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Accurate video-based ball tracking in team sports is important for automated game analysis, and has proven very difficult because the ball is often occluded by the players. In this paper, we propose a novel approach to addressing this issue by formulating the tracking in terms of deciding which player, if any, is in possession of the ball at any given time. This is very different from standard approaches that first attempt to track the ball and only then to assign possession. We will show that our method substantially increases performance when applied to long basketball and soccer sequences.