This paper describes models for detecting individual and team ball possession in soccer based on position data. The types of ball possession are classified as Individual Ball Possession (IBC), Individual Ball Action (IBA), Individual Ball Control (IBC), Team Ball Possession (TBP), Team Ball Control (TBC) und Team Playmaking (TPM) according to different starting points and endpoints and the type of ball control involved. The machine learning approach used is able to determine how long the ball spends in the sphere of influence of a player based on the distance between the players and the ball together with their direction of motion, speed and the acceleration of the ball. The degree of ball control exhibited during this phase is classified based on the spatio-temporal configuration of the player controlling the ball, the ball itself and opposing players using a Bayesian network. The evaluation and application of this approach uses data from 60 matches in the German Bundesliga season of 2013/14, including 69,667 IBA intervals. The identification rate was F = .88 for IBA and F = .83 for IBP, and the classification rate for IBC was κ = .67. Match analysis showed the following mean values per match: TBP 56:04 ± 5:12 min, TPM 50:01 ± 7:05 min and TBC 17:49 ± 8:13 min. There were 836 ± 424 IBC intervals per match and their number was significantly reduced by -5.1% from the 1st to 2nd half. The analysis of ball possession at the player level indicates shortest accumulated IBC times for the central forwards (0:49 ± 0:43 min) and the longest for goalkeepers (1:38 ± 0:58 min), central defenders (1:38 ± 1:09 min) and central midfielders (1:27 ± 1:08 min). The results could improve performance analysis in soccer, help to detect match events automatically, and allow discernment of higher value tactical structures, which is based on individual ball possession.