A Markov chain model of elite water polo competition - Pfeiffer, M.; Hohmann, A.; Siegel, A.; Boehnlein, S. (Biomechanics and Medicine in Swimming XI, 2010)
INTRODUCTION: In performance analysis in game sports, it is important to respect the the interactive process between the two teams or players. So, in game analysis problems mostly occur in adequate modelling of the competition. The concept of match-play analysis through mathematical simulation by means of the Markov-chain model was established in several sports games (Lames, 1991; McGarry & Franks, 1994), and in this study used to analyse the performances of the German and Serbian Water Polo team at the World League Final 2007 in Berlin. METHODS: The starting point of our state-transition-model was the possession of the ball. The offensive play was modelled on the basis of offensive attempts, which were characterized by 28 different states. The states represent the different player positions in man-even (6-6) and man-up offense (6-5) as well as specific game situations (e.g. goal). The transitions from one state of the match to another represent the tactical behaviour of the teams and can be quantified in a transition matrix of the states with the transition probabilities. We formalized this matrix by means of a finite Markov-chain (stochastic modelling) to determine the performance relevance of each tactical behavior by mathematical simulation. In this study, 11 games with participation of the two teams were analyzed. RESULTS: The objectivity was determined with two observers in three games. The Cohens-Kappa values of 0.80 to 0.86 can be classified as excellent (Robson, 2002). For both teams the tactical transitions "Win of ball-Counter attack", "Back player-Man-up (6-5)" und "Back player-Center forward" showed the highest performance relevance. Significant differences between the two teams could only be found for the tactical pattern "Flanker player-Driving in". DISCUSSION: Our results confirm the possibility to model a water polo match by means of a Markov-chains. The simulative calculation of the performance relevance of tactical behavior underlines the importance of the fast break and of intense activities of the back players.