Although a large body of research investigates what characterizes good leaders and how to best select them, internal promotions in organizations often yield underperforming leaders. The leadership literature provides several explanations for why “bad” leaders exist. However, all this work builds on the premise that the choice of an inefficient leader is a failure of the selection process. In this paper, we take a different stance and suggest that—in some cases organizations might select underperforming leaders because it is efficient do so. In essence, we argue that selecting a leader within a fixed group of individuals is similar to allocating any other limited resource. Leader selection has an opportunity cost because the leader is no longer available as a follower. We identify cases in which it is optimal not to select the most competent individual as leader. Finally, we propose to use tournament theory to efficiently select leaders and discuss how to set incentives within a group to identify competencies and to select the most appropriate leader accounting for the context in which the group operates.