Biomechanics and Medicine in Swimming XI

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tack and double-center attack) and one man-up offense (6-5) as well as specific game situations (turn over, driving-in, and goal/penalty) (Table 1). The final state of “goal/penalty” is defined as the criterion of performance, necessary for judging the performance relevance of all other tactical behaviour. The typical tactical behaviour of the teams is expressed in the transition between two subsequent states (“tactical patterns”). Table 1. State model used for game analysis in water polo (for both teams) No. State Abbrev. Turn over TO Counter-attack CA One-center-attack OCA Back-position in OCA BPOCA Flanker-position OCA FPOCA Center-position in OCA CPOCA Driving-in DI Double-center-attack DCA Back-position in double-center attack BPDCA Flanker-position in double-center attack FPDCA Center-position in double-center attack CPDCA Man-up-Attack MUA Back-position man-up (BPMUA) BPMUA Flanker-position man-up (FPMUA) FPMUA Center-position man-up (CPMUA) CPMUA Goal/penalty G Stochastic model: The transition probabilities between two states describe the water polo match as a process that can be understood as a first order Markov chain, when the following two properties are given: (1) the probability for the next state depends only on the current state (Markov-property), and (2) the transition probability from one state to another is independent of their chronological position in the match process (chain-property). The transition probabilities between the states can be transformed into a two dimensional transition matrix. Each element of this matrix has the property p ij (n) ≥ 0 and the line sum is equal to 1. In the theory of a Markov chain, several kinds of states are distinguished. Absorbing states are important, because the process ends in these states, and a new process starts. For our purpose of performance diagnosis, the state “goal/ penalty” is defined as the absorbing state. The transition probability to the absorbing state is called the goal probability (GP). The GP can be calculated for both opponents by multiplication of a start vector (distribution of the states) with the observed (empirical) transition matrix. Inso-doing, the probabilities for the absorbing condition of “goal/penalty” are attained for both teams. Simulation to quantify the performance relevance of tactical behaviour patterns: Based on the empirical transition matrix of a water polo match, it is also possible to calculate the GP on the basis of a numerically manipulated (simulated) transition matrix. In order to determine the performance relevance of a tactical behaviour pattern of interest, the empirical transition probability between these two states was manipulated by a certain percentage in each observed match. After this the goal probability was once more calculated and defined the performance relevance (δGP) of a tactical behaviour pattern as the difference between the goal probability (GP) as calculated by the original (observed) transition-matrix and the goal probability as calculated by the manipulated transition-matrix. With reference to this simulation method there are two special problems: 1. to find the adequate quantitative size of the manipulation of the investigated transition probability, and 2. to establish an algorithm that determines how the other (not manipulated) transition probabilities have to be changed, so that the stochastic character of the matrix chaPter4.trainingandPerformance (sum of each row equals 1.00) is preserved. Regarding (1): according to Lames (1991), the function to deflect the transition probabilities is: δTP (TP) = C+B∙4∙TP (1-TP). TP is the transition probability and δTP the change of the transition probability of the investigated tactical pattern. The constant values applied in the present study were C = 1 and B = 5, which were also determined by Lames (1991) and thoroughly tested by Pfeiffer (2004, 2005). Regarding (2): each compensation procedure was based on a proportional compensation of all other transition probabilities, as no a priori information existed to justify any targeted compensation: δTP yi = -(T yi /(1-TP)) ∙δTP x . Figure 1 demonstrates how the performance relevance (δGP) of a tactical behaviour is calculated by a simulation on the basis of a standardized manipulation of the transition probability. Figure 1. Part of a transition matrix of a water polo match with an example of the simulative calculation of the performance relevance (δGP) of the tactical pattern “back position in position attack” to “driving-in” (BPPA 1 – DI 1) of team 1. The increase of the transition probability between the states “back position in position attack” to “driving-in” of team 1 by 2.48 % elevates the GP by 0.6 % (Figure 1). This value documents the performance relevance (δGP) of the manipulated tactical behaviour pattern. Thus, the performance relevance (δGP) of any tactical pattern is quantified by the scale in which the goal probability (GP) changes after the transition matrix has been modified in terms of the tactical behaviour in question. results In the present study, eleven matches of the World League Final 2007 in Berlin were analysed in regard to eleven tactical patterns (transition probabilities) (Table 2). Table 2. Analysed tactical patterns (in each case for both teams) No. Tactical pattern (transition) Abbrev. Turn over – Counter-attack TO-CA Turn over – One-center-attack TO-OCA Back-position – Center-position (both “One-center-attack”) BPOCA-CPOCA Back-position (One-center-attack) – Driving-in BPOCA-DI Back-position (One-center-attack) – Double-center attack BPOCA-DCA Back-position (One-center-attack) – Man-up-attack BPOCA-MUA Flanker-position – Center-position (both “One-centerattack”) FPOCA-CPOCA Flanker-position (One-center-attack) – Driving-in FPOCA-DI Flanker-position (One-center-attack) – Double-centerattack FPOCA-DCA Flanker-position (One-center-attack) – Man-up-attack FPOCA-MUA Center-position (One-center-attack) – Man-up-attack CPOCA-MUA The differences between the German and Serbian teams were analyzed by t-test (independent two-sample). In all tests, p < 0.05 was accepted as significant. 279
BiomechanicsandmedicineinswimmingXi Objectivity of the game observation model: The instrumental consistency of the observation model (objectivity) was examined by the inter-rater consistency (Cohen’s Kappa) of two observers. Three different games (SRB-ROM, SRB-GER, SRB-HUN) were selected for this purpose. The Cohen’s Kappa value of the observation model varied between .80 < κ < .86, which represents an “excellent” classification (Robson, 2002). Performance relevance of tactical patterns: Due to the small number of games investigated and to the high variance in the empirical match data of the observed teams in the Water Polo World League Final 2007, no significant differences between the performance relevance of the different tactical behaviour patterns of Germany and Serbia could be found. Nevertheless, the differences reported below at least exhibited a clear tendency (p < 0.10). The descriptive results showed that the performance relevance of the “Turn over to counter attack” (TO-CA) in general was the most worthwhile tactical pattern in the observed international water polo matches. Especially in the German team this specific transition was much more important than in the Serbian and all other teams (M GER = 1.39+0.81 [n = 3] vs. M SRB = 0.45+0.99 [n = 6] resp. M ALL = 0.43+0.1.41; [n = 15]). Furthermore, in the winning teams the transition from winning the ball into swimming a fast break was much more effective than for the losers (M WIN = 0.70+1.18 [n = 10] vs. M LOS = 0.33+1.70 [n = 7]). In addition to that, the winning teams also showed a higher effectiveness when turning over the win of the ball into a more static position attack. This can be seen by the transition from “Turn over to One-center-attack” (TO-OCA), which was only positive in the winners of the observed games (M WIN = 0.32+0.1.08 [n = 12] vs. M LOS = –0.34+1.21 [n = 12]). Concerning the position attack itself, the performance relevance of the tactical pattern to pass the ball from the “Back-position in the One-center position attack to the Center-position” (BPOCA-CPOCA) is positive in all teams, but by far highest in the German team (M GER = 1.34+1.07 [n = 6] vs M SRB = 0.27+1.34 [n = 6]). On the other hand, for the winners this kind of center play was much less relevant than for the defeated teams (M WIN = 0.60+1.14 [n = 12] vs. M LOS = 1.70+3.04 [n = 12]). Also important in water polo is the tactical manoeuvre from the position attack to the man-up situation, when an opposition player has been excluded from a period of play. So, the transition from ball possession in the “Back-position in the One-center position attack to the man-up attack” (BPOCA-MUA) was also positive in all investigated teams, and again highest in the German team (M GER = 1.39+1.58 [n = 6] vs M SRB = 0.49+1.05 [n = 6]). But as already seen above, this kind of advantage was less relevant for the winners than for the losers (M WIN = 0.55+0.74 [n = 12] vs. M LOS = 1.86+2.71 [n = 12]). The reason for the latter two, somewhat surprising findings might result from the fact that the winning teams seem to put more emphasis on playing fast polo, i.e. on counter attacks and also on the pattern of “driving-in” into the area in front of goal. So, the transition from holding the ball in the “back-position to driving-in” (BPOCA-DI) is much more effective in the winning teams than in the losers, where it even had a negative effect on the total score (M WIN = 0.20+0.69 [n = 12] vs. M LOS = –0.22+1.06 [n = 12]). dIscussIon In this study, performance diagnosis in water polo by stochastic path simulation was used for the first time. In comparison with traditional notational analysis methods in water polo (Bratusa, Matkovic & Dopsaj, 2003; Dopsaj & Matkovic, 1999; Hohmann, 1992; Platanou & Nikopopoulos, 2003), the main advantage of this approach is that it delivers not only a statistical description of the analyzed tactical behaviour, but is also capable of: (a) analyzing the performance relevance of the various tactical behaviour patterns, and (b) providing a prognosis on the probable effects of certain modifications to the tactical behaviour of interest, based on a mathematical simulation of the interactive game process. Performance diagnosis through stochastic path simulation by means of the Markovchain model, hence, is a worthwhile performance diagnostic procedure in water polo, allowing the calculation of optimal tactical behaviour. 280 reFerences Bratusa, Z. F., Matkovic, I. Z. & Dopsaj, M. J. (2003). Model characteristics of water polo players movements in the vertical position during competition. In J. C. Chatard (Ed.). Biomechanics and Medicine in Swimming IX (pp. 481-486). Saint-Étienne: l´Université de Saint-Étienne. Dopsaj, M. & Matkovic, I. Z. (1999). The structure of technical and tactical activities of water polo players in the first Yugoslav league during the game. In K. L. Keskinen, P. V. Komi, & A. P. Hollander (Eds.). Biomechanics and Medicine in Swimming VIII (pp. 435-438). Jyväskylä: Gummerus Printing House. Hirotsu, N., Miyaji, C., Ezake, N., Shigenaga, T. & Taguchi, A. (2004). A model for finding optimal tactics in volleyball using Markov decision processes. The Engineering of Sports, 5(2), 447-453. Hohmann, A. (1992). Analysis of delayed training effects in the preparation of the West-German water polo team for the Olympic games 1988. In D. MacLaren, T. Reilly & A. Lees (Eds.). Swimming Science VI (pp. 213-217). London: E & F Spon. Hohmann, A., Zhang, H. & Koth, A. (2004). Performance diagnosis through mathematical simulation in table tennis in left and right handed shakehand and penholder players. In A. Lees, J. F. Kahn, A. Maynard (Eds.). Science and Racket Sports III (pp. 220-226). London: Routledge. Hughes, M. (2008). An Overview of the Development of Notational Analysis. In M. Hughes & M. Franks (Eds.). The essentials of performance analysis - an Introduction (pp. 51-84). Chippenham: Routledge. Hughes, M. & Bartlett, R. M. (2008). What is Performance Analysis? In M. Hughes & M. Franks (Eds.). The essentials of performance analysis - an Introduction (pp. 8-20). Chippenham: Routledge. Hughes, M. & Franks, I. (2004). Notational analysis of sport. New York: Routledge. Hughes, M. & Bartlett, R. M. (2002). The use of performance indicators in performance analysis. Journal of Sports Sciences, 20(10), 739-754. Lames, M. (1991). Leistungsdiagnostik durch Computersimulation [Performance diagnosis by computer simulation]. Frankfurt am Main: Harri Deutsch. Lames, M. & McGarry, T. (2007). On the search for reliable performance indicators in game sports. International Journal of Performance Analysis in Sport, 5(1), 62-79. McGarry, T. & Franks, I. M. (1994). A stochastic approach to predicting competition squash match-play. Journal of Sports Sciences, 12(6), 573-584. McGarry, T. & Perl, J. (2004). Models of sports contests - Markov processes, dynamical systems and neural networks. In M. Hughes & M. Franks (Eds.). Notational analysis of sport (2 ed.) (pp. 227-242). New York: Routledge. Pfeiffer, M. (2004). Computer Simulation to Evaluate the Performance Relevance of Tactical Behaviour in Handball. In F. Seifritz, M. Mester, J. Perl, O. Spaniol, & J. Wiemeyer (Eds.). 1st International Working Conference IT and Sport & 5th Conference dvs-Section Computer Science in Sport (pp. 56-59). Cologne: German Sport University. Pfeiffer, M. (2005). Leistungsdiagnostik im Nachwuchstraining der Sportspiele. [Performance diagnosis in the game sport training of young athletes]. Köln: Sport & Buch Strauß. Pfeiffer, M. & Hohmann, A. (2008). Performance Diagnostics of tactical behaviour at the FIFA World Cup 2006. In International Convention on Science, Education and Medicine in Sport (vol. 1) (p.175). Guangzhou: People’s Sports Publishing House. Platanou, T. & Nikopopoulos, G. (2003). Assessment of sport orientation in the field of water polo. In J. C. Chatard (Ed.). Biomechanics and Medicine in Swimming IX (pp. 493-498). Saint-Étienne: l´Université de Saint-Étienne. Robson, C. (2002). Real world research. Oxford: Blackwell Publishers. Zhang, H. (2003). Leistungsdiagnostik im Tischtennis [Performance diagnosis in table tennis]. Hamburg: Dr. Kovac.
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