Biomechanics and Medicine in Swimming XI
Biomechanics and Medicine in Swimming XI
Biomechanics and Medicine in Swimming XI
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278<br />
A Markov Cha<strong>in</strong> Model of Elite Water Polo<br />
Competition<br />
Pfeiffer, M., hohmann, A., siegel, A., Böhnle<strong>in</strong>, s.<br />
Institute of Sport Science, University of Bayreuth, Bayreuth, Germany<br />
When it comes to water polo, performance diagnostics offers many<br />
different methods to analyze a game. In this context, problems mostly<br />
occur <strong>in</strong> adequately modell<strong>in</strong>g the game, <strong>in</strong> part because the various<br />
approaches lack scope for uniform performance criteria. In this study<br />
the concept of match-play analysis through mathematical simulation by<br />
means of the Markov-cha<strong>in</strong> model was applied to water polo <strong>and</strong> used<br />
to analyse the performance relevance of tactical behaviour patterns at<br />
the World League F<strong>in</strong>al 2007 (Berl<strong>in</strong>) with focus on the German <strong>and</strong><br />
Serbian teams. The results suggest that <strong>in</strong> <strong>in</strong>ternational-level water polo,<br />
the performance relevance of “Turn over to counter attack” <strong>and</strong> “Turn over<br />
to One-center-attack” were the most worthwhile tactical behaviour<br />
patterns. No significant differences between Germany <strong>and</strong> Serbia<br />
could be found.<br />
Key words: game analysis, water polo, tactical behaviour, simulation,<br />
Markov cha<strong>in</strong><br />
IntroductIon<br />
From a performance diagnostic po<strong>in</strong>t of view, the key task of notational<br />
analysis is to analyze the game structure <strong>and</strong> f<strong>in</strong>d determ<strong>in</strong><strong>in</strong>g factors,<br />
<strong>in</strong> this case tactics, of performance. A look at the literature shows that<br />
a large number of methods have been developed – based on rapid technological<br />
developments <strong>in</strong> the area of computers, video etc. – to analyse<br />
the structure of game sports by game observation, <strong>in</strong> order to identify<br />
performance <strong>in</strong>dicators (Hughes & Bartlett, 2002). A comprehensive<br />
review of the evolution of notational analysis <strong>in</strong> sports games is given<br />
by Hughes <strong>and</strong> Franks (2004), Hughes (2008) <strong>and</strong> Hughes <strong>and</strong> Bartlett<br />
(2008). Most of these methods use structure-oriented observation models,<br />
which enable the researcher to register isolated elementary actions<br />
<strong>in</strong> a match, but do not allow for the obta<strong>in</strong><strong>in</strong>g of data on the <strong>in</strong>teraction<br />
process itself.<br />
Consider<strong>in</strong>g a sports game as a dynamic system or an <strong>in</strong>teractionprocess,<br />
different stochastic models have been developed. The models of<br />
the f<strong>in</strong>ite Markov cha<strong>in</strong> were successfully applied to describe <strong>and</strong> predict<br />
play<strong>in</strong>g profiles or patterns (McGarry & Franks, 1994; McGarry & Perl,<br />
2004), <strong>and</strong> to determ<strong>in</strong>e the performance relevance of tactical behaviour<br />
(Hirotsu, Miyaji, Ezake, Shigenaga & Taguchi, 2004; Hohmann, Zhang<br />
& Koth, 2004; Lames, 1991; Zhang, 2003). In the game analysis approach<br />
of Lames (Lames, 1991; Lames & McGarry, 2007), comparable<br />
quantitative values for the performance relevance of selected tactical<br />
patterns are determ<strong>in</strong>ed by the method of simulation. The concept of<br />
performance analysis through mathematical simulation by means of the<br />
Markov cha<strong>in</strong> model was first established <strong>in</strong> the area of return games<br />
<strong>and</strong> successfully transferred to <strong>in</strong>vasion games (e.g. h<strong>and</strong>ball <strong>and</strong> soccer;<br />
Pfeiffer, 2004; Pfeiffer, 2005; Pfeiffer & Hohmann, 2008). In this study,<br />
the same approach was applied to water polo to analyse the relevance of<br />
specific tactical behaviour to performance <strong>in</strong> general <strong>and</strong> with focus on<br />
the German <strong>and</strong> Serbian Water Polo teams at the World League F<strong>in</strong>al<br />
2007 <strong>in</strong> Berl<strong>in</strong>.<br />
Methods<br />
Observation model: The water polo match is described as a system that<br />
gradually moves through different states. The start<strong>in</strong>g po<strong>in</strong>t of our observation<br />
model was the possession of the ball (state “Turn over”). The<br />
offensive play was modelled on the basis of all offensive attempts, which<br />
were characterized by 16 different states of the game. These states represent<br />
different player positions <strong>in</strong> even-man offense (6-6; position at-