We examine how the performance of teams and of the individuals within them varies with disparity in team member ability and with the reward structure in place. We carry out an experiment on a sample of 240 participants which first played a Counter‐Strike Game to determine their level of proficiency, then played in three‐person teams made up of a high, a medium and a low level performer. We observed the effect of both a competitive reward and of a cooperative one on team performance. The results indicate that when the disparity in ability is large, teams compensated using a competitive reward outperform those subject to a cooperative reward, but when the disparity in ability is small, reward structure has no influence on team performance. Hierarchical Linear Modelling (HLM) analysis confirms these findings at the individual level. Our study has implications for optimal team composition and the structuring of rewards. Copyright © 2016 John Wiley & Sons, Ltd.