 4.71 3.42 4.82 3.53 4.92 5.02 3.65 3.76

1.98 2.14 2.98 3.13 2.30 3.27 2.47 3.42 3.57 2.63 3.72 2.80 3.88 4.04 2.97 3.14

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solution as to how judgments could be made, that is not to say that this is the (only) information that people will use when making these judgments. The next section goes on to test this. 3.2. Response data In order to ascertain whether or not participants used the tau-based variable identified, participants’ responses were analyzed. 3.2.1. Could prospective judgments regarding end gap size be made? The main goals of this experiment were to determine first if participants can make prospective judgments as to the ‘passability’ of a gap and if so, identify what information they may be using to do so. By plotting ‘end gap size’ against the response data (% judged as pass) we are able to see if the passability of the upcoming gap can be made prospectively. Ideally, assuming participants are sensitive to a prospective informational quantity relating to end gap size, an ‘S shape’ curve should be revealed as it is expected that when the end gap size is large, the % judged as pass will be 100% and when the end gap size is small, the % judged as pass will be 0%. When the value of the end gap is close to the critical value, the judgments should be more difficult and so, the % judged as pass should reflect this and be around 50%. Fig. 4 is a line graph showing the mean% Judged Pass responses for participants plotted against end gap size. The mean% Judged Pass responses account for all responses for that end gap, i.e., independent of start gap. As can be seen from the graph, the expected ‘S shape’ is revealed where a high percentage of pass judgments are found for large end gap sizes and a low percentage of pass judgment for small end gap sizes. Although the responses for the 12-m cut-off (shorter display duration) are slightly lower for the smaller end gap sizes and higher at the larger end gap sizes than those for the 8-m cut-off, these differences were not found to be significant (p > .05). Generally, it is observed that larger end gaps yield a higher percentage of pass judgments than lower end gaps, suggesting that participants

Fig. 4. Plot of mean% Judged Pass responses on the Y axis against the end gap size (m) on the X axis for all participants.

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are able to pick up information ahead of time, that inform them, to some extent, as to the passibility of the end gap. The next section attempts to identify the nature of this information. 3.2.2. Are participants predicting responses based on any single parameter in the display? Several informational variables could potentially inform the judgments being made by participants. It may not be the case that it is one variable only but the aim is to attempt to identify the quantity that can explain the response data best.

Fig. 5. Percentage judged as pass as a function of (a) size of gap at cut-off (m); (b) Start Gap Size (m); (c) velocity of defender’s run (m/s). Panel (a) shows the mean% judged as pass for both cut-off values.

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The tau difference variable presented previously encompasses the temporal properties of the situation, i.e., how it is changing over time. Conditions were designed so as to avoid participants being able to simply predict the response based on a single parameter that does not take into account the spatiotemporal changes, such as: (a) a large gap size at cut-off always yielding a ‘pass’ response; (b) a large start gap always yielding a ‘pass’ response; (c) observed velocity of the defenders run (which varied slightly because although the velocity in the z axis was the same, the velocity in the motion path varied due to the different angles produced by the parameters). In order to be able to refute these as sole informational quantities informing judgments, distinct curves should be observed when pass responses are plotted as a function of each one in turn. Fig. 5 shows the percentage judged as pass responses plotted as a function of (a) gap size at cut-off, (b) start gap, and (c) observed velocity of approach. The emergence of distinct curves spanning a large range of ‘pass’ responses suggests that participants are not making predictions simply based on any of these variables alone, i.e., for example, a 7-m start gap is not consistently producing a high percentage of ‘pass’ responses. This, in turn, suggests that the participants are using information that captures the temporal changes of the scenario. Also the fact that distinct curves emerge along the x axis suggests that a single value of that variable could not predict a response value, i.e., there is no critical value of the variable that will separate yes and no responses. This is true for cut-off gap size, Start Gap Size, and velocity of approach. 3.2.3. Can the tau model explain responses? To recap, when the ‘% Judged Pass’ responses are presented as a function of the informational variable(s) used for making the judgments, an ‘S’ shape function is expected. Whatever informational variable provides a satisfactory fit to the data, should separate the two binary responses; in this case, pass and not pass. Having identified the difference in Tau Z and Tau X as a means of explaining the situation by separating passable and not passable conditions, this was plotted against the response data (see Fig. 6). A logistic (S-shaped) function was fitted to the data using the following equation (where ‘a’ and ‘b’ are constants; ‘u’ is the upper bound and x is the variable in question):

Fig. 6. Responses plotted as a function of the difference in sZ and sX. The 32 points on the graph represent the mean response for each condition (at each cut-off).

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f ðxÞ ¼ 1=ðð1=uÞ þ ða  b ÞÞ

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ð1Þ

2

The r values yielded by the logistic regression are determination coefficients indicating the fit of the curve to the data. The critical value (CV) of the variable, where 50% of responses are judged as pass was also calculated. This should be close to the critical value of 0. In this case, it was found to be .100. The slope of the curve between 40% and 60% is also included. This value indicates how rapid or how gradual the switch is between one response (pass) and the other (not pass) about the critical value. A steeper gradient suggests a rapid switch and a flatter gradient suggests a more gradual switch and a greater range of uncertain judgments. Here the slope was 1.25 (where 1 is 45° from the horizontal).

4. Discussion 4.1. Summary of findings The introduction to the current article identified gap passability as an affordance that has received little attention in a sport context, despite being an important aspect of games like rugby and American Football where ‘‘making a break” (through a gap between opposing players) is often the key to a successful attack. Successful action in this situation would require players to perceive the affordance of passability ahead of time. Some source of information within the EAS that defines the affordance must be available to the player in order to make a passability judgment. Lee’s (1976) seminal contribution presented a conceptual framework for understanding the role of tau in regulating action, suggesting that the information carried in this variable is not only action relevant and directly available but can be optically specified. The aim of this experiment was to explore the role of tau in judging passability of a gap between defenders presented in a virtual rugby environment. In modeling the scenario, tau theory was found to provide an elegant, parsimonious model to explain ‘passability’ of the closing gap in question. The model considered first-order extrapolations i.e., where player trajectories did not change. By modeling the situation as the closure of two gaps, one in the direction of attacker motion and one between the defenders, the difference in these time to closure values, which can be optically specified, could provide information as to the passibility of the upcoming gap, should things not change. Of course, being able to demonstrate that tau can theoretically and mathematically explain the situation does not necessarily mean that it is an informational variable that we use or are attuned to when making such judgments. The fact that a rough ‘s shaped’ curve was revealed when ‘% judged as yes’ was plotted as a function of end gap size, suggested that prospective judgments were indeed being made. Firstly, the ‘% judged as pass’ responses were plotted as a function of other variables in order to refute them as sole predictors of the judgments. Inspection of Fig. 5a, b, and c shows that for gap size at cut-off, start gap and observed velocity, response data separates according to conditions and does not lie across a continuous scale where one value on that scale could predict a corresponding value (% judged yes) on another scale. This was taken to imply that temporal changes in the scenarios are important for making judgments. The tau differential model encompassed these temporal changes. This variable was able to explain 82% of the variance in the data, suggesting that this tau-based information informs judgments in this task. Also, the high slope value revealed suggests quite a rapid switch between not pass and pass responses, as would be expected if it were this informational quantity that is informing judgments. This switch should occur around a 0 value for tau difference. The critical value was close to this (0.100). It could be concluded therefore that the tau differential variable is an informational quantity that at least partly, defines the passability affordance. 4.2. Interpretation of findings The recap for the current task findings suggests that the passability affordance was able to be defined by information contained in the optically specified tau differential variable that is lawfully related to a state of affairs. Participants – on average – were able to make judgments ahead of time as to the passability of the upcoming gap. It is important to discuss, however, issues with the Please cite this article in press as: Watson, G., et al. Judging the ‘passability’ of dynamic gaps in a virtual rugby environment. Human Movement Science (2010), doi:10.1016/j.humov.2010.08.004

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experimental setup adopted to run the current task, as these may have significant consequences for the generalizability of the findings. 4.2.1. Decoupling perception and action and ecological validity First, the main issue with the current setup was that of separating the natural coupling between perception and action. While the ecological approach relies on the reciprocity between animal and environment, the experiments presented in this chapter saw the participant sitting stationary on a chair delivering responses via a button press. However, their motion forward was simulated, thus still providing optic flow information. Still, they were ‘perceiving’ only and not ‘acting’. This raises issues as to ecological validity of the task, in relation to the natural setting to which findings are intended to be generalized. Results from ‘perception only’ tasks have been compared to those of ‘perception–action’ tasks in order to demonstrate the importance of maintaining this coupling. For example, road-crossing work is a similar domain where simulation is used in order to recreate safe road crossing situations in which to explore visual timing. Verbal or button press responses as to ‘crossability’ judgments are expected to be less accurate than judgments to physically cross the road due to information and movement being decoupled (Bootsma, 1989; Cornus et al., 1999). In this literature, several studies have shown that verbal or button press judgments generally showed an underestimation of time to contact and subsequent analysis suggested that had they crossed the road, they would have done so safely (Hancock & Manser, 1997; Manser & Hancock, 1996). Studies where participants were able to actually cross the road in a virtual environment provided comparable results to ‘real behavior’ (e.g., Lee et al., 1984). Related to sport, in a decision-making task approached from an information-processing perspective, interesting results were revealed when Williams, Davids, and Burwitz (1994) demonstrated that an expertise advantage was not as great in a task where they were to verbally respond to a football defense scenario, compared to when they were to actually respond physically, suggesting that results from ‘perception only’ tasks will differ from those from ‘perception–action’ tasks. Having said this, as mentioned in the introduction, Oudejans et al. (1996), when studying the catchableness of fly-balls, saw similar judgments when participants were to make judgments as to the catchableness of a tennis ball and when they were asked to actually attempt to catch it. However, in this case, the fielders were allowed to make a very brief movement before making the judgment. Considering these findings, it could be said that the lack of any movement element in the present task prevents results being generalized to the real-life setting. However, differences in these cases have been characterized by timing. This does not therefore provide reason to immediately refute tau variables as the source of information. It is also important to consider literature pertaining to the existence of two visual systems when considering perception and action. This position proposes that the dorsal stream (processes visual information necessary for the control of actions) and the ventral stream (processes visual information necessary in the recognition of objects) are different processing routes (Milner & Goodale, 1995) or in fact separate systems (van der Kamp, Savelsbergh, & Rosengren, 2001). It is thought that the visual information in the dorsal stream often cannot be verbalized, yet that in the ventral stream can, thus yielding differences for example, in the use of visual information when judging distances while walking than when verbally judging (Rogers, Andre, & Brown, 2003). However, the current task would have to be repeated replacing the button press with an action in order to comment on how perceptual judgments would compare to actions. As mentioned in the introduction, geometry does not solely define an affordance (Pepping & Li, 2000). While acknowledging this and bearing in mind the importance of action capabilities in the real-world setting, findings from the current perceptual judgment task do suggest that a passability affordance could be geometrically defined through the tau difference variable which could be used in order to guide subsequent action. 4.2.2. Issues with VR as a methodological tool While VR presents many advantages for this line of research including depth perception, egocentric viewpoint updated in real time, and complete control of variables, it does present some issues corresponding to some of these features. When carrying out a study using an HMD, it is important to consider literature which reports that distance perception is systematically underestimated when wearing HMDs (Creem-Regehr, Willemsen, Gooch, & Thompson, 2005; Loomis & Knapp, 2003; Please cite this article in press as: Watson, G., et al. Judging the ‘passability’ of dynamic gaps in a virtual rugby environment. Human Movement Science (2010), doi:10.1016/j.humov.2010.08.004

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Willemsen, Colton, Creem-Regehr, & Thompson, 2009). If distance is underestimated, then this will affect time to contact judgments. Second, VR does not capture the true reciprocal nature of a defender-attacker relationship. While the tau difference variable explained a high proportion of variance in the data, the model was based on first-order extrapolations, i.e., if things do not change. The task was very much a stripped down version of the real world scenario. In sport, and in the real life gap crossing scenario, parameters are likely to change; attackers will move to avoid defenders and defenders will move to intercept attackers. However, information regarding the ‘‘current future” (Lee et al., 2009), i.e., what will happen if things don’t change, ‘‘establishes the required temporal relation that can subsequently be influenced” (pp. 851). The fact that velocities remain constant in the present experimental trials simply means that if things do not change then this will happen, but this does not immediately refute the veridical nature of the tau-based information. 4.3. Conclusions and implications The present work has made an effort to explore affordances in the context of sport. The viewpoint that the theory of affordances has the potential to become a guiding principle for research on perception and action in sport (Fajen et al., 2009) is supported entirely. In studying affordances in sport, you are moving away from a dominating cognitive approach to perception–action and the nature of expertise in decision making. Affordances is a theory that can encapsulate the very nature of expert decision making in sport, i.e., the ability to perceive when the environment affords a certain action and considering one’s own action capabilities when doing so. This is not to say that decisions are mediators of actions, it is to say that, unlike the cognitive ‘‘pattern recognition” approach to decision making, an expert decision maker may perceive and action-scaled affordance defined via optic variables, and this will prospectively guide an appropriate action, despite what tactical decision had been made prior. An example to demonstrate this point would be an out half in rugby calling a premeditated move to pass the ball wide, but realizing that a gap has appeared between defenders affording a short pass to a supporting player, rather than completing the prescribed move. Acknowledgments The authors wish to thank Dave Lee for his input to the current work in providing the mathematical specification of the optic information. Lee (1998) also deals with similar optic angle specification. Appendix A. Optical specification of variables From Fig. 3: The defender’s width, W, as presented to the attacker, is assumed to stay constant. By definition,

PðaÞ ¼ 1=sðaÞ ¼ a=a : from which follow the mathematical identities

qðabÞ ¼ qðaÞ þ qðbÞ qða=bÞ ¼ qðaÞ  qðbÞ: A.1. The optic information From similar triangles we have

W=Z ¼ w=1

ðA1Þ

X=Z ¼ x=1:

ðA2Þ

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Differentiating Eq. (A1) with respect to time

WZ  =Z 2 ¼ w :

ðA3Þ

Dividing Eq. (A3) by Eq. (A1)

qðZÞ ¼ qðwÞ

ðA4Þ

whence

sðZÞ ¼ sðwÞ:

ðA5Þ

Let kW be the critical distance of the defender’s near shoulder from the attacker’s line of locomotion, such that the attacker could just avoid being intercepted. Then, assuming the attacker and defender each maintain a constant velocity, when the defender is closing on the attacker’s line of running and the distance (X  kW) is shrinking, s(X  kW) will be negative and collision will not ensue providing

sðX  kWÞ < sðZÞ < 0:

ðA6Þ

To see how Eq. (A6) is optically specified, it is simpler mathematically to first use qs rather than ss. From Eqs. (A1) and (A2),

qðX  kWÞ ¼ qðZx  kZwÞ ¼ qðZðx  kwÞÞ whence, from the first mathematical identity given above,

qðX  kWÞ ¼ qðZÞ þ qðx  kwÞ and from Eq. (A4) and the second mathematical identity given above

qðX  kWÞ ¼ qðwÞ þ qðx  kwÞ ¼ qðx=w  kÞ:

ðA7Þ

Converting to ss, Eq. (A7) becomes

sðX  kWÞ ¼ sðx=w  kÞ:

ðA8Þ

Thus, from Eqs. (A5) and (A6) collision will not ensue providing

sðx=w  kÞ < sðwÞ < 0:

ðA9Þ

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