In this paper we consider the volleyball under the Markovian assumption that the probability of winning a single rally is independent of the other rallies and constant during the game. Fixing two parameters which indicate the probabilities of winning a rally for the serving team, we derive the exact expression of the probability of winning a set and a match in the present rally point- and in the former sideout scoring systems. We observe that the present point system reduces the winning probability of the stronger team, adding interest/randomness to the game. Furthermore we study the mean duration of the games in both the scoring systems, obtaining, as well known in the practice, that this change reduced the (expected) length of the matches.
Markov Chain Volleyball
FERRANTE, MARCO;FONSECA, GIOVANNI
2013
Abstract
In this paper we consider the volleyball under the Markovian assumption that the probability of winning a single rally is independent of the other rallies and constant during the game. Fixing two parameters which indicate the probabilities of winning a rally for the serving team, we derive the exact expression of the probability of winning a set and a match in the present rally point- and in the former sideout scoring systems. We observe that the present point system reduces the winning probability of the stronger team, adding interest/randomness to the game. Furthermore we study the mean duration of the games in both the scoring systems, obtaining, as well known in the practice, that this change reduced the (expected) length of the matches.
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