In our elaboration we have assumed the cyclical nature of actions during the game and the existence of the factors which determine the result of an action (points scored by the host team - P(0), and points scored by the visitors P(1)). The cycles were analysed with the use of the marked alternating renewal process and the Markovian renewal process. We sought dependencies statistically significant (correlation) between the current action of the visiting team (host team) and the next action of the visiting (host) team taking into consideration the following: points scored by the host team - P(0), points scored by the visitors - P(1), time of ball possession by the host T(0), time of ball possession by the visitors - T(1). The separated cycles were defined in the two ways: by means of the change in the ball possession and the accurate (scored) throw of the ball to the basket. In the description of a match we assume a repetitive character of particular actions during the game and the existence of the factors which determine the result of the game, as opposed to the total randomness. The match analysed in time was treated as a stream of particular events. The events in the stream of events divide the match into cycles. What we took into consideration was variable (alternating) process of the ball possession and the process of cycles between the well-aimed (scored) throws to the basket. The separated cycles were characterised by means of their duration and the number of the scored points - the so called mark of the cycle. The aim, however, was to define the cycles, which would reflect the final result of the match. The research material constituted 3 matches of professional male teams, as part of Suproliga and The Cup of Saporta (tab. 1), recorded by means of the video technique, in the season 2000/2001, preliminary elaborated by Trus.
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