Can the existence of positive productivity spillovers between co-workers be explained by the presence of complementarities in a firm’s production function? A simple theory is presented, which demonstrates that this is possible, but only when workers’ pay is at least in part determined by the level of team output. Furthermore, negative spillovers may arise when workers can change the overall probability of team success unilaterally. Play-by-play data from major league baseball are used to test whether such spillovers exist between hitters over the course of a game, exploiting the fact that hitters perform their tasks sequentially. The results indicate that the overall spillovers between team-mates are positive but small. However, these cannot be explained by the incentives inherent in the team’s production function, which are found to have a negative effect on performance. Consistent with theory, the payment of individual performance bonuses or of lower base salaries is found to weaken the responsiveness of players to the pay-offs from their performance. Joint with Alex Bryson.