Human Movement Science 30 (2011) 40–55

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Human Movement Science

journal homepage: www.elsevier .com/locate/humov

The dynamical structure of handball penalty shots as afunction of target location

Michael Bourne a, Simon J. Bennett a, Spencer J. Hayes a, A. Mark Williams a,b,⇑a Research Institute for Sport and Exercise Sciences, Liverpool John Moores University, UKb Discipline of Exercise and Sports Science, The University of Sydney, Australia

a r t i c l e i n f o a b s t r a c t

Article history:Available online 9 December 2010

PsycINFO classification:230023233720

Keywords:KinematicsPerceptionSkillAnticipation

0167-9457/$ - see front matter Crown Copyright �doi:10.1016/j.humov.2010.11.001

⇑ Corresponding author. Address: Faculty of HeAustralia. Tel.: +61 2 9351 9067.

E-mail address: m.williams@sydney.edu.au (A.M

We used principal components analysis (PCA) to investigate varia-tions in the dynamical structure of handball penalty shots as a fac-tor of target location and phase of shot. Participants completed atotal of 10 successful shots to each of four target locations in thehandball goal. Three dimensional movement time series data wereanalyzed. Also, data were analyzed across three temporally distincttime windows in line with the evolving kinematic chain. Statisticalanalyses were undertaken to determine differences across targetlocations. There were no significant differences between dynamicalstructures as a factor of target or phase. Covariance between timeevolutions as a factor of target reduced in line with the ranking ofthe component. When shots were analyzed as three distinct timewindows, only the low time evolution covariances suggested dif-ferences between targets in any time window. Our findings showthat the dynamical structure underpinning the handball penaltyshot does not differ greatly across locations. However, the timeevolution of principal components suggests there are some varia-tions in dynamics which may differentiate shot direction.

Crown Copyright � 2010 Published by Elsevier B.V. All rightsreserved.

1. Introduction

In fast ball sports such as handball and tennis, speed and accuracy of response are critical tosuccessful performance. The time taken to process ball flight information and initiate an appropriate

2010 Published by Elsevier B.V. All rights reserved.

alth Sciences, The University of Sydney, East Street Lidcombe, NSW 2141,

. Williams).

M. Bourne et al. / Human Movement Science 30 (2011) 40–55 41

action often exceeds the total amount of time available to respond (Williams, Davids, & Williams,1999). In such situations, anticipation skill is thought to be an important distinguishing factor be-tween elite and sub-elite performers. Several researchers have highlighted the importance of beingable to perceive information arising from the early (i.e., advance) postural orientation of an opponentwhen seeking to anticipate his/her intentions (e.g., Abernethy, 1990; Shim, Chow, Carlton, & Chae,2005; Williams, Ward, Knowles, & Smeeton, 2002). However, research is needed to more clearlyunderstand how, what, and when elite performers pick up information from an opponent’s move-ments when making an anticipation judgment. In this paper, we examine the viability of using anassumption free method of statistical analysis in the form of Principal Component Analysis (PCA) toidentify the sources of information that may be available to observers to guide anticipation.

In pioneering work into the perception of human motion, Johansson (1973,1976) reported that itwas possible to recognize human biological motion from only light sources placed on major joint loca-tions. It was postulated that the relative motions between joint centers provide sufficient informationfor the recognition of human motion. Johansson concluded that the ability to perceive multiple pointlights as representing a single human motion was not determined by experience of viewing the spe-cific motion per se, but by a general perceptual functionality based on the perception of common mo-tions and deviations of points relative to this ‘‘reference’’ motion. Johansson postulated that naiveobservers should be able to recognize the displacement of multiple point lights as biological motioneven when that specific class of motion has not been observed previously, albeit he did suggest thatprior experience may play an important role in assigning meaning to a grouping of elements.

Since the early work of Johansson researchers have confirmed that point light displays provide en-ough information for observers to recognize human biological motion. Troje (2002) showed thatobservers can distinguish the gender of a walker from point light displays. Two types of informationwere identified, namely, motion mediated structural cues and dynamical information. The motionmediated structural cues contain geometrical information about the performer, while the dynamicalinformation represents the displacement characteristics of the motion. Troje suggested that it was thedynamical displacement information which was important in categorizing motion and gender, sup-porting Johansson’s assertion that his ‘‘vector analysis model’’ explains how biological motion is per-ceived. Moreover, Troje argued that dynamical and structural information may be inter-dependentsuch that it may be necessary to classify structure (i.e., the human form) before its motion can be clas-sified. Intuitively, however, it would appear unnecessary for performers to classify their opponent’sstructure in fast ball sports and consequently, the main task in anticipating ball direction may be toidentify the dynamical information sources which distinguish between different motions.

PCA has recently emerged as a technique for identifying the low dimensional dynamics of motion(cf. Daffertshofer, Lamoth, Meijer, & Beek, 2005; Huys, Daffertshofer, & Beek, 2004; Post, Daffertshofer,& Beek, 2000; Troje 2002). Historically, researchers who have attempted to identify the motion infor-mation underpinning anticipation in sport have used film-based occlusion tests (see Abernethy &Russell 1987; Abernethy & Zawi 2007; Abernethy, Zawi, & Jackson 2008; Farrow, Abernethy, & Jackson2005; Muller, Abernethy, & Farrow, 2006; Starkes, Edwards, Dissanayake, & Dunn, 1995). Huys et al.(2009) provided an alternative to the occlusion approach by examining the effects on anticipationwhen dynamical information in the display was occluded or neutralized, respectively. Huys and col-leagues used the PCA results to identify the appropriate information sources to manipulate. In subse-quent testing using stick figure displays, it was shown that neutralization of an information sourceaffected the dynamics to a lesser extent than occlusion, although the changes in dynamics did notresult in a decrement in anticipation performance scores across all occlusion conditions.

In a follow up study, Williams, Huys, Canal-Bruland, and Hagemann (2009) used the data generatedby PCA to interchange the dynamical information from ‘‘local’’ (i.e., a single body location) or ‘‘global’’(i.e., multiple body locations) areas when viewing tennis shots presented as stick figure images. Theauthors reported that skilled players were more attuned to using ‘‘global’’ information pick-up thanless skilled counterparts. These studies illustrate the practical utility of using PCA to identify the infor-mation underpinning anticipation judgments.

Huys, Smeeton, Hodges, Beek, and Williams (2008) were the first to apply PCA in the analysis anddifferentiation of whole body actions in sport. They reported that five principal components werenecessary to explain 96% of the variance in time series data for tennis shots to different locations.

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Moreover, the differences identified within the principal components were spread globally across thebody. Huys et al. (2008) suggested that the execution of passing shots in tennis was governed by a lowdimensional control structure and that differences between shots were present in both dynamicalstructures and scaling parameters (i.e., the magnitude of displacement of an anatomical landmarkindependent of displacement pattern).

Although the approach used by Huys et al. (2008) was successful in identifying what information maybe available to facilitate anticipation, the research design did not identify when this information may beextracted from the display. The authors did comment, however, that the tracking of dynamics as a func-tion of time could be an important new direction for researchers in future. While the corresponding timeevolution of a principal component outlines its variation over time, it is difficult to isolate a specific timeover which the information contained in the component is likely to be relevant. The application of PCA tosub-sections of discrete data sets to search for temporally relevant low dimensional dynamics is anunexplored application which may provide a useful method for quantifying actions that have histori-cally been broken down into ‘‘phases’’ of a time series in biomechanical analysis. To this end, we usedPCA (see Daffertshofer et al., 2005; Huys et al., 2008) to identify whether the low dimensional dynamicswhich underpins penalty shooting in handball varies as a consequence of target (i.e., location) andwhether different information exists in separate ‘‘time windows’’ throughout the shot.

When executing the handball penalty throw and forehand drive shot in tennis, athletes will typi-cally look to transfer energy from foot contact through the kinetic chain to the dominant hand in orderto project the ball with speed and accuracy, albeit via a racket in the case of tennis (for an explanationof energy transfer in sports biomechanics, see Bartlett (1999). It is expected that these similarities be-tween the two skills will be reflected in the present study such that our results will have commonal-ities with those reported by Huys et al. (2008). We expect the first and second principal components toreflect any shared dynamical structure across targets and anticipate few significant differences in theeigenvalues, corresponding time evolutions or eigenvector coefficients for these components. For thelower ranked principal components, we anticipate differences in dynamical structure as a factor of tar-get to manifest as differences in the corresponding time evolutions or significant differences in theeigenvector coefficients of components with similar time evolutions. In addition, it is predicted thatshots to varying locations will not differ in the early ‘‘time windows’’, based on a shared starting posi-tion, but that differences in corresponding time evolutions and eigenvector coefficients will be evidentin the mid-to-late windows as more critical differences in dynamics emerge.

2. Method

2.1. Participants

Participants were five international-level, male handball players (age = 24.5 yrs; SD = 2 yrs; playingexperience = 10.6 yrs; SD = 4.6 yrs; mean no of hours practice per week = 16). Participants were cur-rent members of the Great Britain handball team and had been in the squad for an average of 2.5 years.All participants played in attacking positions within the team and were rated by the coaching staff asthe best shooters. Three of the participants were right handed and two were left handed. Since our aimwas to understand the inter-participant consistency of inter-target differences, rather than to look atlaterality per se, data from the left handed participants were converted so that the absolute value ofthe medio-lateral (x) coordinates were positively or negatively switched relative to the medio-lateralaxis using the equation n (right) = n (left)

* - 1 and vice versa in order to be compared to that of the right-handed participants. The ‘‘naming’’ of the targets was switched accordingly so the data from shots tothe top left target for the left handed participants were compared to shots to the top right target afterthe conversion. Participants gave their informed consent prior to taking part and the research wasconducted in accordance with the ethical guidelines of the lead institution.

2.2. Apparatus

A standard handball goal conforming to International Handball Federation (IHF) guidelines(3 m � 2 m) was employed. The goal was divided in such a way as to leave four equal sized sections

M. Bourne et al. / Human Movement Science 30 (2011) 40–55 43

at each corner of the goal (Fig. 1). Targets were defined relative to the goalkeeper’s viewing perspec-tive and were labeled: top right (TR), bottom right (BR), top left (TL), and bottom left (BL). These sec-tions formed the four targets at which the participants would shoot during data collection. Thesetargets were chosen as the extreme points in the goal area and hence the targets most likely to giverise to differences in movement form. The targets were marked with chalk so that a successful hitcould be instantly ratified. A screen mimicking goalkeeper position was placed in front of the central

Fig. 1. Overhead schematic of the data collection set-up used to capture motion analysis data for all trials. The schematicincludes a participant view of the goal face and an outline of where the targets are located in the goal. The targets are labeledtop right (TR), top left (TL) bottom right (BR) and bottom left (BL) relative to the goalkeeper position.

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portion of the goal. The screen protected a camera filming trials from the goalkeeper perspective. Aline was drawn 7 m in front of the goal to replicate the penalty shot line in handball.

Whole body, three-dimensional displacement data were recorded at 240 Hz using a six camerainfrared motion capture system (Qualisys, Sweden). Cameras were positioned at approximately 45�,90�, 135�, 180�, 215�, and 260� to the transverse plane of the starting position adopted by participants.Retro reflective markers (15 mm diameter) were placed on the left and right shoulder, elbow, wrist,hip, knee, ankle, and third toe. A Panasonic NV-GS50 digital camcorder (Panasonic U.K. Ltd, UnitedKingdom) was placed behind the ‘‘goalkeeper screen’’ to film each trial from the perspective of agoalkeeper.

2.3. Procedure

Participants were instructed to warm up as they would for a training session. Warm up proceduresincluded shooting at the experimental targets to facilitate habituation to the test environment. A totalof 10 successful shots were completed by each participant to each of the four targets while they stoodbehind the 7-m line. Participants were instructed that one foot had to remain in contact with theground behind the 7-m line until ball release, as per IHF rules. When ready, participants took up astandardized start position and directed to shoot at a designated target (1 of 4). The order in whichtargets were aimed at was randomized by the experimenter and each shot was verified as successfulby the participant, the experimenter, and a third party. No discrepancies across the three parties wereexperienced. Participants were asked to project the ball as if they were taking a penalty throw in acompetitive match. To complete the 40 successful shots, participants took an average of 47 shots(range = 40–55).

2.4. Data analysis

For each participant, four trials per target were selected for data analysis and processing. Trialswere selected only if they were successful and were distributed across the data collection sessionto account for any changes in technique due to fatigue. On average, 10% of all trials had to be discardedfor each participant due to lost markers. By using four trials, it was possible to include data from allfive participants in the analysis (see also Huys et al., 2008). The start of each trial was defined asthe first frame of right wrist movement (left for left handed participants) in either the x (medio-lateral) or y (anterior-posterior) directions. The end point of each trial was defined by the point ofground contact of the ‘‘free’’ foot post ball release.

The data sets were exported from the Qualisys track manager application into Matlab versionR2007b (The Mathworks, Natick, Massachusetts, USA). Each trial was re-sampled to the maximal triallength of 567 samples. The maximal trial length was chosen over the mean length to allow more datapoints to be included in the analysis. The four trials from each participant shooting to a given targetwere subsequently used to calculate a ‘‘mean trial’’. Thus, time series data from a single mean trial foreach participant across the four target locations was submitted to a separate PCA. The time series werenormalized to unit variance and organized into N-dimensional state vectors representing individualparticipants shooting at each target (N = 1 [mean trial] � 42 [time series] = 42). The 42 time series rep-resent the 14 marker locations in the 3 Euclidean axes. To assess the presence of dynamics in specifictime windows of the data, target specific state vectors were split into three equal time windows of 189samples. A total of 12 new state vectors were created per participant encompassing three time win-dows for each of the four targets. Each new time window state vector was analyzed using PCA. Whilefor a given state vector all principal components cumulatively account for 100% of the observed var-iance in the data, we only included principal components that cumulatively amounted to P90% of theobserved variance in our statistical analysis (see Daffertshofer et al., 2005; Forner-Cordero, Levin, Li, &Swinnen, 2005; Huys et al., 2008; Post et al., 2000). The percentage that each principal componentcontributed to the total variance of the state vector was calculated. Eigenvalues were subsequentlyconverted to z-scores and entered into repeated measures ANOVA to determine if the contribution dif-fered significantly as a consequence of rank or target. The corresponding time evolutions nk(t) of theselected principal components were subjected to covariance analysis, generating a covariance matrix.

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Covariances were standardized (cf. Field, 2000) to provide an r value for each covariance using theequation:

COVnkðtÞPCx&nkðtÞPCy

sðnkðtÞPCxÞ � sðnkðtÞPCyÞ:

where COV is the covariance between two corresponding time evolutions and s is the standard devi-ation of each time evolution. The eigenvector coefficients vk

i were analyzed using ANOVA with target(4) and marker location (42) as repeated measures factors for complete time series PCA or target timewindow (3) and marker location as repeated measures factors for time window PCA. Eigenvector coef-ficients were only entered into ANOVA if the analysis of eigenvalues and corresponding time evolu-tions suggested that the dynamics of principal components were comparable across targets.Significant effects were investigated using simple contrast tests. If sphericity was violated, degreesof freedom were adjusted using the Huynh-Feldt correction. To anticipate, the outlined data analysisprocesses provided insight into general inter-target dynamical differences. However, it became clearthat a second PCA encompassing all of the complete time series data would provide further opportu-nity to quantify how the displacement of individual marker locations distinguishes shots to differenttargets. Thus, a second PCA was run on a new N-dimensional state vector which included all time ser-ies from all participants across the targets (N = 1 [mean trial] � 5 [participants] � 4 [targets] � 42[time series] = 840). The aim of this second PCA was to identify if principal components which capturethe greatest shared covariance across the targets represent individual target marker location displace-ments equally, as reflected in the eigenvector coefficients, or if a particular component was more rep-resentative of shots to specific targets. Principal components which cumulatively accounted for P90%of the maximal covariance in the 840 dimension state vector were extracted and the eigenvector coef-ficients entered into repeated measures ANOVA with target (4) and marker location (42) as repeatedmeasures factors. For each of the resulting 168 conditions the eigenvector coefficients related to indi-vidual participants (5) were entered as cases.

To provide a description of the displacement characteristics of penalty shooting to different targets,an assessment of linear displacement in the x, y, and z directions was completed for each marker loca-tion per target. The maximal linear displacement was taken as the distance traveled (mm) by a markerbetween the two most divergent measurements along a single Cartesian axis. The mean maximal dis-placement of each marker was calculated across all targets for each Cartesian axis. Target specificmaximal displacement means were then ranked against how much they deviated from the overallmean. The overall direction of displacement (anterior or posterior, medial or lateral, up or down)was noted. Marker locations where the two targets from a specific side or height of the goal were asso-ciated with the two largest displacements were highlighted to identify any side or height rather thantarget specific patterns of linear displacement.

3. Results

3.1. Individual target PCA

Over 90% of the variance explained by PCA was consistently encapsulated within four principalcomponents. The first principal component accounted for more than 50% of the total variance irrespec-tive of target (see Table 1). ANOVA revealed a significant difference between the eigenvalues of thefirst to fourth principal components, F(3, 12) = 220.038, p < .05. Contrast analysis indicated that theeigenvalue of the first principal component was significantly larger than the eigenvalue of all otherprincipal components, while the eigenvalue of the second principal component was significantly lar-ger than that of the fourth. No significant differences were identified between the variance accountedfor by a principal component as consequence of target, F(3, 12) = .783, p > .05.

Covariance analysis indicated that the corresponding time evolution of the first principal compo-nent was comparable across targets (M P .90). For the second, third, and fourth principal components,a covariance of <.80 was observed, which suggests there were differences between the dynamics ofshots to different targets at the level of these components. The mean inter-target time evolution

Table 1Mean percentage of total variance accounted for by the first to fourth principal component for targets one to four and theirassociated standard deviations.

TR TL BR BL

Mean PC1 54.3 52.0 54.6 53.9PC2 21.4 24.7 23.2 23.8PC3 12.5 11.7 12.1 12.6PC4 6.0 6.3 5.8 5.2Cumulative variance 94.2 94.7 95.6 95.4

s PC1 10.2 5.7 7.7 7.6PC2 4.8 4.2 4.1 5.8PC3 3.5 3.8 3.0 4.5PC4 1.7 1.8 2.6 1.0

46 M. Bourne et al. / Human Movement Science 30 (2011) 40–55

covariances of the first four principal components are outlined in Table 2. The intra-target time evo-lution covariances presented in Table 2 indicate that only a moderate amount of dynamical structureis shared between participants when shooting to the same target. This finding indicates that there is alimit to the extent to which any subsequent generic findings are able to explain individual shootingdynamics.

To continue to investigate the nature of inter-target shooting dynamics, where a high (>.90) meaninter-target covariance was observed for like components (e.g., TRPC1–TLPC1), the eigenvector coeffi-cients were investigated to examine whether the similar dynamics was a product of different anatom-ical contributions. First, the means of the absolute eigenvector coefficients were visually mapped inorder to identify potential dynamical structures characterizing each principal component. As seenin Fig. 2, there were some underlying patterns in the weighting of anatomical markers onto principalcomponents as a function of target location. For instance, the eigenvector coefficients of the first prin-cipal component were consistent between targets in the medio-lateral and anterior-posterior direc-tions for specific marker locations, as well as being consistent across marker locations in thesedirections, indicating a global contribution to the variance explained by the principal component.Some minor variations between targets were observed in the vertical direction, while the value ofthe eigenvector coefficient was less uniform across marker locations. For comparison, when theeigenvector coefficients of the second to fourth principal components are represented visually theinter-target variance of these components appears to increase (see Fig. 2).

Table 2The mean inter-target and intra-target covariance data for the first to fourth principal component time evolutions. Inter-target datarepresent the mean between target time evolution covariances observed across participants. Intra-target data represent the meaninter-participant time evolution covariances observed for shots to the same target. Both datasets are arrived at via covarianceanalysis of the relevant corresponding time evolutions for the nth principal component.

Target PC1 PC2 PC3 PC4

Inter-targetTR-TL .91 .68 .62 .59TR-BR .93 .89 .82 .81TR-BL .92 .63 .65 .84TL-BR .83 .64 .71 .65TL-BL .92 .82 .81 .65BR-BL .91 .71 .72 .83mean .9 .73 .72 .73s .14 .3 .3 .2

Inter-targetTR .78 .42 .48 .54TL .65 .61 .72 .57BR .79 .42 .49 .57BL .57 .59 .69 .49mean .70 .51 .59 .54s .10 .11 .13 .04

Fig. 2. Absolute group mean eigenvector coefficients for the first four principal components of shots to four targets. Eachdiagram compares the absolute group mean eigenvector coefficients for one of the four principal components, relative to fourdifferent targets (TR, TL, BR, and BL).

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Eigenvector coefficients from the first principal component were entered into ANOVA with re-peated measures on the target (4) and marker location factors (42). The marker location factor wasincluded to determine if there were any significant differences between targets for specific markerlocations. Only eigenvector coefficients from the first principal component were entered into the AN-OVA as the agreement between the eigenvalues and the corresponding time evolutions suggested thatthis principal component was shared across targets. As determined by the findings of the correspond-ing time evolution covariance analysis, the other principal components were not shared to the sameextent across target locations. Although running a statistical analysis on the eigenvector coefficients ofthe second to fourth principal components was not suitable, the visual mapping provides an exampleof the inter-target dynamical differences of these lower components.

Fig. 2 (continued)

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No significant differences were revealed between eigenvector coefficients from the first principalcomponents as factor of target (F(1.146, 4.584) = .980, p > .05). No significant Target �Marker locationinteractions were identified.

3.2. Three-window PCA

Only two principal components were necessary to explain P90% of the variance in the data whenPCA was applied to the three identified time windows (see Table 3). ANOVA identified a significantdifference between eigenvalues as a function of principal component, F(1, 4) = 65.414, p < .05, andtime window, F(2, 8) = 33.324, p < .05, as well as a significant Principal Component � Time Windowinteraction, F(2, 8) = 32.319, p < .05. Specifically, the eigenvalues of windows one and two weresignificantly greater than those of window three for the first two principal components. No significant

Fig. 2 (continued)

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difference was observed between time window eigenvalues as a consequence of target (F(3, 12) = .327,p > .05).

There was a mean covariance of r = .91 for time evolutions from identical principal componentsacross the four target locations, which indicate the presence of some shared dynamics (see Table 4).The covariance between time evolutions decreased from window one to window three, while in addi-tion the time evolutions of the second principal components were found to co-vary less than those ofthe first principal components. Based on the same criteria applied during the covariance analysis oftime evolution data for the complete time series (>.90), covariance analysis suggested shared dynam-ics across targets in four time window components. Individual repeated measures ANOVA on theeigenvector coefficients from each of these four time window components found no significant differ-ences as a function of target: W1-PC1 (F(3, 12) = 1.692, p > .05), W1-PC2 (F(3, 12) = 3.007, p > .05), W2-PC1 (F(3, 12) = .689, p > .05) and W3-PC1 (F(3, 12) = 1.113, p > .05).

Fig. 2 (continued)

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3.3. All targets PCA

Altogether, 91% of the covariance in the data was captured in the first four principal components.The first four components accounted for 45.1%, 26.4%, 12.8%, and 7.4% of the variance respectively.Covariance analysis did not reveal any association between the components (M = 0.00, SD = 0.00).Repeated measures ANOVA found no significant differences between eigenvector coefficients as a fac-tor of target for the first (F(3, 12) = .820, p > .05), second (F(3, 12) = .600, p > .05), third (F(3, 12) = .222,p > .05), or fourth (F(3, 12) = .362, p > .05) principal components. In addition, no significantTarget �Marker Location interactions were identified. For reference, the PCA was able to identifysignificant differences in eigenvector coefficient between marker locations for the first, F(41, 164) =3.441, p < .05, third, F(41, 164) = 3.700, p < .05, and fourth, F(41, 164) = 1.626, p < .05, principal compo-nents. The identification of marker location differences confirms the PCA procedure was sensitive todifferences in the data albeit no target specific differences were present. The findings of the second

Table 3Mean eigenvalues of the target specific time window principal components and their associated standard deviations. Eigenvalueshave been converted to represent percentage of overall variance observed.

W1 W2 W3

PC1 PC2 PC1 PC2 PC1 PC2

Mean TR 89.0 9.2 74.0 19.7 77.6 17.1TL 86.8 10.9 70.8 22.8 67.7 23.9BR 89.6 7.7 76.0 18.2 77.3 17.7BL 86.7 11.7 78.0 18.5 78.5 16.7

s TR 7.9 6.8 12.5 7.4 8.0 5.8TL 9.3 7.5 10.9 9.2 14.3 10.4BR 2.5 2.8 8.3 4.5 10.0 8.2BL 7.9 6.6 5.3 5.2 10.4 8.7

Table 4Mean covariance of the corresponding time evolutions for the four targets across windows and principal components.

Target W1-PC1 W1-PC2 W2-PC1 W2-PC2 W3-PC1 W3-PC2 Mean

TR-TL .97 .95 .89 .88 .91 .88 .91TR-BR .94 .9 .95 .86 .94 .91 .92TR-BL .98 .97 .92 .89 .96 .87 .93TL-BR .92 .85 .94 .87 .83 .78 .87TL-BL .97 .92 .98 .95 .84 .83 .92BR-BL .97 .92 .96 .84 .97 .87 .92mean .96 .92 .94 .88 .91 .86 .91

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PCA confirm those of the first analysis. The majority of the dynamics which underpin handball penaltyshooting appear not to differ irrespective of target location.

3.4. Linear displacement of marker locations

The magnitude of marker location displacement in the medio-lateral, anterior-posterior, and ver-tical directions was investigated. All of the shots analyzed shared the same displacement characteris-tics of an anterior displacement of the throwing arm coupled with the throwing arm moving medially.Of the 42 marker locations investigated, 19 showed side-of-goal specific patterns. Shots to right-sided

Fig. 3a. Outline of the target associated with the largest mean linear displacement of a marker location in the medio-lateral (x),anterior-posterior (y) and vertical (z) directions.

Fig. 3b. Schematic outlining whether the linear displacements associated with a marker location in the medio-lateral (x),anterior-posterior (y) and vertical (z) directions showed any ‘side of goal’ (two largest linear displacements associated with thetwo left or right targets) or ‘height of goal’ (two largest linear displacements associated with the two top or bottom targets) bias.

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targets were associated with the largest displacements in 12 of the 19 marker locations showing sidespecific patterns. Nine marker locations showed height biased patterns of displacement with top tar-gets associated with eight of these. The top right target was associated with the largest linear displace-ments in 20 of the 42 marker locations. The bottom right target was the only target to not beassociated with any of the largest displacements. The linear displacement findings are summarizedin Figs. 3a and 3b.

4. Discussion

We examined whether there are differences in the underlying dynamics of handball shots directedto four separate target locations. We ran PCA on complete time series data sets (see Daffertshofer et al.,2005; Huys et al., 2008) and on separate time window data sets that reflected the early, mid, and lateparts of the shot. We predicted, based on the work of Huys et al. (2008), that variations in shot direc-tion would emerge as differences in either the time evolution or the eigenvector coefficients of thelower ranked principal components.

4.1. Individual target PCA

PCA identified a low number of dynamical structures that contributed to the majority of varianceobserved in the handball penalty shot. No more than four principal components were necessary to ex-plain over 90% of the variance observed in shooting to any target, which is comparable to other wholebody actions such as walking (Daffertshofer et al., 2005; Raptopoulos, Dutra, de Noronha Castro Pinto,& de Pina Filho, 2006) and tennis ground strokes (Huys et al., 2008). In accord with work showing thatthe pick up of relative motion plays a role when making anticipation judgments in sport (Abernethy,Gill, Parks, & Packer, 2001; Huys et al., 2008; Williams et al., 2009), it is likely that, when presented aspoint light displays, the low-dimensional structures identified in the current paper would contain en-ough relative motion information to allow the recognition of handball shots. Although anticipation isnot the focus of the present paper, it is expected that the findings will form the groundwork for futureresearch investigating this skill in handball. We foresee that the current findings will inform the selec-tion of visual stimuli in future research focusing on anticipation in handball.

A major question was whether the dynamical structures vary as a function of the target. An inves-tigation of the principal components for inter-target differences indicated that the dynamical struc-tures which accounted for over 50% of the variance in the action could be represented in a singleprincipal component irrespective of target location. Specifically, for the first principal componentcovariance of corresponding time evolutions was high (>.9) and no significant differences were

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identified in eigenvalues or eigenvector coefficients. Visual mapping of the eigenvector coefficients forthe first principal component highlighted that this component is associated with global displacementof the marker locations in the medio-lateral and anterior-posterior directions. The corresponding timeevolutions of the second to fourth principal components co-varied less as a factor of target. This reduc-tion in covariance may indicate the presence of minor, but consistent differences within the dynamicsof shots to different targets or may reflect the increased inter-participant variability identified withinthe time evolutions of the second to fourth components.

4.2. All targets PCA

A second PCA containing all time series data did not identify any significant differences betweenshots to different targets at the level of the eigenvector coefficients. The absence of any significant dif-ferences in how target specific motion data project onto ‘shared’ components across both completetime series PCA procedures indicates that penalty shots to the various target locations differ far lessin their dynamical structures than initially hypothezised.

The linear displacement of marker locations as a factor of target highlighted some inter-targetcharacteristics (see Figs. 3a and 3b). In general, there appeared to be a link between the height andside of the target and the amount of linear displacement that was necessary to shoot toward that tar-get. However, even in the linear displacement data there were few differences between targets. As canbe seen in Fig. 4, which presents non-normalized data for the right wrist from a shot to the top righttarget and bottom left target in the medio-lateral, anterior-posterior, and vertical directions, the dis-placement paths (i.e., magnitude and length) did not differ for two of the most divergent targets.

To summarize, the findings of the various complete time series data analyses suggest that shots tovarious target locations in a handball goal do not differ in regard to their dynamics. Any inter-targetdifferences that are present appear to be minor and are likely embedded in the dynamics representedby the second to fourth principal components or in the scale of displacement as outlined in the lineardisplacement analysis. This finding is consistent with Huys et al. (2008) who found that neither shotdirections nor shot depths were characterized by a unique dynamical structure in tennis.

4.3. Time window analysis

When the handball shots were analyzed as three distinct time windows, only two principalcomponents were needed to explain >90% of the variance. The first principal component of thetime-window data accounted for a larger amount of the variance (67.7% to 89.6%) than the corre-sponding principal components generated from complete time series datasets, as well as previousresearch work (e.g., Daffertshofer et al., 2005; Post, Daffertshofer, and Beek, 2000). Given the amountof variance accounted for by the first two principal components, it is possible that characteristics ofthe handball shot could be accurately perceived using the dynamical information contained in thesetwo components within one time window. Further investigation would be needed to confirm this

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Fig. 4. Comparison of the linear displacement of the right wrist in the medio-lateral (x), anterior-posterior (y), and vertical (z)directions for a top right (TR) and bottom left (BL) trial from a single participant.

54 M. Bourne et al. / Human Movement Science 30 (2011) 40–55

suggestion, and as mentioned previously, we foresee that our current findings will inform future fol-low-up work on anticipation skill.

Covariance analysis of the corresponding time evolutions revealed that there was enough covari-ance between targets in some principal components (e.g., W1-PC1) to suggest that shots to varioustargets do not differ greatly in relation to their dynamical structures. The subsequent analysis of eigen-vector coefficients for these components found no significant differences suggesting there was no spe-cific marker location in these dynamical structures which could be used to distinguish shot directionin isolation. Only the low covariation between time evolutions of the second principal component inwindows two and three highlighted any differences between targets in any time window. In line withour hypothesis, we expected greater differences between targets to emerge; particularly in the finaltime windows based on what is known regarding the phasing of handball shooting and throwingmechanics (see Fradet et al., 2004; Schorer, Fath, Baker, & Jaitner, 2007). These expected differenceswere not evident in the time window data and confirm the findings of the complete time series data.It is possible that in handball penalty shooting differences in ball flight will occur from minor modi-fications in wrist and finger mechanics in the final stages of the throw, which our data collection pro-cedures were not sufficiently detailed enough to pick up. In support of this latter argument, Wagner,Klous, and Muller (2006) reported that ulnar deviation of the wrist was an important factor in ballflight and velocity during a handball penalty throw.

Future work is required to determine whether the addition of data from the wrist and fingerswould elicit some discriminating differences in dynamics during the final time window. Regardless,the introduction of the time window PCA approach has brought a new perspective to identifyingdynamical structures which can distinguish different whole body motions in sport. In future research-ers looking to identify the dynamical information that differentiates two motions should consider anyadditional benefits a time window or phased PCA approach may provide. Those interested in under-taking investigations using the temporal occlusion approach in particular should look initially to ana-lyze their motions of choice using a time window PCA approach or investigate the application of othernon a priori statistical methods in a ‘time window’ fashion.

5. Conclusions

We introduced a new approach to the application of PCA. To our knowledge this paper is the first toapply PCA to the same data set arranged in different time forms. The three iterations of the processwere undertaken in an effort to thoroughly investigate how dynamical structures vary as a functionof target. Our findings show that in the case of the handball penalty throw, PCA can provide insightinto changes in the dynamical structure of the handball shot as a function of target. Our research sug-gests that any dynamical structure differences between shots to different target locations are to befound in the dynamics of the second to fourth principal components as reflected in the correspondingtime evolutions of our initial PCA analysis and the subsequent analysis using different time windows.It is suggested that the dynamical structure of handball penalty shooting does vary somewhat as afunction of target location, albeit the observed differences were much more subtle than initially ex-pected. We must also consider that shooter individuality will be reflected in the dynamical structuresobserved, based on the findings of the initial intra-target covariance analysis. More sensitive data col-lection and analysis procedures may increase the possibility of identifying significant differences atthe level of the eigenvector coefficients. Those wishing to follow up this work should look to includemotion data from the wrist and fingers to observe whether hand motion data significantly alters thefindings of the PCA.

More generally, researchers should consider the relative benefits of using PCA to analyze time win-dows of motion and explore these for pertinent information. Such decisions may be dictated by theunique constraints of the task (e.g., situations where there are performance benefits associated withidentifying target differentiating dynamics within limited amounts of data). Finally, to understandhow inter-target penalty shooting dynamics influence anticipation behavior, the information derivedfrom the current analyses must be tested in follow up experimental work. The objective of any follow

M. Bourne et al. / Human Movement Science 30 (2011) 40–55 55

up work should be to identify which, if any, of the dynamical structures provide observers the oppor-tunity to distinguish between different motions in a reliable manner.

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