We set up a game theoretical model to analyze the optimal attacking intensity of sports teams during a game. We suppose that two teams can dynamically choose among more or less offensive actions and that the scoring probability of each team depends on both teams' actions. We assume a zero sum setting and characterize a Nash equilibrium in terms of the unique solution of an Isaacs equation. We present results from numerical experiments showing that towards the end of game it is optimal for the loosing team to start playing more offensively and for the winning team to play more defensively. This is even the case if the effects of the action changes cancel out so that the scoring intensities remain the same.