Global Information Pickup Underpins Anticipation of Tennis Shot DirectionRaoul Huys1, Rouwen Cañal-Bruland2, N. Hagemann3, Peter J. Beek2, Nicholas J. Smeeton4, A. Mark Williams5
1Université de la Méditerranée, France. 2Research Institute MOVE, Faculty of Human Movement Sciences, VU University Amsterdam, The Netherlands. 3University of Münster, Germany. 4University of Brighton, United Kingdom. 5Liverpool John Moores University, United Kingdom.
ABSTRACT. The authors examined the importance of local dynamical information when anticipating tennis shot direction. In separate experiments, they occluded the arm and racket, shoulders, hips, trunk, and legs and locally neutralized dynamical differences between shot directions, respectively. The authors examined the impact of these manipulations on resulting (display) dynamics and the ability of participants with varying perceptual skills to anticipate shot direction. The occlusion manipulation affected the display dynamics to a larger extent than did the neutraliza-tion manipulation. Although the authors observed a decrement in performance when local information from the arm and racket was occluded or neutralized and when information from the trunk and legs was neutralized, the results generally suggest that partici-pants anticipated shot direction through a more global perceptual approach, particularly in perceptually skilled participants.
he ability to infer relevant features from observing a person’s bodily movements is well documented.
People can indicate a walker’s gender through observation in the absence of obvious cues (cf. Davis & Gao, 2004; Pollick, Kay, Heim, & Stringer, 2005). Similarly, emotions such as anger, disgust, fear, happiness, sadness, and pain may be gleaned from a dancer’s bodily movements (Dit-trich, Troscianko, Lea, & Morgan, 1996) and from people engaging in dialogue (Clarke, Bradshaw, Field, Hampson, & Rose, 2005). Furthermore, humans are able to predict future events on the basis of observation of another person’s actions, an ability that has been studied extensively in the sporting domain. In racket sports and soccer, expert players are capable of predicting successfully an opponent’s inten-tions before the occurrence of a key event such as ball–racket or ball–foot contact (Abernethy & Russell, 1987; Savels-bergh, Williams, Van der Kamp, & Ward, 2002; Williams, Ward, Knowles, & Smeeton, 2002).
Given Johansson’s (1973, 1976) pioneering work, it is assumed that kinematic patterns convey the information underlying biological motion perception. Johansson pre-sented naive observers with motion patterns of a human walking and running in the form of point light displays (PLDs). In PLDs, only points of light that indicate the loca-tion of anatomical landmarks (such as shoulders, elbows, hips) are visible against an otherwise homogenous black background. When displaying motion, PLDs convey kine-matic information (i.e., position and its derivatives, such as velocity and acceleration). Johansson found that the observers recognized walking and running after very brief periods of exposure. PLDs have been subsequently used to
show that people are able to use the information conveyed in kinematic patterns to indicate an actor’s gender (Cutting, 1978; Runeson & Frykholm, 1981; Runeson & Frykholm, 1983), estimate the weight of a lifted object and the inten-tion to obscure its weight (Runeson & Frykholm, 1983), and predict the direction of tennis strokes (Ward, Williams, & Bennett, 2002). Experts continue to show superior antici-pation skill over less expert counterparts even when action sequences are presented as PLDs rather than in conven-tional video format (Ward et al.; for contrasting results, see Shim, Carlton, Chow, & Chae, 2005).
Although this research has highlighted how the inher-ently high-dimensional kinematic patterns conveyed in PLDs can be used to facilitate recognition and anticipation, limited effort has been devoted to identifying the nature of the information picked up by performers. In general, high-dimensional motion patterns may be decomposed in terms of a few dynamical structures or components. For instance, Troje (2002) decomposed male and female walk-ing patterns into four rhythmical components using prin-cipal component analysis (PCA), an unbiased statistical method to examine ordered macroscopic structures in high- dimensional (motion) patterns (Daffertshofer, Lamoth, Meijer, & Beek, 2005). Troje subsequently used these com-ponents to classify and synthesize male and female walk-ing patterns. Naive participants were required to judge the gender of (stick figure) walkers that were simulated using dynamical information, motion-mediated (structural) infor-mation (e.g., hip–shoulder ratio), or both. The dynamics of motion were more informative for gender classification than were motion-mediated structural cues. Furthermore, the combination of dynamical and motion-mediated infor-mation hardly improved performance, relative to dynamical information only. These findings suggest that when one views kinematic motion patterns, only a few dynamical structures provide helpful information for facilitating accu-rate motion perception (see also Haken, 2000).
Huys, Smeeton, Hodges, Beek, and Williams (2008) used a methodology similar to Troje’s (2002) to study the execu-tion of tennis shots to different directions (see also Smee-ton, Huys, Hodges, & Williams, 2005). Using PCA, they showed that (low dimensional) dynamical structures (or
T
Correspondence address: Raoul Huys, UMR 6233 Institut des Sciences du Mouvement Etienne-Jules Marey, Université de la Méditerranée, Faculté des Sciences du Sport, CP 910, 163 Av. de Luminy F-13288, Marseille Cedex 09, France. E-mail address:[email protected]
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modes) underlie tennis shot execution and that all regions across the body contributed to the dynamical structures, although they did so to a varying degree. Furthermore, they showed that the perception of the first three modes under-pins anticipation skill in tennis. However, it does not follow from these results that information across the entire body is picked up during anticipation. It may be that only informa-tion pertaining to a limited region is picked up and utilized, as suggested by Abernethy (1990a) for squash and Ward et al. (2002) for tennis. In the present article, we extended the methodology used by Huys et al. (2008) and examined whether local dynamical information (i.e., pertaining to a limited body area) underlies the anticipation of shot direc-tion in tennis in two experiments. We created simulations of tennis shots in which dynamical information regarding shot direction was either locally withheld (i.e., through occlu-sion; Experiment 1) or locally neutralized (i.e., dynamical differences were nullified; Experiment 2). Before introduc-ing the specific motivations and expectations for each indi-vidual experiment, we briefly introduce the decomposition of high-dimensional data into low(er) dimensional dynami-cal structures through PCA, discuss recent insights into the structures underlying the execution of tennis shots and their anticipation, summarize the relevant literature on anticipa-tion in racket sports, and indicate some of the methodologi-cal limitations with existing literature.
Dynamical Structures in High-Dimensional Patterns and Their Identification
Biological systems and their corresponding motion pat-terns are generally high dimensional, at least in terms of the number of elements contributing to the motion. The high dimensionality of movement systems and the corre-sponding control problem it poses, known as the degrees of freedom problem, has a long-standing history in the study of human movement (cf. Bernstein, 1967; Turvey, 1990). A solution to this problem has generally been sought in terms of coordinative structures or synergies (i.e., the notion that, in the execution of motor actions, soft-molded, temporary linkages or constraints are operative and effectively reduce the number of degrees of freedom to be controlled). The degrees of freedom problem and the synergy concept were initially posed in biomechanical terms. With the advent and application of methods and concepts from synergetics (cf. Haken, 1977; Haken, 1996) and the dynamical systems theory (cf. Strogatz, 1994) to the study of human move-ment, the synergy concept was reformulated in terms of a coherent (macroscopic) pattern under nonequilibrium con-straints in open systems. The degrees of freedom problem became couched in terms of the (minimal) number of order parameters required to describe a system’s state (cf. Haken, 1996; Kelso, 1995; Mitra, Amazeen, & Turvey, 1998).
An unbiased statistical method to examine ordered mac-roscopic structures in high-dimensional motion patterns is provided by PCA (for a tutorial, see Daffertshofer et al., 2005). PCA aims to effectively approximate N-dimensional
data with fewer dimensions M, by finding the direction of maximal covariance in the high-dimensional data space and subsequently subtracting it from the original data set. The iterative replication of this procedure results in the subtrac-tion of orthogonal principal components (also referred to as modes or structures) of diminishing variance. Algebraically, this is realized by diagonalization of the data’s covariance matrix. The corresponding eigenvalues, λn (n = 1… N), of the covariance matrix may be interpreted as reflecting the amount of variance covered by the corresponding modes vn (after having been rescaled so that their sum equals 1). The coefficients of each corresponding eigenvector, vi(i = 1 … N), reflect the degree to which the corresponding time-series i contributed to the particular mode vn. PCA has been successfully applied in a variety of contexts. For instance, high-dimensional data sets have been effectively represented by a considerably lower dimensional descrip-tion in juggling (cf. Huys, Daffertshofer, & Beek, 2004; Post, Daffertshofer, & Beek, 2000), learning to ride a pedalo (Haas, 1995; see also Haken, 1996), trunk kinemat-ics and muscle activity (electromyography) during walking (Lamoth, Meijer, Daffertshofer, Wuisman, & Beek, 2006), and brain activity (magnetoencephalography; Boonstra, Daffertshofer, & Beek, 2005).
Dynamical Structures Underlying the Execution and Anticipation of Tennis Shots
Huys et al. (2008) used PCA to examine the whole body movements (including the racket) of tennis players deliver-ing short and deep inside-out and cross-court shots. They found that the tennis shots could be represented by a low-dimensional description in that the first three components accounted for approximately 89% of the variance. Analysis of the corresponding eigenvectors in terms of their coeffi-cients (i.e., the contribution to the modes from distinct body regions) indicated that the various body areas contributed differentially to these modes (i.e., the variance was not evenly distributed). In addition, consistent specific differences asso-ciated with shot direction (and for shot distance, albeit less so in terms of the eigenvector coefficients) were identified at the hips, shoulders, left arm, and feet, although the most pro-nounced differences were observed in the (racket-holding) right arm and racket. The distribution of these differences was also heterogeneous; dynamical differences regarding the action and resulting shot direction were found to originate from all locations across the body, albeit in a nonuniformly distributed manner. These differences could potentially be picked up and used to facilitate anticipation.
Huys et al. (2008) examined whether these components were actually used for anticipating shot direction in two follow-up experiments. The main components (in terms of variance accounted for) were used to simulate dynamic stick figure displays of inside-out and cross-court shots. Skilled and less skilled tennis players indicated shot direc-tion after observing the displays. The anticipation accuracy reported by participants in simulations representing the
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first three components was as good as that observed in the control condition in which all modes were presented (origi-nal shots). Moreover, the less skilled participants tended to perform more accurately when presented with low-dimensional displays than they did when presented with high-dimensional displays (i.e., the original shots). These results suggest that low-dimensional dynamical information underlies anticipation and that perceptual skill is character-ized by the ability to pick up this information from high-dimensional displays.
Localized Information Pickup
The finding that dynamical structures underlying the exe-cution and anticipation of tennis shots are defined in terms of whole body movements implies that information across the entire body may be picked up for accurate anticipation. However, researchers have suggested that the information pickup pertaining to a limited number of body regions underpins effective anticipation. For example, Ward et al. (2002) examined the visual search patterns of skilled and less skilled tennis players while they attempted to antici-pate the direction of (filmed) strokes. Players spent longer periods of time fixating on the racket, trunk–hip area, head–shoulder area, and the racket–ball contact region than they did fixating on other areas of the display. However, the skilled players spent more time fixating on trunk–hip and head–shoulder areas and alternated their gaze more frequently between and within these areas than did their less skilled counterparts, who spent more time fixating on the racket and ball areas of the display (see also Williams et al., 2002).
Abernethy (1990a, 1990b) and Abernethy and Russell (1987) used a spatial occlusion paradigm to examine the importance of specific body locations when anticipating squash and badminton shots, respectively. Participants were presented with filmed squash and badminton shots in which different parts of the displays such as the racket, arm and racket, head, lower body, and irrelevant background fea-tures were occluded. The expert group demonstrated more accurate anticipation than did the nonexpert group. In addi-tion, the accuracy of expert and nonexpert players in both sports deteriorated significantly when either the racket or the arm and racket were occluded simultaneously. These small differences across studies are likely because of sport-specificity and methodological differences, and they may, to a large extent, be explained by (bio)mechanical factors (cf. Abernethy, 1991). Squash and badminton rackets are lighter and have less inertia than tennis rackets, and, conse-quently, the execution of a tennis shot requires more force generation than does a squash or badminton shot. It also requires the use of larger muscle groups in the kinematic chain. The motion executed by the additional body regions may contain useful information for anticipation.
Although it has been suggested that experts are better than novices at picking up information from areas such as the trunk, head, and shoulders (Ward et al., 2002; Williams
et al., 2002), the most discriminating factor may be the abil-ity to extract information from the endpoint of the move-ment (e.g., arm and racket regions). This latter observation mirrors recent findings in studies of observational learning showing that information from the endpoint of an action (e.g., the toe in a soccer-kicking task; see Hodges, Hayes, Breslin, & Williams, 2005) or the relative motion of the end effector (e.g., the whole arm in a cricket-bowling task; see Breslin, Hodges, Williams, Curran, & Kremer, 2005) is suf-ficient to facilitate information pickup for skill learning.
In sum, although the analysis of tennis shots in terms of their underlying dynamics suggests that specific differences between shots to different directions are present across the entire body, research using perceptual manipulations sug-gests that only the information pertaining to a limited num-ber of body locations is actually used for anticipation.
Methodological Issues
Although spatial occlusion and eye movement record-ing techniques have considerable merit, researchers need to use caution when interpreting data obtained using these methods. For example, gaze direction cannot be directly equated with information pickup. Since Helmholtz’s work (1866/1925), it has become well known that information can be picked up using the parafovea and visual periphery. In general, however, a saccadic eye movement to a particular stimulus is either preceded by or mandates a shift in visual attention (e.g., Hornak, 1992; Robinson & Kertzman, 1995; Walker & Findlay, 1996). However, visual attention need not be restricted to the area of gaze (Castiello & Umiltá, 1992; Williams, Davids, & Williams, 1999). Although an observer’s point of gaze may be directed at an opponent’s shoulder, information may still be picked up from other (nearby) areas, such as the trunk. Thus, in the context of tennis, for example, skilled observers who foveate on an opponent’s hips, shoulders, arm, and racket (cf. Ward et al., 2002; Williams et al., 2002) may be potentially pick-ing up information from other areas simultaneously. One problem with the spatial occlusion methodology is that occluding a certain body area changes the dynamics of the resulting display. The extent of these changes relative to the nonoccluded control condition depends on the size of the occluded area and its contribution to the various (low-dimensional) structures. Locally, the kinematic patterns of the nonoccluded areas are unaffected, but it cannot be ruled out that changes in the (low dimensional) dynamical components affect anticipation performance. This potential confound has escaped attention. Also, by omitting informa-tion from the occluded area, potentially important relations between this area and other areas of the display are no longer available. Thus, an effect because of occlusion does not necessarily imply that the information pertaining to the occluded area is important on its own. Although the poten-tially confounding effect cannot be completely nullified when (locally) manipulating displays, they can be mini-mized by manipulating the information arising from these
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areas (see Experiment 2) instead of occluding (or omitting) information pertaining to certain locations.
An additional concern is that failure to find a significant effect because of occlusion does not necessarily imply that the information pertaining to this area is not used under normal circumstances. It may be that perceivers are per-ceptually flexible and are able to rely on the information arising from the remaining areas when constrained in a spe-cific manner. Perceptual flexibility has been documented for a variety of contexts, ranging from laboratory tasks such as relative phase estimation (cf. Huys, Williams, & Beek, 2005) to more ecologically valid situations involv-ing juggling (cf. Huys & Beek, 2002; Van Santvoord & Beek, 1994) and catching fly balls (Michaels & Oudejans, 1992). In sum, the investigation of specific areas that may carry important information for anticipation has been based predominantly on indirect methods and those that potentially distort more information than those considered to be under investigation.
In our experiments, we examined the importance of the dynamics pertaining to distinct body areas for anticipating tennis shot direction by manipulating the corresponding dynamics. The dynamics in question were identified in a previous study by Huys et al. (2008). The following spe-cific body areas were chosen for manipulation: the arm and racket, shoulders, hips, trunk (i.e., shoulders and hips), and legs. These areas were chosen because several researchers have suggested that they are important for anticipation (cf. Abernethy, 1990a; Abernethy, 1990b; Abernethy & Russell, 1987; Williams et al., 2002). The legs were included on the basis of the results of Huys et al. (2008). In both experi-ments, stick figures served as stimulus material. In Experi-ment 1, we occluded these areas (i.e., occlusion), whereas in Experiment 2, we eliminated the dynamical differences in shot direction in these areas (i.e., neutralization).
EXPERIMENT 1
Several researchers have used spatial occlusion tech-niques to identify the postural cues underpinning anticipa-tion (cf. Abernethy, 1990a; Abernethy, 1990b; Abernethy & Russell, 1987; Williams et al., 1999). Our aim in this initial experiment was to verify previously reported findings to validate the procedure used in Experiment 2. However, as previously mentioned, spatial occlusion inevitably changes the structure of the (macroscopic) dynamical features in the resulting display and the variance pertaining to these features. Huys et al. (2008) reported that the various body areas (and the racket) contribute differently to the low-dimensional dynamics of shot execution. Consequently, the degree to which the occlusion of different areas affects the display relative to a nonoccluded control condition is likely area specific.
We expected that occlusion of the arms and racket would result in a significant deterioration in response accuracy in both skilled and less skilled participants. Moreover, occlu-sion of the shoulders, hips, and trunk was expected to have
a more detrimental effect on skilled players than it would on their less skilled counterparts (see Goulet, Bard, & Fleury, 1989; Ward et al., 2002; Williams et al., 2002). Further-more, as shot-specific differences are present in the feet and legs (Huys et al., 2008), we predicted that occlusion of these areas may negatively affect anticipation performance. The feet and legs have not been identified previously as important for anticipation. However, as indirect evidence suggested that skilled participants use a more global or holistic approach than do less skilled players (cf. Williams et al.), we predicted that the effect of occluding the feet and legs, if any, would most likely be restricted to the perceptu-ally skilled participants. We expected to corroborate the latter suggestion through correlation analysis.
Method
Participants
A total of 40 recreational tennis players were recruited. These players had a minimum of 2 years of experience in the sport and continued to play and practice on a weekly basis. A within-task criterion was used to separate players into two distinct perceptual skill groups. Several authors have highlighted the advantages of selecting players using a within-task criterion to reduce performance variability on measures of perceptual cognitive skill (e.g., see Sav-elsbergh & Whiting, 1988; Savelsbergh et al., 2002; Wil-liams & Ericsson, 2005). However, some caution should be exercised when comparing the findings from studies in which different participant selection criteria were used. Participants were allocated to groups based on their perfor-mance scores on the nonoccluded, control condition. Those who scored more than 75% on accuracy were classified as the perceptually skilled group, whereas those who scored between 55% and 65% were classified as perceptually less skilled players. In accordance with this criterion, we classified a total of 17 players (M age = 21.4 years, SD = 2.5 years) as perceptually skilled and 15 players (M age = 21.5 years, SD = 2.7 years) as perceptually less skilled. The remaining participants in this experiment and in Experi-ment 2 scored below 55% or between 65% and 75% and were excluded from the analysis. Both experiments were carried out in full compliance with the ethical guidelines of Liverpool John Moores University, and informed consent was obtained prior to participation on each occasion.
Apparatus and Stimulus Production
In the experiments reported in the present article, simu-lations of tennis shots were composed of stick figures that were generated in MatLab (MatLab 6.5, MathWorks, Natick, MA). Each simulation was saved in audio-video interlaced format. The simulations were based on the data and analysis of Huys et al. (2008); in that study, whole body and racket displacements from 18 markers (left and right shoulder, elbow, wrist, hip, knee, ankle, toe, and four racket positions) were recorded as 6 right-handed interme-diate-level tennis players performed four different types of
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shots: forehand inside-out and cross-court shots to short (near) and deep (far) targets. For all time series, the por-tion between the beginning of the forward racket swing and the moment of racket–ball contact was selected for further analysis. Means and standard deviations for all time series were calculated, normalized to unit variance, and subsequently arranged in a 5,184-dimensional state vector (6 Participants × 4 Conditions × 4 Trials × 18 Positions × 3 Cartesian Directions) that was analyzed using PCA. For each condition (i.e., shot direction and shot distance combi-nation), Huys et al. (2008) determined the mean eigenvector for each mode.
As we focused on anticipation of shot direction, we constructed a mean eigenvector for each mode n and shot direction (i.e., inside-out and cross-court) by averaging out differences across the eigenvector coefficients correspond-ing to the short and deep targets:
(The subscripts S and D denote short and deep shots, respec-tively.) From the resulting eigenvectors, we constructed new time-series qi(t) by calculating the product of the PCA projections, ξn(t), and the corresponding eigenvector vn for modes to 1 to 54: qi(t) = ξn(t) ⋅ vi
n, n = 1 to 54, and i = 1 to 54. The first 54 modes were chosen because there were 54 time series’ associated with each shot execution (18 Mark-ers × 3 Dimensions) and because they explained more than 99.99% of the variance in the entire 5,184-dimensional data set. Next, Huys et al. (2008) multiplied each time-series qi(t), which represents a time evolution of one of the body or racket locations, by the corresponding standard devia-tion before adding its mean value.1 The time series gener-ated by this procedure represented whole body and racket locations of typical inside-out and cross-court shots. These time series were resampled to generate simulations (black stick figures against a white background) at a sampling rate of 30 frames per s. The duration of each simulation was approximately 1.5 s.
In the present experiment, we used six conditions: a con-trol condition in which the entire stick figure was shown and conditions in which the dots and sticks corresponding to the legs, hips, shoulders, trunk (i.e., hips and shoul-ders), or the arms and racket were occluded (OC, OL, OH, OS, OH&S, and OA&R, respectively). The occlusions were achieved by omitting the relevant dots and sticks in the stick figures (see Figure 1).
The clips were imported into Adobe Premier 6.0 (Wash-ington, DC) on a Sony notebook computer (Tokyo, Japan). During the 5-s intertrial interval, the participants saw a blank screen. The order of trials in the test tape was selected at random from a batch of 96 trials and placed on a timeline. The test tape was separated into two blocks of 48 trials, with a combined duration of approximately 11 min. A practice test tape of 10 trials (5 inside-out and 5 cross-court shots) from the control condition was constructed to be similar to the test tape.
To examine dynamical changes across the occlusion conditions, we used PCA to analyze the data for each condition. In particular, we examined the λ spectrum and computed the covariance between the projections, ξn(t), of the first three modes of each manipulation with those of the control condition. As the eigenvalues can be interpreted as a representation of the amount of variance accounted for (cf. Daffertshofer et al., 2005), changes because of occlu-sion indicate a redistribution of the variance pertaining to the corresponding dynamics. A covariance different from 1 indicates that the time evolution of the corresponding dynamics has changed relative to the control condition.
The PCA indicated that the redistribution of variance pertaining to the principal components because of occlu-sion relative to the control condition was stronger in the areas that contained most points of light; the effect was most pronounced in the arm and racket occlusion and the leg occlusion (see Figure 2). Furthermore, the covariance was slightly different from 1 for the projections of Mode 1 for arm and racket occlusion and trunk occlusion, but it deviated more from 1 for the legs occlusion. For Mode 2, the covariance was noticeably unequal to 1 for the trunk, legs, and arm and racket, whereas for Mode 3, it deviated from 1 for the arm and racket occlusion, as well as the trunk and legs occlusion (though much less so). These results indicate that the low-dimensional (display) dynamics and the distribution of the variance pertaining to these dynamics changed because of the occlusion, mostly so for the arm and
Control Shoulders Hips
Trunk Arm and racket Legs
FIGURE 1. Schematic representation of the experimental conditions in the two experiments. The black lines and dots indicate the area of the stick figures that were not manipu-lated; the grey lines and dots indicate the manipulated areas. The control condition (OC or NC), shoulder condition (OS or NS), and hip condition (OH or NH). The trunk condition (OT or NT), arm and racket condition (OA&R or NA&R), and legs condition (OL or NL). O = occlusion; N = neutralization; D = direction.
v v vin
Sn
Dn
i i= +( ) /( ) ( ) 2 .
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racket and leg occlusions, even though the kinematics of the nonoccluded locations remained unaltered.
Procedure
Participants were tested as a group in a large lecture room. The simulations of tennis shots were presented on a 2.7 m × 2.0 m screen. Participants were seated randomly between 3 m and 12 m from the screen and were unable to see each other’s responses. The participants’ vertical visual angle ranged from approximately 9° to 30°, and the horizontal visual angle ranged from 8° to 27°. The par-ticipants were told that they would be shown tennis shots played either inside-out or cross-court. They were asked
to imagine themselves as the opponent and to anticipate stroke direction. Also, they were informed that shots were delivered by a (headless) stick figure, that clips would be occluded at ball–racket contact, and that the ball would not be present in the simulation. Participants were requested to indicate the direction of each shot (in terms of left and right) immediately after the simulation had finished, by means of a pen-and-paper response. Prior to data collection, they were presented with 10 examples of shots to each direction in two blocks of 5 shots. The participants were given a 2-min break between the two blocks of 48 trials. The entire experiment lasted approximately 18 min.
Data Analysis
We determined the number of correct answers (c) and the corresponding percentage of correct responses for each experimental condition. The response data were subse-quently transformed using Bartlett’s modified arcsine trans-formation, p =
where n = number of trials (J. H. Bartlett as cited in Zar, 1996). These p values were subjected to an analysis of variance (ANOVA) with occlusion location as the within- subject factor and perceptual skill as the between-subjects factor. Whenever the sphericity assumption was violated, the degrees of freedom were adjusted using the Huynh–Feldt correction and reported accordingly. Significant effects were further examined by means of Tukey’s honestly sig-nificant difference method (at α = .05). Partial eta-squared values were calculated as a measure of effect size. It should be noted that the transformed data were used for the sta-tistical analysis, but untransformed means and standard deviations are reported. In addition, we computed the cor-relation coefficient (r) between the transformed accuracy scores (p) for all pairs of the manipulated conditions (i.e., for all occlusion conditions except the control condition). A positive correlation between conditions indicates that a performance adjustment because of the manipulation of one location goes hand in hand with a similar performance adjustment because of the manipulation of the other loca-tion, which suggests that a commonality underpins the performance adjustments. We reasoned that a positive cor-relation indicates that information that is defined in terms of relations across the corresponding locations is picked up and used.
Results and Discussion
There was a significant effect for perceptual skill, F(1, 30) = 33.029, p < .0001, ηp
2 = .524. The skilled players (M = 77%, SD = 14%) were more accurate than their less skilled counterparts (M = 59%, SD = 13%). There was also a significant effect for occlusion location, F(4.661, 139.825) = 7.761, p < .0001, ηp
2 = .206. Post hoc analysis indicated that the response accuracy was significantly lower when the arms and racket were occluded than in any other
FIGURE 2. (A) Eigenvalue spectrum and (B) covariance between the occlusion (O) conditions and the control condi-tion for the first three modes. OC = control; OS = shoulder; OH = hip; OT = trunk; OL = legs; and OA&R = arm and racket.
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condition (p < .05). Furthermore, a significant Percep-tual Skill × Occlusion Location interaction was observed, F(4.661, 139.825) = 3.856, p < .005, ηp
2 = .114 (see Figure 3). The skilled players were more accurate than the less-skilled players in all conditions except in the arm and racket condition (p < .05), whereas the less skilled players did not differ in response accuracy across conditions (p > .05). The perceptually less skilled players performed at chance level (α = .05) in the arm and racket occlusion condition only, whereas the perceptually skilled players performed above chance level in all conditions.
We provided a total of 10 additional trials under the nonoccluded control condition in the habituation phase to familiarize participants with the test protocol. Although anticipation training studies generally fail to find signifi-cant learning effects in terms of response accuracy (but not response time; cf. Smeeton, Hodges, Ward, & Williams, 2005; Williams, Ward, & Chapman, 2003; Williams et al., 2002; Williams, Ward, Smeeton, & Allen. 2004), we ran the same ANOVA without the control condition to examine this potential confounding effect. We found significant main effects for skill, F(1, 30) = 19.262, p < .0001, ηp
2 = .391, and occlusion location, F(3.856, 115.682) = 6.881, p < .0001, ηp
2 = .187. However, the Skill × Occlusion Location interaction was not significant, F(3.856, 115.682) = 1.879, p > .1, ηp
2 = .059. The correlation coefficients (r) between occlusion con-
ditions are presented in Table 1.2 The correlations were, on average, higher in the skilled group than in the less skilled group. Significant positive correlations among the shoulders, legs, and trunk occlusions were found for the less skilled group, whereas the anticipation accuracy of the skilled group in these occlusion conditions also correlated positively with the hip occlusion condition. Significant posi-
tive correlations between two occlusion conditions (e.g., the hips and shoulders) indicate that a change in anticipation accuracy because of the occlusion (manipulation) of one area (the hips) goes hand in hand with a similar response change because of occlusion of the other area (the shoul-ders). Our results suggest that both skill groups used infor-mational quantities that were defined across locations and that the skilled participants picked up information in a more global manner (i.e., across more locations) and were better attuned to the globally defined information (the correlations were stronger) than were the less skilled participants.
In line with our expectation, we found evidence that the performance of the perceptually less skilled group deterio-rated under occlusion of the arms and racket, as response accuracy was below chance level only in this condition. However, the ability of the less skilled players to pick up and use the corresponding information appears limited. The performance of the skilled players deteriorated sig-nificantly under arm and racket occlusion, in line with the results of previous research (cf. Ward et al., 2002; Williams et al., 2002). Yet, in contrast to our prediction there was no significant deterioration in response accuracy for the hips, shoulders, and trunk occlusion. This finding suggests that the information pertaining to the arms and racket is most important for anticipation (cf. Abernethy, 1990a; Abernethy, 1990b; Abernethy & Russell, 1987). It does not necessarily imply that information pertaining to the other regions is not used when available; it merely implies that it is not critical on its own or in relation to other locations. The correlation analyses and the performance comparison against chance level corroborated this interpretation, indicating that (a) information pertaining to the arm and racket is of special importance and (b) the information across the shoulders,
FIGURE 3. The response accuracy scores as a function of occlusion condition and perceptual skill level. The error bars indicate the standard deviation. PLS = perceptually less skilled; PS = perceptually skilled; OC = control; OT = trunk; OA&R = arm and racket; OS = shoulder; OL = legs; and OH = hip.
100
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TABLE 1. Correlation Coefficients Between the Occlusion Conditions for the Perceptually Less Skilled and Perceptually Skilled Groups
Variable OH OT OA&R OL
Perceptually Less Skilled Group
OS .17 .58* .17 .56*
OH — .15 .15 .35OT — .19 .55*
OA&R — –.04
Perceptually Skilled Group
OS .51* .50* .41 .69**
OH — .69** .14 .57*
OT — –.05 .57*
OA&R — .25
Note. OT = trunk; OA&R = arm and racket; OS = shoulder; OL = legs; and OH = hip occlusion. *p < .05. **p < .01.
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hips, and leg is to some extent picked up and used (mainly) by skilled participants.
In sum, our results suggested that although information pertaining to the arm and racket may be of special impor-tance for the perceptually skilled players when anticipating tennis shot direction, some information may also be obtained from the shoulders, hips, and legs. At the same time, howev-er, we found indications that the occlusion methodology may induce confounding effects, and consequently, the findings from such research should be interpreted with caution.
EXPERIMENT 2
In Experiment 1, we invited participants to anticipate the direction of simulated tennis shots in which specific areas of an opponent’s body were occluded (i.e., omitted from the display). Although our results were broadly in line with earlier research (Ward et al., 2002; William et al., 2002), we found that occluding the arm and racket changed the distri-bution of the variance of the predominant dynamics, which precluded a clear interpretation of the results. A further limitation of the occlusion paradigm is that it does not allow an investigation of the information used for anticipation under more natural conditions (i.e., when the entire action is visible). In the present experiment, we examined the importance of specific areas for anticipation of tennis shot direction while removing, or at least minimizing, the poten-tially confounding effect because of occlusion. We locally eliminated the dynamical differences between inside-out and cross-court shots by averaging them out in the same areas as described in Experiment 1. In this methodology, the search for information is arguably less constrained than in the occlusion conditions. We again examined the effect of manipulation on the main display dynamics.
Our expectations in regard to anticipation performance were slightly modified relative to those in Experiment 1. We expected anticipation accuracy to decrease in both skill groups when dynamical differences regarding shot direc-tion were eliminated in the arm and racket, but we expected the reduction to be smaller than in Experiment 1. Also, we anticipated that the reduction would not reach significance for the less skilled participants. Furthermore, we expected that if neutralization of information pertaining to dynamical differences in the shoulders, hips, and trunk would reduce anticipation accuracy, this effect would be limited to the perceptually skilled players (cf. Shim et al., 2005; Ward et al.; Williams et al.). On the basis of the results of Experi-ment 1 and suggestions from previous studies (Ward et al., 2002; Williams et al., 2002), we anticipated that the skilled participants would use a more global perceptual approach than would the less skilled participants.
Method
Participants
As in Experiment 1, a sample of 40 recreational tennis players with a minimum of 2 years of playing experience
participated. We created groups of perceptually skilled (n = 15; M age = 20.5 years, SD = 2.6 years) and perceptually less skilled (n = 17; M age = 18.9 years, SD = 1.4 years) players based on the same within-task criterion we used in Experiment 1. None of these participants had taken part in Experiment 1. Informed consent and ethical approval were obtained as in Experiment 1.
Apparatus and Stimulus Production
Stimulus generation was the same as in Experiment 1, except that the dynamics of the same body (and racket) locations were neutralized with respect to shot direction. A total of six conditions were used: a control condition (which was the same as that in Experiment 1) and condi-tions in which the dynamics pertaining to the dots and sticks representing either the legs, hips, shoulders, trunk, or the arms and racket were neutralized (NC, NL, NH, NS, NH&S, and NA&R, respectively). To neutralize the dynamics of the relevant locations for all of the 54 modes, we calculated the mean eigenvector coefficients across the inside-out and cross- court shots for these locations (i.e., dynamical differ-ences across shots were averaged out):
(The subscripts IO and XC denote inside-out and cross-court shots, respectively). We then used these coefficients to generate simulations. For all other locations, the original eigenvector coefficients (containing shot-direction differ-ences) were used. The same practice tape as in Experiment 1 was used to familiarize participants with the task.
As in Experiment 1, we used PCA to examine the effect of the neutralization conditions relative to the control condi-tion. The results indicated that changes in the distribution of the variance pertaining to the principal components in the neutralized data were minimal relative to the control condi-tion and that the projection of the first three modes were very similar to those of the control condition (see Figure 4). Although the covariance across projections was slightly dif-ferent from that for the arm and racket condition, the effect of neutralization was much smaller than that of occlusion in Experiment 1 (compare Figures 2 and 4).
Procedure and Data Analysis
The procedure and data analysis were the same as in Experiment 1.
Results and Discussion
There was a significant effect for perceptual skill, F(1, 30) = 18.812, p < .0001, ηp
2 = .385. The skilled participants (M ± SD, 72% ± 11%) responded more accurately than their less-skilled counterparts (M ± SD, 61% ± 11%). Although there was no significant effect for neutralization location, F(4.156, 124.65) = 1.1770, p > .1, ηp
2 = .056, there was a significant Perceptual Skill × Neutralization Location interaction, F(4.156, 124.65) = 6.700, p < .0001, ηp
2 = .183. Post hoc testing showed that the less skilled players’
v v vin n
IOn
XCi i= +( ) /( ) ( ) 2
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166 Journal of Motor Behavior
performance did not differ significantly across conditions, whereas the perceptually skilled players demonstrated a decrement in performance (relative to the control condi-tion) in the trunk, arm and racket, and leg conditions. These results are presented in Figure 5.3
The correlation coefficients (r) between neutralization conditions were, on average, higher in the skilled group than in their less skilled counterparts (see Table 2).4 Sig-nificant positive correlations were found between the arm and racket and shoulders and legs, and the trunk and legs neutralizations for the less-skilled group. For the skilled group, significant positive correlations were observed for the arm and racket and trunk and legs neutralization and
between the trunk, hips, and legs conditions. These results suggest that both skill groups used information that was defined across these different locations, but the skilled participants used this information more than did their less skilled counterparts.
The Perceptual Skill × Neutralization Location interaction indicated that the less skilled players were not significantly affected by any neutralization condition. Apparently, these par-ticipants were dependent on the information pertaining to one specific area. At the same time, they were able to pick up and use any information to anticipate to a moderate extent only.
FIGURE 4. (A) Eigenvalue spectrum and (B) covariance between the neutralization (N) conditions and the control condition for the first three modes. NC = control; NS = shoulder; NH = hip; NT = trunk; NL = legs; and NA&R = arm and racket.
A
50
40
30
01
23
45
6NC
NSNH
NTNL
NA&Rλ
Var
ianc
e %
Cor
rela
tion
%
1.000
0.999
0.998
NS NH NT NL NA&R
BMode1 Mode2 Mode3
20
10
FIGURE 5. The response accuracy scores as a function of neutralization (N) condition and perceptual skill level. The error bars indicate the standard deviation. PLS = perceptu-ally less skilled; PS = perceptually skilled; NC = control; NT = trunk; NA&R = arm and racket; NS = shoulder; NL = legs; NH = hip.
100
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0NC NT NA&R NS NL NH
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TABLE 2. Correlation Coefficients Between the Neutralization Conditions for the Perceptually Less Skilled and Perceptually Skilled Groups
Note. NT = trunk; NA&R = arm and racket; NS = shoulder; NL = legs; and NH = hip occlusion. *p < .05. **p < .01.
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As expected, the response accuracy scores for the skilled players decreased significantly when the arm and racket and the trunk dynamics were neutralized. In addition, neu-tralization of the leg dynamics hampered performance. The observation that the information pertaining to the legs may contribute to anticipation has, to our knowledge, not been previously reported. This result can be understood in view of the findings of Huys et al. (2008), who reported that dynamical differences between shot executions to different directions were present in the legs and feet. These differ-ences can be picked up by the skilled players to facilitate anticipation. Our results suggest that information pertain-ing to the arm and racket, trunk, and legs is important for skilled anticipation. The correlation analyses corroborated these results (significant correlations were found between these areas) and suggested that, when available, informa-tion corresponding to these areas is picked up and used concurrently. The suggestion that skilled anticipation is not based on information arising from a single area, but that perceptually skilled players instead use a more global, or holistic approach is in line with the proposal of Williams et al. (2002; see also Ward et al., 2002).
GENERAL DISCUSSION
We examined the importance of information pertaining to distinct body areas (the arm and racket, shoulders, hips, trunk, and legs) when attempting to anticipate shot direction in ten-nis by manipulating the corresponding dynamics. In Experi-ment 1, we occluded these areas, whereas in Experiment 2, we locally eliminated dynamical differences relating to shot direction. Before discussing the implications of our results for anticipation performance, we briefly discuss the impact of our manipulations on the resulting display dynamics.
Methodological Issues
The differences in distribution of the variance pertaining to the display dynamics between the control condition and neutralization manipulations were negligible. In contrast, we found marked differences in the occlusion condition, especially for the arm and racket occlusion. The impact of the manipulations on the prevailing dynamics in the resulting display was further highlighted by the covari-ance between the projections corresponding to the control condition and the manipulated areas. These effects can be understood by considering two interacting factors. First, the number of manipulated elements correlates positively with the degree of redistribution of the variance, which also depends on the nature of the manipulation. In accordance, the redistribution of the variance in Experiment 2 was considerably smaller than that in Experiment 1 because the number of elements in the Experiment 2 display did not change. The variance associated with executing a tennis stroke is larger than the variance that differentiates inside-out shots from cross-court shots. Consequently, the effect of eliminating dynamical differences is therefore smaller than the effect of eliminating the dynamics altogether. Given
that the contribution from the different areas and the degree of shot-specific differences is heterogeneous (see Huys et al., 2008), the effect of the manipulations on the degree of redistribution of the variance and on the change in the time evolution pertaining to the dominating components depends on the elements manipulated. Although the effect induced by the first factor may be controlled by the experimenter(s), the second factor is much harder to control.
To determine whether redistribution of the variance could have confounded anticipation performance in the occlusion condition, we computed the response scores in the arm and racket condition and compared them with response scores in the control condition for both skill groups in the occlusion and neutralization experiments. The arm and racket condition was chosen because it had the largest potential confounding effect. These scores were subjected to an independent t test, which indicated that the impact of occlusion on anticipation accuracy was significantly larger than that of neutralization, t(30) = −3.819, p < .01. This result suggests that the effect of occlusion may have been confounded by changes in the display dynamics. The observation that none of the other occlusion conditions resulted in significant decrements in performance seems counter to this suggestion. However, this absence may have been partly because of large response variability across the skilled participants. The variance was 40.93 and 11.24 in the control condition for the skilled participants in the occlusion and neutralization experiments, respectively. In conclusion, although we cannot be sure that the redistribu-tion of the display dynamics confounds the results of spatial occlusion (and if so, to what degree), we found indications pointing in that direction.
Although the disruptive effect of neutralization on the display dynamics was smaller than that of occlusion, the display dynamics were obviously altered; the neutralization of certain areas inevitably alters the (dynamical) relations between that area and other areas. By implication, this methodology cannot be used to identify isolated areas that are critical for anticipation performance. However, in con-trast to occlusion, it allows for the identification of areas that contribute to anticipation accuracy in conditions that allow for spatially unconstrained information pickup. In that regard, it seems reasonable to suggest that occlusion constrains observers’ visual search patterns (at least the occlusion of locations normally looked at), whereas neu-tralization does not, even though it may be that the changed dynamics induce the impression to observers that some-thing is wrong. However, our data cannot support or refute this suggestion, and further research, perhaps involving the recording of visual point-of-gaze, confidence ratings, or verbal reports, is needed to clarify this issue.
Does Local Dynamical Information Underwrite Skilled Anticipation Performance?
We found no clear indications that the perceptually less skilled players’ anticipation accuracy was affected by the
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168 Journal of Motor Behavior
manipulations. In contrast, the perceptually skilled partici-pants showed a decrement in accuracy across all occlusion and neutralization conditions compared with the control condition, although only significantly so in some cases. For the skilled group, occlusion of the arm and racket had a negative impact on performance accuracy, whereas neutral-ization of this area and the trunk and the legs resulted in a decrement in accuracy. These results can be appreciated in view of the presence of different informational constraints (in terms of availability and distortion) under both manipu-lations. Although the occlusion experiment suggested that, for the perceptually skilled group, information pertaining to the arm and racket is critical for anticipation, be it in isola-tion or in relation to other areas, the neutralization experi-ment suggests that information pertaining to trunk and legs is also used by skilled participants when available.
The correlation analysis suggested that the skilled group picked up information that is defined across some body locations (including the racket) to a larger extent than did the less skilled group, which suggests that the former used a more global (or holistic) perceptual strategy than did their less skilled counterparts (see also Williams et al., 2002). At the same time, the skilled participants appeared more vulnerable to the manipulation of local information. These results, which may appear contradictory, can be understood by considering two issues. First, as previously discussed, the effect of local neutralization is not confined to the area that is manipulated. In other words, performance decrement because of the neutralization of an area does not simply testify to the importance of that area on its own. Second, vulnerability to information distortion necessitates sensitiv-ity to that information.
What could be the functional significance of adopting a more global approach if the information from a specific area (the arm and racket) is critical and, in all likelihood, sufficient? We propose that a more global strategy may provide greater perceptual robustness. Specific variation in local kinematics is inevitable across different shots and players. By implication, the adaptation of a local perceptual strategy renders the observer more vulnerable to such vari-ability. At the same time, Huys et al. (2008) showed that shot direction-specific differences (that are in a statistical sense invariant) are distributed across the entire body. A more holistic search helps to pick up the invariance (i.e., information) to a greater extent than would be possible with a more local strategy and renders the observer more robust against shot-direction-independent variability. The implica-tion of these insights for perceptual (racket-sport) training seems to be twofold. First, learners should be stimulated to direct attention to all bodily areas (and racket) that contrib-ute to the action, rather than to limited regions only. Second, learners should be challenged to discover the invariant fea-tures across shot executions. This process may be achieved by presenting them with low-dimensional displays (as per the stimulus material of Huys et al.), a rich repertoire of video clips (i.e., different shot executions delivered by dif-
ferent players), or both. From a practical point of view, it would be interesting to find out which method would lead to quicker and more robust training improvement.
In sum, we found evidence to suggest that although information pertaining to the arm and racket is indispens-able for accurate anticipation, information arising from the trunk and legs is also picked up and used. In addition, it appears that the perceptually skilled players use a percep-tual approach that is more globally oriented than that used by their less skilled counterparts.
Conclusion
We introduced a new methodology to investigate the importance of dynamical information pertaining to specific body locations (and the racket) when attempting to antici-pate shot direction in tennis. The methodology allowed us to examine the effects of manipulations on resulting (display) dynamics. We found that spatial occlusion has a considerable impact on the dominant dynamics and their distribution and found some indication that this effect may confound results. In addition, our results suggest that infor-mation underpinning effective anticipation is not picked up locally, but rather is distributed over a large part of the sys-tem that executes the action. Furthermore, the perceptually skilled players appear to utilize a more global or holistic approach than do the less perceptually skilled players when attempting to anticipate an opponent’s intentions.
A promising methodological extension of the present approach may be found in the wavelets Karhunen–Loève transform (cf. Starck & Querre, 2001), which allows one to track differences between the specific locations involved in action execution as a function of time (unlike PCA). In view of the growing evidence of the varying contribution of specific locations to anticipation throughout action execu-tion (cf. Farrow, Abernethy, & Jackson, 2005; Hagemann, Strauss, & Cañal-Bruland, 2006; Huys et al., 2008; Wil-liams et al., 2002), this method may be particularly well suited to directly investigate the informational basis under-lying anticipation.
NOTES1. Huys et al. (2008) found shot direction-dependent differences
in the standard deviations of the time series. To eliminate these dif-ferences, we calculated the average mean and standard deviation for inside-out and cross-court shots for each participant. For the subsequent simulations, we used the average mean and standard deviation of 2 participants.
2. In 6 of the 10 analyses between conditions, some overlap between the areas occurred (e.g., between the hip and leg occlu-sion, see Figure 1). Altogether, 12 instances of overlap were pres-ent across skill groups, with six significant and six nonsignificant correlations, respectively. In eight instances, overlap was absent, with three significant and five nonsignificant correlations, respec-tively. We cannot exclude the possibility that the overlap could partly explain the correlations found, but the comparisons suggest that any potential effect is likely to be small.
3. We performed the same additional analysis as in Experiment 1 to examine the potential confounding effect that may have arisen as a result of the 10 practice trials in the control condition. Omitting
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the control condition did not markedly impact the statistical results, and no indications of a learning or habituation effect was evident between the first and second blocks of trials (all ps > .1).
4. Much as in Experiment 1, overlap between areas could partly explain the results, but again, the effect, if present, appeared to be small.
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Submitted June 22, 2006Revised January 15, 2007
Second revision May 8, 2007Third revision April 14, 2008
Accepted April 16, 2008
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
