The purpose of this paper is to show how the concept of performance diagnosis by mathematical simulation (Lames 1991; Perl, 1993) can be transferred to table tennis. According to that concept, the series of the interactive game actions (e.g. serve, return, offense, defense, and so on) can be described by means of a statistical transition matrix between the different states of action. After the series of the game actions is modeled by a Markov chain, the relevance of each game action for the final win or loss of the game can be simulated. Method: 152 matches of the top 50 male world class players were assessed. For the match analysis the sample was divided into four groups: shakehand vs. shakehand player, shakehand vs. penholder player, penholder vs. shakehand player, and penholder vs. penholder player. The game observations included the categories (1) game action, (2) stroke position, (3) stroke direction, and (4) stroke technique. The objectivity of the game observation system was determined by the common variance between the results of two independent observers, and Cohen`s kappa. Results: The common variance between the results of the two observers varied between 91.9 percent (robj =.96) for the stroke technique, and 97.4 percent (robj=.99) for the stroke position. Cohen`s kappa varied between .91 (technique) and .97 (stroke position). The correlation coefficients between the observed and the mathematically modeled point probabilities for the four game observation categories varied between r=.998 and r=.999 (p<0,001), which proved the validity of the Markov model. The simulation procedures showed that the neutral play actions have a particular relevance for the game success in elite table tennis. When the transition rates from the neutral game actions of one player to the defense action of the opponent were raised only by a small amount, then the probability of wining the game was highly increased compared to the other game actions (F=121,33; p<0.001). The relevance of stroke faults was nearly the same in the forehand and the backhand position. Only in the case when penholder competed with shakehand players, stroke faults showed a higher performance relevance in the forehand of the penholder players (T=-5.00; p<0.001). Among the different stroke directions, a strike from the long backhand side to the long backhand side of the opponent was most successful (F=89,56; p<0.001). Especially in shakehand players, the topspin showed the highest relevance of all techniques for the win of the match (F=8.07; p<0.001). Discussion: The results show that the performance diagnosis on the basis of the mathematical simulation of success probability by means of the Markov-chain model is a worthwhile procedure in table tennis. An advantage of the Markov procedure is that the model explicitly represents the interaction between both opponents when calculating the relevance of each game action.
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