We investigate how the selection process of a leader affects team performance with respect to social learning. We use a lab experiment in which an incentivized guessing task is repeated in a star network with the leader at the center. Leader selection is either based on competence, on self-confidence, or made at random. Teams with random leaders do not underperform compared to rather competent leaders, and they even outperform teams whose leader is selected based on self-confidence. The reason is that random leaders are better able to use the knowledge within the team, i.e., the wisdom of crowds. We can show that it is the declaration of the selection procedure which makes non-random leaders overly influential. The central position in the communication network already makes a leader highly influential. Knowing that the leader is not selected at random pushes team members to weigh the leader's opinion even more. We set up a horse race between several rational and naïve models of social learning to investigate the micro-level mechanisms. We find that overconfidence and conservatism contribute to the fact that too confident leaders mislead their team in finding good estimates. JEL-Code: D83, D85, C91.