We examine how the presence of connections in scientific committees affects researchers' decision to apply and their chances of success. We exploit evidence from Italian academia, where in order to be promoted to an associate or full professorship, researchers are firstly required to qualify in a national evaluation process. Prospective candidates are significantly less likely to apply when the committee includes, through luck of the draw, a colleague or a co-author. This pattern is driven mainly by researchers with a weak research profile. At the same time, information from 300,000 individual evaluation reports shows that applicants tend to receive more favorable evaluations from connected evaluators. Overall, this evidence is consistent with both the existence of a bias in favor of connected candidates and with academic connections reducing information asymmetries. Our study shows that connections are an important determinant of application decisions in academia and, more generally, it highlights the relevance of self-selection for empirical studies on discrimination.