Validity of a Soccer Defending Skill Scale (SDSS) Using Game Performances

Paper : Growth and Development Validity of a Soccer Defending Skill Scale Validity of a Soccer Defending Skill Scale (SDSS) Using Game Performances Koya Suzuki * and Takahiko Nishijima ** * Doctoral Program in Health and Sports Sciences, University of Tsukuba ** Institute of Health and Sport Sciences, University of Tsukuba koya@stat.taiiku.tsukuba.ac.jp 1-1-1 Tennodai, Tsukuba City, Ibaraki 305-8574 Japan [Received May 23, 2003 ; Accepted November 6, 2003] The purpose of this study was to examine the validity of a soccer defending skill scale (SDSS) measured by the location of players in soccer games using structural equation modeling. The samples were 469 defending performances in the final of FIFA World Cup Korea / Japan 2002 TM (Brazil vs. Germany), which were determined by distances, and angles, between attackers and defenders, and the number of players. Results for the general CFA model consisting of the selected 9 items indicated a good fit to the data (CFI=.994, RMSEA=.032). The causal structure model of the defending skills was statistically valid (CFI=.991, RMSEA=.037). The multidimensional CFA model indicated a much better fit to the data than the general CFA model (χ 2 = 17.378 with 8 df, p < 0.05). It was concluded that the SDSS with 9 items successfully was able to measure the game performance according to the causal structure of the tactical defending phase, and the SDSS was able to measure multi-dimensional abilities consisting of the defending phase and the defending object. Keywords: structural equation modeling, confirmatory factor analysis, multitrait-multimethod matrix [] 1. Introduction There are two approaches that are widely employed in performance analysis for team sports: notational analysis and biomechanics. Such factors as frequency of use of techniques, frequency of success or failure and their comparisons are used as performance indicators in the notational analysis approach [Hughes and Franks (1997); Hughes et al. (1988)]. However, because game performance is expressed as the result of interaction with an opponent, many factors are involved. Therefore, it is difficult to evaluate game performance from unidimensional frequency data, with a resulting ambiguity in interpretation [Hughes and Bartlett (2002); Lees (1998)]. In addition, most notational analysis research is based on a research design that compares frequency data of successful teams and unsuccessful teams, assuming that frequency and comparative differentials are the decisive factors in game performance [Eaves and Hughes (2003); Hughes and Jones (2003)]. There are game statistics using indicators that make objective observation possible, but because observation indicators are unable to encompass offensive and defensive tactical values, disparities arise with the point of view for evaluation of the team s state by specialists such as managers and coaches. As a result, the notational analysis approach is effective for game statistics, but it is not applicable as a method to evaluate team or individual skills. In contrast, the sports biomechanics approach constructs a hierarchical technique model of movement and uses a quantitative indicator corresponding to a skill model for each aspect of movement [Bartlett (1999); Bartlett (2001); Lees (2002)]. As a result, multidimensional performance measurement becomes possible, and the measured value can be given objectivity for interpretation. However, although the quantitative measurements in sports biomechanics are objective and exact, evaluation standards are undecided, so compared to qualitative indicators such as the subjective judgment of managers and coaches, it cannot be said that they suffice as feedback information for coaches [Lees (2002)]. 34

Suzuki, K. and Nishijima, T. In regard to the above problems in game performance analysis, Hughes and Bartlett (2002) have related the necessity to develop the multidimensional qualitative indicators that are recognized by managers and coaches instead of simple unidimensional quantitative analysis. We can develop measurement indicators to solve these problems by turning the qualitative evaluation view recognized by specialists into multidimensional quantitative data and analyzing them. Briefly, what is required in order to develop skill measurement indicators of game performance is to clarify the structure of game performance that specialists recognize and identify the causal relationship among the indicators measured. Moreover, by measuring structural game performance that managers and coaches recognize, it will become possible to estimate the specific skills of teams and individuals, which are latent factors. Skill tests and game performance are methods of measuring sport specific skills [Strand and Wilson (1993)]. Performance measured through the skill test, which deals with the representative movement aspects revealed in games, shows a discrepancy with actual game performance, so, since the 1980 s, research evaluating specialized skills from game performance has become the mainstream. The major feature of these researches is that they construct criteria using multivariate analysis techniques on large volumes of data [Han and Schutz (1992); Nishijima et al. (1987)]. In recent years, researches have been conducted that study the causal relationship of latent variables constructed from multiple measurements through the application of structural equation modeling [Suzuki et al. (2001); Suzuki and Nishijima (2002)]. These researches have constructed hierarchical game performance structures in soccer and created performance indicators based on the structures. On the other hand, it must be borne in mind that multiple factors are involved in game performance. Suzuki and Nishijima (2002) have studied the causal relationship of attacking skill according to attacking phases from game performance structures in soccer. In their research, they have reported that there are factors that cannot be explained merely by employing the three sub-skills that are used to explain attacking skill. In football guides [Wade (1967); Worthington (1980)], game performance structures are explained from the role of the player and from attacking and defending phases. It can be considered that game performance in soccer is completed when both skill types are invoked. In this case, the correlation matrix is a multitrait-multimethod matrix (two or more traits are each measured with two or more methods). It can be assumed that each measured value is being influenced simultaneously by the traits and the methods at the time of measurement. A method has been proposed to analyze such characteristic multivariate data [Marsh (1988); Marsh (1993)]. By constructing a multidimensional confirmatory factor analysis model (multidimensional CFA model) assuming trait factors and method factors, it becomes possible to separate and study the obtained measurement values on the effects due to traits and the effects due to methods [Marsh and Richards (1994); Rees et al. (2000)]. By applying this method, we can explain simply phenomena in which several mixed skills seem to be involved in performance completion. By separating the involvement of both kinds of skills in soccer game performance, the role of the player and attacking and defending phases, it becomes possible to clarify them as a simple structure. The purpose of this paper was to verify the validity of measurement items derived from a qualitative game performance structure using the traditional CFA model 1, a causal structure model and the multidimensional CFA model to make a soccer defending skill scale (SDSS) that measures team defending skill from soccer game performance. 2. Methods 2.1. Terms The tactical terms used in this paper follow the Japan Football Association and Japan Soccer Writers Council (2002), Japan Football Association Technical Committee (2000) for the original Japanese version and Lablanc and Henshaw (1994), Hughes (1980a) for English terms. 2.2. Samples Samples used in this research were 439 defending 1 Shows modelizing of ordinary confirmatory factor analysis. In this paper, in order to argue comparison with the multidimensional CFA model, taken as traditional CFA model. 35

Validity of a Soccer Defending Skill Scale Table 1 Characteristics of samples. Numbers of defending performances Total Team Brazil Germany Total defense performances 439 253 186 Thirds of the field atacking third 76 48 28 Middle third 298 172 126 Defending third 95 63 32 Start point of defence Delaying attack Intercept passes / out of play Forcing play in one direction End point of defence Win (or Temporary finish of defence) Success Squeezing workspace Failure performances in the FIFA World Cup Korea/Japan 2002 (Brazil vs. Germany). The defending performance of each team is shown in Table 1. Each sample defending performance was assumed to be independent, and we carried out statistical processing of the multivariate analysis. 2.3. Scaling procedure In regard to defending performance, we assumed success as the result of the involvement of composite skills corresponding to the differing defending objects per each defending skill and defending skills in a time series causal relationship according to the defending phases. In order to measure game performance that considers defending phases and defending objects, we hypothesized a qualitative defending skill structure based on a structure of defending phases and defending objects. Regarding the construct validity of the performance items, we confirmed a measurement model of the relationship between the construct factor (latent variable) and the measurement items (observed variable) [Schutz and Gessaroli (1993)], the causal structure among sub-skills according to defending aspects, and a multidimensional structure consisting of defending phases and defending objects. The scaling procedures for defending performance were as follows: a)to construct the hypothetical structure: cause and effect analysis, brainstorming method, matrix diagram; b)to test objectivity of measurement items: intraclass correlation coefficient; c)to select measurement items: frequency distribution characteristic verification, confirmatory factor analysis by phase; d)to test construct validity: confirmatory factor analysis (traditional CFA model); e)to test causal structure: structural equation modeling (multiple-indicator model); To test multidimensionality of measurement items: structural equation modeling (comparison of Point of receiving a pass (1st) Figure 1 Cyclic structure in defending phases. multidimensional CFA model and traditional CFA model). 2.4. Defending phases Point of passing Point of receiving a pass (2nd) Takii (1995) relates that there are but 2 scenes in soccer: attack and defense, dependent on whether one is in possession of or not. On the other hand, Wade (1967) explains soccer from 3 scenes, evoking a preparatory state, or midfield play, in which control of the play is not entirely certain. As the expression used in actual matches, "loose ball," suggests, there is a state in which is not in possession of either team. In this regard, the present study takes as operational definitions that attack has been achieved the moment has been stolen and one pass has been made to an attacker, and that the moment that attack has been achieved, the other team begins the defending phase. Defending phases are assumed to consist of the delaying attack phase, the forcing play in one direction phase and the squeezing workspace of attackers phase. The delaying attack phase is from the time that the first pass is made until the attacking player receives. The forcing play in one direction phase begins at the moment the attacking player receives and ends when he passes it. The squeezing workspace phase is from the end of the forcing play in one direction phase to the time is stolen or a pass intercepted, or else is put out of play, and if was not stolen or a pass intercepted, or was not put out of play and the opponents attack was not stopped, we judged a simultaneous transferal to the delaying attack phase and conducted measurements on both phases. Briefly, as we see in Figure 1, it is a cyclic 36

Suzuki, K. and Nishijima, T. Table 2 Measurement items of defending skills Points of measurement Point of receiving a pass (1st) Point of receiving a pass (2nd) Point of passing Point of receiving a pass (2nd) Defending phases Delaying attack Forcing play in one direction Squeezing workspace of attackers Defending objects Attacker with the ball Attackers without Attacking space Attacker with the ball Attackers without Attacking space Attacker with the ball Attackers without Attacking space Note. Measurement items code in the table corresponds to the code in appendix 1. Scales Measured Measurement items movements Units 1 2 3 4 5 6 Delay 1) Position of a 1st defender to the attacker with 150 > 120 > 90 > 60 > Angle 150 120 90 60 30 30 > 2) Body shape to direction of attack in the 60 > 90 > 120 > 150 > Angle < 30 attacker with 30 60 90 120 150 3) Open players in attack Person 5 4 3 2 1 0 Marking 4) Positioning of defenders Person 0 1 2 3 4 5 5) Circumstances tried to use the Covering of attacking space behaind the defence Person 5 4 3 2 1 0 space 6) Distance 10 > 8 > 6 > 4 > Circumstances of back-line defenders 10 (m) 8 6 4 2 2 > One side cutting 7) Direction of a pass in the attacker with the 60 > 90 > 120 > 150 > Angle < 30 150 ball 30 60 90 120 8) Number of pass courses which a 1st DF stops Person 0 1 2 3 4 5 up Pass courses cutting 9) Number of pass course which defenders Person 0 1 2 3 4 5 except a 1st DF stops up 10) Open players in attack Person 5 4 3 2 1 0 11) Distance 10 > 8 > 6 > 4 > Circumstances of back-line defenders 10 (m) 8 6 4 2 2 > Balance control 12) Distance 30 > 25 > 20 > 15 > Side space 30 (m) 25 20 15 10 10 > 13) Distance 25 > 20 > 15 > 10 > Control of a back-line 25 (m) 20 15 10 5 5 > Challenge 14) Challenge of a 1st DF to the attacker with the Distance 9 > 7 > 5 > 3 > 9 ball (m) 7 5 3 1 1 > 15) Body shape to direction of attack in the 60 > 90 > 120 > 150 > Angle < 30 attacker with 30 60 90 120 150 16) Challenge of a 2nd DF to the attacker with Distance 11 > 9 > 7 > 5 > 11 3 > (m) 9 7 5 3 Concentration in defence 17) Number of pass courses Person 5 4 3 2 1 0 18) Distance 50 > 40 > 30 > 20 > Width 50 Reducing width and (m) 40 30 20 10 10 > depth in attack 19) Distance 25 > 20 > 15 > 10 > Depth 25 (m) 20 15 10 5 5 > structure, and we assumed this cyclic structure to continue until is stolen or put out of play. Further, we excluded cases in which a shot was made without a pass after was received, and we assumed that cases in which a one-touch pass was made instead of receiving as equivalent to the delaying attack phase and the forcing play in one direction phase. 2.5. Defending skills Hughes and Bartlett (2002) point out the fact that it is necessary that the variables used in game performance analysis be selected after clarifying the performance structure, in the same way as the variables used in biomechanics research, and the necessity to measure in game performance analysis the qualitative parts that coaches are cognizant of during matches. In this respect, in order to construct a hypothetical structure for objects of analysis, we first assumed a soccer game defending phase structure based on previous researches [Hughes (1973, 1980a, 1980b); Ohishi and Yamanaka (1983); Takii (1995); Wade (1967); Worthington (1980); Yamanaka (1980)]. Second, taking 7 coaches officially qualified by the JFA (Japan Football Association) as objects, we completed a matrix diagram and cause and effect analysis [Hosotani (1982); QC methods development sectional meeting (1979)], following the brainstorming method [Clark (2002)], and establelished measurement items, expressing them in a fishbone diagram [Suzuki and Nishijima (2002); Suzuki et al. (2001)]. We measured game performance for 3 defending objects in each defending phase: attacker with, attackers without and attacking space. 2.6. Measurement method We recorded a CS digital broadcast image on 30 June 2002 on a digital video recorder and measured on replay. The ball and the players on the pitch were always within the recorded image. Measurement of defending performances conformed to the method of Suzuki and Nishijima (2002), and we paused the recorder and replayed it at the point of each measurement. In order to minimize the error in measurements taken from the image, defending performances were measured employing a reduced map of the pitch used for notational analysis of game performance [Hughes and Franks (1997)]. The measurement items make up a ratio scale of distance, angle, etc., as shown in Table 2. Taking into consideration the measurement error that arises 37

Validity of a Soccer Defending Skill Scale when the coordinates from the image to the reduced map are plotted, and also practicality on the spot, we measured the ratio scale data at interval scale levels. Assuming that a scale level of 5 or more points is best when employing interval scale analysis in structural equation modeling [Bentler and Chou (1987)], we established a 6-point interval scale. Whenever automatic measure of game performance was possible by applying motion analysis techniques previously developed by Taki et al. (1996), direct measurement of players positional information through the use of the ratio scale was permitted. In addition, that allowed us to eliminate errors of measurement arising at the time of measurement, dependent on the measurer. Because it was expected in this study that measurement errors would occur dependent on the measurer, we tested the objectivity, which is the reliability among the measurers, for the 3 measurers. Because we hypothesized a multivariate normal distribution among the measurement items, items whose mode was 1 or 6 were excluded from the sequent analysis in advance. The concrete method of measurement is shown in Table 2 and Appendix 1.1 and Appendix 1.2. In the delaying attack phase, delay performance performances against an attacker with were measured (Figure 1, 2), as were marking performances against attackers without (Figure 3, 4) and covering performances against attacking space (Figure 5, 6). The measurement point for each performance was the moment the attacking player received. In the forcing play in one direction phase, one side cutting performances against an attacker with were measured (Figure 7, 8), as were pass course cutting performances against attackers without (Figure 9, 10) and balance control performances in space defense against attacking space (Figure 11, 12, 13). The measurement point for each performance was when the attacking player completed a pass for the one side cutting performance; for the rest, it was when the attacking play made a pass. For the squeezing workspace phase, challenge performances against an attacker with (Figure 14, 15), concentration in defense against attackers without (Figure 16, 17) and reducing width and depth in attack against attacking space (Figure 18, 19) were measured. The measurement point for each performance was at the point when the attacking player completed a pass. When the opponent s attack continued without a pass by the attacking player, for the performance of measuring the completion of a pass, performance was measured at the point when an attacking player received. Further, when an attacker s pass was intercepted by the defender before it crossed in front of the opposing player, we took the measurement value in the squeezing workspace of attackers phase to be the highest value of 6. 2.7. Statistical analysis We calculated the intraclass correlation coefficient in order to test the objectivity of the measurement items. The 3 measurers measured 30 defending performances from the beginning of the match. In order to eliminate influences from the others, the measurers did their measuring individually. We conducted confirmatory factor analysis on each defending phase, based on a hypothetical structure of defending performance and selected from the defending skill factors 9 measurement items with a high validity. We constructed a traditional CFA model using the selected measurement items and confirmed the measurement model. We used the maximum likelihood method to estimate parameters. For goodness of fit indices, we used the absolute index χ 2 value, goodness of fit index (GFI), adjusted goodness of fit index (AGFI), normed fit index (NFI), Tucker-Lewis index (TLI), comparative fit index (CFI), root mean square of approximation (RMSEA), and for relative comparison among multiple models, using the effective Akaike information criterion (AIC), Browne-Cudeck criterion (BCC) and expected value of the cross-validation index (ECVI), the models goodness of fit was judged comprehensively by the above indices. GFI, AGFI, NFI and CFI show goodness to be best at nearly 1, and for the RMSEA, AIC, BCC and ECVI values, the smaller the value, the better the goodness [Bollen and Long (1993); Kano and Miura (2002)]. In order to insure identification of models, the variance of each latent variable and the paths from error variables and to measurement variables were constrained to 1 [Bollen (1989), pp. 238-254]. Based on the results of confirmatory factor analysis, a causal structure model was constructed in accordance with the defending phase using a multiple-indicator model, and it was confirmed using structural equation modeling [Bollen (1989); Kline (1998)]. In order to insure identification of the model, we constrained to one the variances of the exogenous latent variables and one of the paths of the 38

Suzuki, K. and Nishijima, T. Covering of attacking space Marking Delay Delaying attack Delaying attack Balance control Pass courses cutting One side cutting Forcing play in one direction Forcing play in one direction Reducing width and depth in attack Concentration in defence Challenge Squeezing workspace of attackers Squeezing workspace Figure 2 Hypothetical structure of defending performances. Defending performances attacking space attackers without attacker with Defending objects Defending phases were confirmed from 2 models using the chi-square difference test [Bentler and Bonett (1980)]. For the significance test of the path coefficient, correlation (covariance) and variance within the model, we used the univariate Wald test. For model modification we used the modification index, and when relationships among variables were confirmed scientifically, fixed parameters were assigned to free parameters [Sörbom (1989)]. For statistical analysis, we used SPSS 11.0J for Windows and Amos 4.0.2J. Level of significance in all statistical hypothesis testing was set at α = 0.05. Table 3 Objectivity of measurement items Defending phases Delaying attack Forcing play in one direction Squeezing workspace Measurement items Mean 1) Position of a 1st defender to the attacker with the ball 5.09 1.37 6 0.93 2) Body shape to direction of attack in the attacker with 2.96 1.90 2 0.88 3) Open players in attack 4.17 1.41 5 0.88 4) Circumstances tried to use the space behaind the defence 2.05 0.92 2 0.77 5) Positioning of defenders 3.08 1.35 3 0.77 6) Circumstances of back-line defenders 2.76 1.65 2 0.78 7) Direction of a pass in the attacker with 3.17 1.56 3 0.81 8) Number of pass courses which a 1st DF stops up 2.13 1.03 2 0.95 9) Number of pass course which defenders except a 1st endogenous latent variables to the measurement variables, and likewise, the paths from the error variables to the measurement variables to 1 [Bollen (1989), pp. 326-333]. In order to test the multidimensionality of the defending skill measurement items, we compared the multidimensional CFA model, which takes the defending phase and the defending object as latent variables, to the traditional CFA model, which has a latent variable only the defending skill seen from the defending phase. In order to insure identification of the multiple CFA model, we constrained the variances of each of the latent variables and the paths from the error variables to the measurement variables to 1. When comparing 2 models, in addition to AIC, BCC and ECVI, statistical significant differences Standard diviation Mode Intraclass correlations 3. Results 3.1. Defending performance structure Figure 2 shows the qualitative causal structure of defending performance compiled by using a matrix diagram, cause and effect analysis and previous researches of individual performance elements, obtained from 7 qualified coaches through the brainstorming method. Defending performance was broadly divided into 3 areas corresponding to the defending phase: delaying attack, forcing play in one direction and squeezing workspace. Delaying attack consisted of delay (defense against an attacker with ), marking (defense against attackers without ) and space covering (defense against space). Forcing play in one direction consisted of one side cutting (defense against an attacker with ), pass course cutting (defense against attackers without ) and defending balance control (defense against space). Squeezing workspace consisted of challenge (defense against an attacker with ), concentration in defense (defense against attackers without ) and reducing width and depth in attack (defense against space). 2.97 1.20 3 0.80 DF stops up 10) Open players in attack 2.86 1.31 2 0.86 11) Circumstances of back-line defenders 2.73 1.67 2 0.94 12) Side space 2.96 1.39 4 0.86 13) Control of a back-line 4.82 1.23 6 0.86 14) Challenge of a 1st DF to the attacker with 3.79 1.78 5 0.95 15) Body shape to direction of attack in the attacker 3.26 2.02 2 0.91 with 16) Challenge of a 2nd DF to the attacker with 3.14 1.75 2 0.95 17) Direction of squeezing space 4.48 1.83 5 0.88 18) Width 3.81 1.91 5 0.98 19) Depth 3.93 1.92 5 0.98 3.2. Objectivity As shown in Table 3, the intraclass correlation coefficient shows a high value greater than 0.77 for all items. 39

Validity of a Soccer Defending Skill Scale Table 4 Factorial structure of each defending phase in CFA models: standardized solution Variable (n=439) attacker with (F1) Factor loadings attackers without (F2) attacking space (F3) Correlated uniqueness a Phase of delaying attack Delay2 1.00 0 0 Marking1 0 0.92 0 Marking2 0 0.23 0 0.10 Covering of attacking space1 0 0 0.99 Covering of attacking space2 0 0 0.28 Factor correlations Factor F1 F2 F3 F1 1.00 F2 0.30 1.00 F3 0.24 0.44 1.00 Phase of forcing play in one direction (F1) (F2) (F3) One side cutting1 0.99 0 0 0.26 One side cutting2 0.05 0 0 Pass courses cutting1 0 0.17 0 Pass courses cutting2 0 0.54 0 Balance control1 0 0 0.08 Balance control2 0 0 0.82 Factor correlations Factor F1 F2 F3 F1 1.00 F2 0.19 1.00 F3 0.62 0.11 1.00 hypothesized the defending o b j e c t s p e r e a c h d e f e n d i n g phase for sub-skills (factors). In confirmatory factor analysis of the delaying attack phase and forcing play in one direction phase, we excluded from the analysis delay 1 (1) and balance control 3 (13), which were the maximum mode 6 (Table 3). The path coefficient corresponding to the item from the factors took only 1 or 2 items corresponding to the hypothesis for free parameters; otherwise the path coefficient fixed to zero. The goodness of fit indices all showed high goodness of fit: AGFI > 0.97, TLI > 0.93, CFI > 0.98 and RMSEA < 0.05, satisfying the standard for adoption of the model (Table 5). Phase of squeezing workspace (F1) (F2) (F3) Challenge1 0.94 0 0 Challenge2 0.64 0 0 Concentration in defence1 0 0.72 0 Concentration in defence2 0 0.60 0 0.36 Reducing width in attack 0 0 0.78 Reducing depth in attack 0 0 0.77 Factor correlations Factor F1 F2 F3 F1 1.00 F2 0.97 1.00 F3 0.95 0.82 1.00 Note. a: The three correlated uniquenesses posited are between marking 2 and covering of attacking space 2, one side cutting 1 and pass courses cutting 2, concentration in defence 2 and reducing depth in attack. Table 5 Goodness of fit indices of CFA models Model of each defending phase Fit indices Delaying Forcing play in Squeezing workspace attack one direction Chi-square values 6.862 6.821 9.915 p values 0.076 0.338 0.078 GFI 0.994 0.995 0.993 AGFI 0.971 0.984 0.971 NFI 0.964 0.931 0.992 TLI 0.929 0.975 0.988 CFI 0.979 0.990 0.996 RMSEA 0.052 0.017 0.046 Note. CFA = confirmatory factor analysis; GFI = goodness-of-fit index; AGFI = Adjusted GFI; NFI = normed fit index; TLI = Tucker-Lewis index; CFI = comparative fit index; RMSEA = root mean square error of approximation. 3.3. Confirmatory factor analysis by defending phase Table 4 shows the results (standardized solution) of the confirmatory factor analysis, in which we 3.4. Confirmatory factor analysis of defending skills Figure 3 shows standardized solution of confirmatory factor analysis assuming for factors s u b - s k i l l s c o r r e s p o nding to defending phases, using the 9 items that represent each performance element. As paths were added in accordance with modification indices, although the chi-square value corresponding to the initial m o d e l s h o w e d a s i g n i fi c a n t decrease, content interpretation was possible. From among those demonstrating a significantly higher chi-square value against the initial model, we added only those paths for which content interpretation was possible; we took as the final solution the path-added model in which the significance of the path coefficient could be confirmed. The goodness of fit indices of the model all showed high goodness of fit: AGFI = 0.968, TLI = 0.988, CFI = 0.994 and RMSEA = 0.032, showing values that satisfy the standard for adoption of the model. The path 40

Suzuki, K. and Nishijima, T. 0.99 Delaying attack 0.34 0.78 0.52 0.28 Delay 2 Marking 1 Covering of attacking space 1 One side cutting 1 e1 e2 e3 e4 0.24 0.61 Delaying attack 0.99 0.33 0.79 0.51 0.27 Delay 2 Marking 1 Covering of attacking space 1 One side cutting 1 e1 e2 e3 e4 0.25 0.58 0.26 0.34 Foring play in one direction 0.46 Squeezing workspace 0.73 0.41 0.85 0.77 0.68 Pass courses cutting 2 Balance control 2 Challenge 1 Concentration in defense 1 Reducing width in attack e5 0.14 0.18 e6 e7 0.21 e8 0.16 e9 d1 d2 Foring play in one direction 0.28 Squeezing workspace 0.44 0.76 0.40 0.85 0.77 0.68 Pass courses cutting 2 Balance control 2 Challenge 1 Concentration in defense 1 Reducing width in attack e5 0.14 0.19 e6 e7 0.21 e8 0.16 e9 GFI=.987 AGFI=.968 NFI=.981 TLI=.988 CFI=.994 RMSEA=.032 Chi-square=26.739 (P=.084) AIC=80.739 GFI=.985 AGFI=.966 NFI=.978 TLI=.984 CFI=.991 RMSEA=.037 Chi-square=31.061 (P=.040) AIC=83.061 Figure 3 solution. CFA model of defending skills: standardized Figure 4 Causal structure model of defending skills: standardized solution. Delaying attack Foring play in one direction e1 e2 e3 e5 e6 Delay 2 Marking 1 Covering of attacking space 1 One side cutting 1 e4 Pass courses cutting 2 Balance control 2 Challenge 1 attacker with attackers without 0.037, satisfying the standard for adoption of the model. The path coefficients among sub-skills were 0.99 between the delaying attack and forcing play in one direction, and 0.28 between forcing play in one direction and squeezing workspace. The path coefficients between sub-skill and measurement items were all statistically significant. 3.6. Comparison of the multidimensional CFA model and the traditional CFA model Squeezing working space Defending phases e7 e8 e9 Concentration in defense 1 Reducing width in attack attacking space Defending objects Figure 5 Multidimensional CFA model consisting of the defending phases and the defending objects of a SDSS. coefficients between sub-skill and measurement items were all statistically significant. The path coefficients of e2 and e5 showed high values of 0.61. 3.5. Causal structure of defending skills Figure 4 shows the standardized solution of the causal structure model among sub-skills in accordance with defending phases. The goodness of fit indices all showed high goodness of fit: AGFI = 0.966, TLI = 0.984, CFI = 0.991 and RMSEA = The initial CFA multidimensional model takes sub-skills of defense according to the defending phase and sub-skills of the defending object as latent variables. Figure 5 is the final model, which has added the path to one side cutting 1 from the squeezing workspace and the covariance between e2 and e5, and which accords with the modification index in the initial model and actual scientific bases. When we compare to the traditional CFA model by taking defending sub-skills according to the defending phase only for the latent variable, the multidimensional CFA model shows better model goodness of fit, even in each absolute value index. AIC, BCC and ECVI, which are relative model comparison indices, all showed lower values for the multidimensional CFA model (Table 6). In addition, the chi-square test between the 2 models showed significant differences (χ 2 value = 17.378, df = 8, p 41

Validity of a Soccer Defending Skill Scale Table 6 Factorial structure of Multidimensional CFA model: standardized solution Fit indices General CFA model consisting of the defending phases < 0.05). Path coefficient between latent variables and measurement items showed mid to high values of 0.49 to 0.78 either or both defending sub-skill according to the defending phase or defending sub-skill according to the defending object (Table 7). Table 7 Comparison of fit indices in two models Competing models Multi-dimensional CFA model consisting of the defending phases and objects Chi-square values 26.739 9.361 p values 0.084 0.498 GFI 0.987 0.996 AGFI 0.968 0.980 NFI 0.981 0.994 TLI 0.988 1.002 CFI 0.994 1.000 RMSEA 0.032 0.000 Comparison indices AIC 80.739 79.361 BCC 81.918 80.890 ECVI 0.173 0.170 Note. CFA = confirmatory factor analysis; GFI = goodness-of-fit index; AGFI = Adjusted GFI; NFI = normed fit index; TLI = Tucker-Lewis index; CFI = comparative fit index; RMSEA = root mean square error of approximation; AIC = akaike information criterion; BCC = Browne-Cudeck criterion; BIC = Bayes information criteiron; ECVI = Expected value of the cross-validation index. Variable (n=439) Delaying attack (F1) Forcing play in one direction (F2) Squeezing workspace (F3) 4. Discussion 4.1. Validity of defending skill scale As Bartlett (2001) and Hughes and Bartlett (2002) have pointed out, team performance analysis to date, in trying to evaluate performance using an aggregate of frequency data and its ratio, has not gone beyond carrying out team specific skill evaluation that evaluates the goodness or badness of team performance by individual play. As historical background, let us bring up the point that the structures of team sports performance have not been clarified. In the sports biomechanics process of skill measurement, it is possible to measure the goodness or badness of performance per movement from a component perspective, in order to extract performance indicators based on the construction of hierarchical structures of movement. In this research, a hierarchical structure of game performance was obtained, as shown in Factor loadings attacker with (F4) attackers without (F5) attacking space (F6) Measurement items Delay2 0.51* 0 0 0.20 0 0 Marking1 0.64* 0 0 0 0.41* 0 0.61* Covering of attacking space1 0.49* 0 0 0 0 0.37* One side cutting1 0 0.43* 0.30* 0.49* 0 0 Pass courses cutting2 0 0.59* 0 0 0.38* 0 Balance control2 0 0.24 0 0 0 0.63* Challenge1 0 0 0.78* 0.38* 0 0 Concentration in defence1 0 0 0.70* 0 0.37* 0 Reducing width in attack 0 0 0.64* 0 0 0.38* Factor correlations Factor F1 F2 F3 F4 F5 F6 F1 1.00 1.00* 0.11 F2 1.00* 1.00 0.18 F3 0.11 0.18 1.00 F4 1.00 0.74* 0.56* F5 0.74* 1.00 0.61* F6 0.56* 0.61* 1.00 Note. *: P < 0.05. a: The two correlated uniquenesses posited are between marking1 and pass courses cutting2. Correlated uniqueness a 42

Suzuki, K. and Nishijima, T. Figure 2, through conducting qualitative analysis by qualified soccer experts, and it was possible to construct game performance indicators that fulfill content validity by leading game performance measurement variables based on the obtained structure. And also from the viewpoint of quantifying the qualitative judgments of managers and coaches, the procedures used in this research solved the problems in team specific skill measurement. The reliability of a test is the necessary condition for validity. In game performance measurements, reliability cannot be confirmed through the repeated measurements of the test-retest method. Therefore, we tested objectivity, which is the reliability among measurers. The intraclass correlation coefficient of the 3 measurers showed a high value of > 0.77 for all items (Table 3), and the defending performance indicators used were confirmed to have high objectivity. In order to confirm the construct validity of the measurement items, we constructed a traditional CFA model in accordance with a hypothetical structure of defending game performance (Figure 3). Measurement items need to be made up of a small number of items, with consideration of their practicability on the coaching scene. First, in order to select those items that best fulfill content validity and construct validity from the 19 items prepared as measurement items, we conducted confirmatory factor analysis per each defending phase (Table 4). Next, we selected the 9 items with high factor loading corresponding to individual factors in the factorial structure by defending phase and conducted confirmatory factor analysis using these items. A model modified many times compared to the initial model met the standard for adoption of the model. In addition to adding the path from squeezing workspace to one side cutting 1, model modifications added paths between error variables. A path between error variables appeared commonly among the items that measured the same defending object. This could be a result that suggests the necessity to hypothesize factors for defending objects. Moreover, the modification indices showed that the model was improved by adding the path from squeezing workspace to one side cutting 1. A possible explanation for this could be due to the influence of the fact that that when a direct pass was measured, one side cutting 1 also measured squeezing workspace at the same time. Furthermore, it is possible to think that the results show that this is not merely a matter of appearance caused by the measurement method, but that the forcing play in one direction performance has a strong relationship with the squeezing workspace of attackers skill. From the above, it became clear that defending skills in soccer consist of delaying attack skills, forcing play in one direction skills and squeezing workspace skill, and that the 9 performance items that measure these skills fulfill the requirements of content validity, objectivity and construct validity based on game performance structures in accord with the defending phase. On the other hand, the existence of 3 factors that cannot be explained by sub-skill alone was inferred. 4.2. Causal structure among defending skills Defending skills in soccer are manifested according to the defending phase, and there are serial causal relationships among the defending skills that are measured. Therefore, the serial causal relationships among defending skills that the defending performance items measure show the validity of the performance items. We constructed a multiple-indicator model using the 9 measurement items that were employed to confirmatory factor analysis in order to clarify the causal relationships among defending skills (Figure 4). The goodness of fit index of the model showed a value in which the chi-square value rejects the null hypothesis. Bollen and Long (1993) propose that a comprehensive judgment is needed, rather than making a decision on the goodness of fit of the model from only 1 indicator. Because all the other goodness of fit indices satisfied the standard for judgment, the multi-indicator model of defending skills that was hypothesized was statistically valid. In regard to causal relationships among defending skills, a forcing play in one direction skill from a delaying attack skill showed a high value of 0.99, but squeezing workspace from forcing play in one direction showed a low causal relationship of 0.28. These results showed that while delaying attack operations have a major effect on the success of forcing play in one direction operations, success in forcing play in one direction performances have little effect on success in squeezing workspace performances. In this research, we measured all 43

Validity of a Soccer Defending Skill Scale items at the highest value whenever was lost to the defender before the attackers completed a pass during the squeezing workspace phase. Therefore, the squeezing workspace value was high, whether or not the forcing play in one direction performance was excellent or poor, for example, when the attacker missed a kick. It may be that this influenced the low path coefficient between a forcing play in one direction skill and a squeezing working space skill. From the above results, a causal relationship among the 3 defending skills according to the defending phase in soccer was confirmed. These results show that the 9 defending performance items are valid as measurement items for the defending phases of soccer. 4.3. Multidimensionality of the defending skill scale Exploratory factor analysis and confirmatory factor analysis are methods for testing the construct validity of measurement items [Sharma (1996)]. Schutz and Gessaroli (1993) have stated that results of exploratory factor analysis should be confirmed by confirmatory factor analysis. By recreating through confirmatory factor analysis the structure obtained from exploratory factor analysis, the credibility of the factorial structure can be confirmed. However, if we were to conduct exploratory factor analysis on variable groups that are influenced by multiple characteristics, such as the measurement items used in this research, it would be predictable that the structures obtained would mix traits. Performing exploratory factor analysis on the 9 items as preliminary analysis resulted in the extraction of 4 factors in which 3 skills corresponding to the defending object and a squeezing workspace of attackers skill and skills that can be interpreted were mixed (Appendix 2). Further, from the results of the confirmatory analysis shown in Figure 3, we inferred the existence of factors that cannot be explained from the 3 sub-skills alone from the relationship among the error variables. These results made it clear that the common procedure of construct validity confirmation cannot be applied to the measured data in this research. Marsh (1989) proposed a "CFA approach to multitrait-multimethod (MTMM) data" as a confirmation procedure for validity in regard to measurement item groups that fuse traits and methods. Applying this method, we constructed a multidimensional CFA model (Figure 5) that assumes a complex involvement of defending skills and skills to the defending object for game performance in defending phases and compared it to the traditional CFA model that has been commonly used to date for validity confirmation procedures (Table 6). The multidimensional CFA model showed better values for all goodness of fit indices, and path coefficients from either sub-skills in the defending phase or sub-skills of the defending object in the multidimensional CFA model in regard to measurement items all uniformly showed high values. It was shown from these results that the 9 items that measure defending performance in soccer are not merely the 3 sub-skills according to the defending phase, but are a multidimensional scale that can measure defending skills that are sub-skills of the defending object defending skills against the attacker with, defending skills against attackers without and defending skills against space and can also separate and measure the influence of sub-skills of the defending phase and of the defending object. In this model, we added correlation (covariance) between e2 and e5. It is believed that the cause of this that is the measurement items to which this error variance belongs are items obtained by the same method. By adding this correlation (covariance), we were able to infer the influence from the sub-skill after subtracting the influence of the measurement method. Adding error correlations has resolved the existence of factors that cannot be explained merely by the 3 sub-skills in the conventional approach of construct validity confirmation using the traditional CFA model. The validity of using the multidimensional CFA model as the validity confirmation procedure of measurement items in which the involvement of multiple traits is hypothesized was demonstrated. Using this model, we do not explain the influence of traits as error correlation, but we are able to extract them as trait variance and confirm the influence that measurement items receive from multiple traits. In this research we developed a measurement scale of defending skills from positional data of players and confirmed the causal structure among defending skills and the multidimensionality of the scale. It 44

Suzuki, K. and Nishijima, T. was made clear that defending skills in soccer consist of delaying attack skills in the delaying attack phase, forcing play in one direction skills in the forcing play in one direction phase and squeezing workspace skills in the squeezing workspace phase, and they constitute a causal relationship according to the defending phase. Furthermore, it was confirmed that the 9 performance items used in this research are a multidimensional scale that measures all aspects of defending skills, which are sub-skills of the sub-skills according to the defending phase and the sub-skills of the defending object. Because the samples used in this research were in a match at the highest skill level in the world, confirming cross-validity, by taking into consideration competitive level and stage of development and confirming the sensibility of the obtained scale, is a task for future study in order to generalize the results. References Arbuckle, J. L. 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