ࡱ> #`bjbj\.\. .>D>Ddxxxxxxx IлGGGGGGG$}JhLGxGxx?I111YxxG1G11V4@xx\5Ļ 86c 5 5UI0I,50Mg0<M\5Mx\5l1нtGG1 IDYaWaxxxxxx Title: LATENT STRUCTURE OF STANDARD INDICATORS OF GAME RELATED EFFICIENCY IN BASKETBALL Authors: GORAN SPORI`1, VLATKO VU ETI1 AND JURICA `ANGO1 Institution: 1Faculty of Kinesiology, Zagreb University, Croatia Correspodence author: Goran Sporia, BEd. Horva anski zavoj 15 10000 Zagreb, Croatia Phone/Fax: 385(1) 3658-641 E-mail:  HYPERLINK "mailto:goran.sporis@kif.hr" goran.sporis@kif.hr Fax: 385 1 3634146 INTRODUCTION Basketball is a complex team sport in which the basic aim is to score more points than the opponent through continuous alternations between offense and defense. There exists a need for a more qualitative and exact description of these particular phases of the game, the individual player or team. The possibility of analysing indicators of situation-related efficiency and parameters of tactical responsibility and player activity, emerges through adequate conduction of game statistics ( Trnini, 1996). By analysing the indicators of situation-related efficiency it is possible to derive the model values of team efficiency and individual player performance in defense and offense, as well as the comparison between players and teams, which is of great importance towards more efficient programming of the preparation process (Milanovi et al. 1993). Trnini (1975) investigated the correlation between defensive and offensive rebounds and the final score and asserted an insignificant correlation between the two. The study was carried out on a sample of 25 basketball matches in the Championship of Yugoslavia. Milanovi (1978) applied regression analysis to a sample of 26 basketball matches in the Championship of Yugoslavia and determined a significant correlation between the following variables: shooting accuracy from various distances and winning in basketball, in particular shooting from a distance, lay ups, and dunks. Plesli (1994) investigated the influence of 14 basketball elements on the final score and asserted a significant positive correlation between the following variables: scoring a goal under the basket, from half-distance, from the free throw line and steals and final score of the basketball game. A negative correlation was asserted between the variables: turnovers and final score of the basketball game. The study was carried out on a sample of 20 basketball matches in the 1989 European Championship played in Zagreb. Trnini et al. (1995) investigated the impact of offensive and defensive rebounds on the final game score and asserted that these elements have a significant influence on the final score. The conclusion was that the variable, defensive rebounds, makes a better distinction between the winning and losing teams. The study was carried out on a sample of 64 basketball matches in the 1994 World Championship, played in Toronto. Regarding this particular sample, Trnini et al. (1995) emphasised a latent structure of manifest variables. Four relatively independent latent dimensions were isolated and named; efficiency of the back defensive line and the front offensive line player, player efficiency in the front defensive and back offensive lines, general efficiency in offense and efficiency of goal scoring from a distance. The authors concluded that neither the 13 standard indicators of situation-related efficiency nor the latent dimensions derived from them are sufficient to fully explain the structure of the basketball game. Dizdar (1997) presented a methodological procedure for the analysis of relations between a cluster of independent variables (predictors) and a dependent variable (criterion) in such specific situations in which the predictors were influenced by additional factors. He concluded that the proposed regression model could be the one to define the relation between situational variables and the final game score in more depth and detail. Klasi (2000) investigated the differences between the winning and losing teams, Cibona and Zadar, in the 1999/2000 season by analysing the standard indicators of situation-related efficiency. He concluded that standard indicators made a good distinction between the teams, especially: number of field goals made, number of defensive rebounds, number of assists and number of steals. The study was carried out on a sample of 7 basketball matches. The latent structure of standard indicators of situation-related efficiency has also been investigated in other sport disciplines. Jankovi (1988) defined a latent structure of technical-tactical elements in volleyball. Using the componential model with Guttman-Kaiser criterion he extracted four major components: general efficiency, efficiency of setting, efficiency of executing the elements in the back line and efficiency in offense. Vuleta et al. (1999) asserted a latent structure of 134 manifest indicators of technical-tactical activity in handball. Using the componential model of factor analysis five significant factors were extracted, three of which contained sufficient interpretative data: efficiency in offense, efficiency in defense, efficiency of the goalkeeper. Specific competition qualities and small samples in previous studies that defy the generalisation of the problem, are a possible reason for the manifestation of various inter-correlations between standard indicators of situation-related efficiency, but also of varied correlation between indicators and the final score in a basketball game. Nonstandard game conditions negate/challenge/invalidate the quality of standard indicators of situation-related efficiency as an instrument of measurement. The influence of referees, spectators, various opponents or playing fields (home or away) alters measuring conditions and contradicts the requirements of the measurement theory (Br i et al., 1997). Conducting the study on a relatively sufficient sample, the quality of standard indicators of situation-related efficiency as a measurement instrument increases. The standard indicators of situation-related efficiency used in this study described the offense and defense with precision and quality. Offense was explained using the following indicators: two-point field goals, three-point field goals, goals from the free-throw line, offensive rebounds, assists and turnovers, while defense was described using defensive rebounds and steals. The indicator personal fouls appeared in offense and defense. These indicators were standardised by FIBA. METHODS Sample of entities (subject sample) The data was collected from 134 basketball matches played during league season and finals in the regional Goodyear League in the 2004/2005 season. Twelve teams entered the competition. In the league season 131 matches were played (22 rounds with six matches each, one match cancelled), and in the finals four teams qualified and played 3 matches (semi-finals and final match). Sample of variables The sample of variables comprised 13 standard indicators of situation-related efficiency recorded for each team during the game: TWO-POINTS FIELD GOALS - SUCCESFULLY (SUT_2_US) the number of successful shots thrown from positions within an area of 6.25m from the basket. TWO-POINTS FIELD GOALS - UNSUCCESFULLY (SUT_2_NE) the number of unsuccessful shots thrown from positions within an area of 6.25m from the basket. THREE-POINTS FIELD GOALS - SUCCESFULLY (SUT_3_US) the number of successful shots thrown from positions beyond an area of 6.25m from the basket. THREE-POINTS FIELD GOALS - SUCCESFULLY (SUT_3_NE) the number of unsuccessful shots thrown from positions beyond an area of 6.25m from the basket. FREE-THROWS MADE (SL_BA_US) the number of goals scored from the free-throw line. FREE THROWS MISSED (SL_BA_NE) the number of missed shots thrown from the free-throw line. OFFENSIVE REBOUNDS (SN) the number of balls caught after rebounding off the hoop or table during the offense game. DEFENSIVE REBOUNDS (SO) the number of balls caught after rebounding off the hoop or table during the defense game. ASSISTS (AS) the number of balls passed between teammates enabling the scoring of a goal. TURNOVERS (IL) the number of balls lost in offense. STEALS (OL) the number of balls won in defense. PERSONAL FOULS (OP) the number of fouls made by a player in offense and defense which included physical contact. BLOCKED SHOTS (BL) the number of blocked or parried shots performed during the phases of transitional or set defense. The data was gathered from official statistics managed by expert statisticians. The official internet site of the Goodyear League was used as a data resource - http://goodyear.adriaticbasket.com. Data processing methods In this study we employed exploratory factor analysis to determine the fundamental latent dimensions i.e. the sources of variations and co-variations between variables. The factors were extracted using the method of principle components and the number of significant factors was determined by means of the Guttman-Kaiser criterion. The initial co-ordinate system was transformed through a non-orthogonal rotation according to the OBLIMIN criterion (Fulgosi, 1988). The following was computed: basic statistical parameters (mean, minimum and maximum results, standard deviation, coefficient of variability, degree of asymmetry and warp degree) the Kolmogorov-Smirnov test for testing of distribution normality correlation matrix between manifest variables characteristic square roots of extracted factors factor structure matrix correlation matrix between factors The data was processed using "SPSS 13.0 for Windows". RESULTS Basic statistical parameters (Table 1.) showed average values of standard indicators of situation-related efficiency and minimal and maximal values of all matches. Table 1. Basic statistical parameters meanminmaxStd.Dev.skewnesskurtosisvariabilitymax DSUT_2_US21.979.0038.004.790.280.3521.8%0.07SUT_2_NE16.905.0037.005.190.580.6630.7%0.09SUT_3_US6.860.0016.003.080.350.2044.9%0.09SUT_3_NE12.743.0028.004.230.580.7233.2%0.07SL_BA_US17.725.0038.006.140.570.1934.6%0.09SL_BA_NE6.260.0020.003.300.780.9952.7%0.10SN8.141.0019.003.360.35-0.1341.3%0.09SO18.914.0033.004.890.040.2225.9%0.06AS11.771.0034.005.460.791.2046.4%0.10OG23.874.0038.004.41-0.141.2918.5%0.06IL13.765.0027.003.870.21-0.1528.1%0.07OL8.900.0022.004.090.53-0.1146.0%0.09BL1.840.008.001.580.900.7386.2%0.18 The standard indicator of situation-related efficiency; BLOCKED SHOTS (BL) varied significantly from normal distribution and had a very distinctive variability coefficient of 86.2%. The indicator (BL) did not (vary) significantly between winning and losing teams, i.e. it made no significant distinction between the two groups. A wide range and high coefficient of variability was observed in following indicators: ASSISTS, FREE-THROWS MISSED, STEALS AND THREE-POINT FIELD GOALS MADE. Table 2. Correlation matrix between manifest variables SUT_2_USSUT_2_NESUT_3_USSUT_3_NESL_BA_USSL_BA_NESNSOASOGILOLBLSUT_2_US 1.00SUT_2_NE-0.171.00SUT_3_US-0.29-0.271.00SUT_3_NE-0.28-0.170.261.00SL_BA_US-0.13-0.14-0.12-0.091.00SL_BA_NE-0.010.05-0.13-0.030.231.00SN-0.010.46-0.120.170.060.121.00SO0.16-0.020.010.060.02-0.070.041.00AS0.45-0.230.20-0.03-0.11-0.040.010.201.00OG-0.07-0.070.100.090.190.260.09-0.120.041.00IL-0.04-0.05-0.24-0.18-0.090.04-0.020.01-0.08-0.011.00OL0.12-0.01-0.010.040.000.19-0.04-0.170.05-0.050.191.00BL0.160.03-0.070.01-0.05-0.080.070.160.17-0.110.010.061 From total of 78 correlation (Table 2.), 28 of them were statistically significant, namely 35%. The highest correlation was registered between variables defining the efficiency of shooting for two or three-points, and correlation between variables ASSISTS and SHOOTING FOR TWO-POINTS (0.45). The high correlation between these two variables is clear, as after every assist a realization is needed, but not vice versa. Every shooting needs not to be preceded by an assist. A high correlation was registered between offensive rebound and unsuccessful shots, particulary unsuccessful shots for two points (0.46). Table 3. Rebound efficiency of winning and losing teams WINLOSSSN88.27SN offensive reboundsSO20.317.5SO defensive reboundsS_UKUPNO28.325.77S_UKUPNO total reboundsUK_SUT_NE33.7137.97UK_SUT_NE shots missedKSEN23.70%21.78%KSEN1 offensive rebounds efficiencyKSEO53.46%51.91%KSEO2 defensive rebound efficiencyKSEU39.48%35.95%KSEU total rebound efficiency  Six factors were extracted from the matrix of cross-correlation by the means of principle components method. Table 4. Characteristic root values of isolated factors EigenvalVariance %Eigenval cum.Cum. %Factor 11.8714.411.8714.41Factor 21.7813.693.6528.10Factor 31.5011.575.1639.67Factor 41.4110.816.5650.48Factor 51.209.237.7659.72Factor 61.027.818.7867.52 Autors found no significant correlation between the factors. Table 5. Factor structure matrix Factor 1Factor 2Factor 3Factor 4Factor 5Factor 6SUT_2_US0.760.40-0.07-0.040.110.18SUT_2_NE-0.2240.24-0.140.82-0.02-0.07SUT_3_US0.136-0.74-0.07-0.28-0.23-0.19SUT_3_NE-0.098-0.800.040.100.010.13SL_BA_US-0.240.160.70-0.15-0.150.16SL_BA_NE0.020.050.690.190.28-0.13SN0.03-0.170.190.82-0.090.14SO0.120.00-0.04-0.05-0.200.78ASIST0.83-0.16-0.02-0.12-0.020.19OG0.10-0.210.660.03-0.08-0.25IL-0.240.31-0.05-0.110.640.15OL0.17-0.080.060.030.80-0.14BL0.21-0.02-0.170.140.220.60 DISCUSION The first latent dimension was correlated with manifest variables SUT_2_US (0.79) and AS (0.83), both of which had a high inter-correlation (0.45) (Table 5.). This factor explains most of the total variance (14.41%). Among other, team offense is determined by the so called point-guard play, which defines the role of a playmaker. A player in this particular position is bound to have high ball manipulation abilities, highly developed catching and passing skills and a capability of penetrating the front defensive line (Trnini, 1996). Penetration of the front defensive line often ends with a simple realisation called the easy basket causing a high percentage of two-point shots. On the other hand, if weak side-help occurs, passing the ball to execute a successful action from under the basket or half-distance follows. Disciplined offensive play consisting of specifically assigned responsibilities (screening, maintaining the court area and court balance) and continuous monitoring of defense positions enable offensive players to execute inside and outside passing accurately and in time. Most often this leads to a clear shot or scoring from under the basket. The variables describing this latent dimension clearly speak of a factor which can be named basic offensive efficiency. The second latent dimension was correlated with variables SUT_3_US (-0.74) and SUT_3_NE (-0.80). Inter-correlation of these variables (-0.27) was statistically significant. This factor explained 13.69% of total variance. It appears that there are more and more players with the ability to successfully score from long distances. Excluding outside players tall players, who can successfully execute shots from outside positions and create the opportunity for fast outside players to penetrate the area under the basket or to assist after penetrating the front defense line to score two or three-point field goals, are greatly sought after. This is confirmed by the percentage of total variance occupied by this factor (correlation coefficient of the variable SUT_2_US with this the latent dimension was 0.40). In line with this, following the penetration, thanks to good defense action loss of ball possession often occurs due to unsuccessful passing or some other error on offense, confirmed by a lesser percentage of total variance taken by this factor (0.31). From the above, the name of this factor is as follows - three-point play factor. The third latent dimension had a high correlation with the following variables: SL_BA_US (0.70), SL_BA_NE (0.69) and OG (0.66). This factor explained 11.57% of total variance. Correlation between these variables was statistically significant, ranging from 0.19 to 0.26. The defense in which irregular hand use dominates over the role of the body and footwork, errors in controlling the defensive positions, poor timing of the help side, "switching" or double teaming, often leads to personal fouls. An early enterance of the bonus means that every subsequent personal foul is fined with free-throws, increasing the functional dependence between these two indicators of situation-related efficiency. This factor can be named the factor of errors in posting the defense and realisation from the free-throw line. The fourth latent dimension was highly correlated with the variables SUT_2_NE (0.82) and SN (0.82). This factor explained 10.81% of total variance. Inter-correlation between these two variables was 0.46 and was statistically significant. This correlation emerged from the fact that a higher number of missed shots enabled a higher number of offensive rebounds (Table 3.). The high impact on the ball, when in an outside position, makes inner/inside passing more difficult. This leads to a situation in which the ball is caught in an unfavorable condition for the realisation of an action, i.e. facilitating a more qualitative defense in a "one-on-one" situation or when double-teaming and rotating the defense. As a result, short passes inside the post area and passing for shots from half-distance are limited. Conversely, considering actions for defending the fast break, during a fast break, and a tendency for inside plays is justified by the prolonged activity after the shot, that is, by the offensive rebound. This factor can be defined as the factor of the defensive back line efficiency and the offensive back line efficiency. The fifth latent dimension was correlated with variables IL (0.64) and OL (0.80). Steals have always been a result of aggressive defensive play, i.e. the decreased ability of the offensive player to adapt to such play. The impact on the ball and passing lines makes timing and passing accuracy impossible and more difficult often leading to ball steals. At the same time, such defensive play enables a large number of brisk and attractive realisations. What emerges from this fact is that overly aggressive defensive actions on the player in possession of the ball could lead to an easy disturbance of defensive balance and penetration of the first line of defense. This factor could be named as the factor of the defensive agressivness on the player with the ball and the offensive agressivness of the player with the ball. Variables SO (0.78) and BL (0.60) were correlated with the sixth latent dimension. Inter-correlation of these two variables was statistically significant, but rather small (0.16). This correlation occurred due to the fact that quality teams have a powerful center rebound line and, in addition to a large number of defensive rebounds, they possess extra quality as shot blockers. The defensive rebound is a essential for all teams to build on the way to victory (Trnini, 1995). It also represents the first phase of the fast break and a result of successful individual or team defense, communication and screening. The block-shot is also a result of successful individual or team defense. In most cases this parameter is an exclusive entitlement of tall players and players with developed explosive strength, the right sense for rebounds and block-shots. The block-shot can also be the result of quality team efficiency, where the player monitors the game during a second or third passing and blocks the opponent's shot. This factor was given a lesser variance percentage by the variable OG (-0.25). It is understood that every successful defense stops their opponent's fast breaks by way of so called tactical personal fouls outside the shooting area. Coaches who expect high performance from their teams are aware that the number of easy baskets has to be brought down, even at a price of personal fouls. Special emphasis is placed on the introductory part of the quarters, while the team still hasn't reached the bonus. Some coaches feel that the first four personal fouls are bound to be "tactical" personal fouls. In conclusion, this factor can be named the factor of basic defensive efficiency. CONCLUSION The primary objective of this research is to determine the latent structure of standard indicators of situation-related efficiency in game of basketball, namely, the sources of variations and co-variations between variables. The strategy of exploratory factor analysis was employed to determine the sources of variations and co-variations between variables. Nonstandard conditions, in which the basketball match is played, dispute the quality of standard indicators of situation-related efficiency as an instrument of measurement. 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The sample of variables comprised 13 standard indicators of situation-related efficiency registered during matches by official statisticians. Six latent dimensions explaining 67.53% of total variability were isolated. The extracted factors were named: factor of the basic offensive efficiency, the three-point play factor, the factor of the errors in posting the defense and the realization from the free throw line, the factor of the defensive back line efficiency and the offensive back line efficiency, the factor of the defensive agressivness on the player with the ball and the offensive agressivness of the player with the ball and the factor of the basic defensive efficiency The latent structure of standard indicators of situation-related efficiency obtained in this study explained 22.1% more total variability variance of manifest variables compared to that of the previous study (Trnini et al. 1995) providing a more exact analysis of the game of basketball. This is explained by the use of a larger sample of entities increasing the reliability of the study and reducing analysis error. The obtained latent structure allowed solid interpretation of the correlation and functional interdependency of the 13 standard indicators of situation-related efficiency. The authors believe that that aforementioned indicators are not sufficient for the interpretation of the complexity of the game of basketball and that studies with additional indicators of situation-related efficiency should be carried out. REFERENCES: Br i, B., Viski-`talec,N.,& Jaklinovi-Fressl, }. (1997). Predictive value of variables for evaluation of technical-tactical elements in handball. Kinesiology, 29 (1), 60-70. Dizdar, D. (1997). Evaluation of one methodological procedure for evaluating sport results. (Master s thesis), Faculty of Physical Education, University of Zagreb. Fulgosi, A. (1988). Factor analysis. In Croatian. Zagreb: `kolska knjiga. Jankovi, V.(1988). Latent structure of the tehnical-tactical elements in volleyball game. Kineziology, 20 (1):57-62 Klasi, S. (2000). Standard indicators of situation related efficiency in the games between Cibona and Zadar  season 1999./2000. (Graduated thesis), Zagreb: Faculty of Physical Education, University of Zagreb. Milanovi, D. (1979). Influence of the scoring-related variables on the final score in basketball game. Kineziology, 9 (1-2): 135-149. Milanovi, D. (1997). Fundamentals of sports training. In D. Milanovi (Ed.), Handbook for sports coaches. Zagreb: Faculty of Physical Educatior}~ ",.08JNZdt&<^~8:<>z ˺˺˺˺˺˺˺ˬˢ˔ˊˢˀˀsˀˊˢh h OJQJ^Jh OJQJ^JhZ5OJQJ^JhRh<6OJQJ^Jh<OJQJ^JhZ5OJQJ^JmHsH hRh<OJQJ^JmHsHhRh<OJQJ^J hu%h<h<6CJOJQJaJhRh<6CJOJQJaJh<- >`f 46J*2BDPV   8 Z `     F v   T"&t0np0ߦߜh OJQJ^JUhczhZ5OJQJ^J hRh<OJQJ^JmHsHh<6OJQJ^JhRh<6OJQJ^Jh<OJQJ^JhZ5OJQJ^JhRh<OJQJ^J=8 v (  $dha$gd<  & Fdhgd< on, University of Zagreb. Plesli, D. (1994). Influence of some basketball elements on basketball final score. (Graduated thesis) Faculty of Physical Education, University of Zagreb. Trnini, S. (1975) Correlation analysis between the frequency of the defensive and offensive rebounds and the final result in basketball game. (Graduated thesis), Faculty of Physical Education, University of Zagreb. Trnini, S., N. Viski-`talec, J. `talec, D. Dizdar I }. Birki (1995). Latent structure of standard indicators of situation-related efficiency in basketball game. Kineziology, 27 (1): 27-37. Trnini, S., D. Milanovi, M. Blaakovi, }. Birki I D. Dizdar (1995). Influence of defensive and offensive rebounds on the final score in basketball game. Kineziology, 27 :`>\XprгЛh< hRh< hLZ2h<OJQJ^JmHsH hRh<OJQJ^JmHsHhZ5OJQJ^JUhRh<OJQJ^Jh<6OJQJ^JhRh<6OJQJ^Jh<OJQJ^J(2): 44-49. Trnini, S. (1996). Analysis and teaching of the game of basketball. Pula: Vikta. Vuleta D., Milanovi, D., Serti, H. (1999). Latent structure of the spatial, phasic, positional and movement characteristics of the handball game. Kineziology, 31 (1): 35  50. Vuleta, D., Milanovi, D. I Serti, H. (2003). Relations between variables of shooting for a goal and outcomes of the 2000 Men s European handball Championship matches. Kineziology, 35 (2): 168-183 ,1h. 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