In a contest in which solvers with heterogeneous expertise exert effort to develop solutions, a recent paper [Terwiesch C, Xu Y (2008) Innovation contests, open innovation, and multiagent problem solving. Management Sci. 54(9):1529–1543] argues that as more solvers enter the contest, every solver will reduce effort due to a lower probability of winning the contest. This paper corrects mistakes in this theory, and shows that there exist high-expertise solvers who may raise their effort in response to increased competition. This is because more entrants raise the expected best performance among other solvers, creating positive incentives for solvers to exert higher effort to win the contest. Because of this positive effect, we find that a free-entry open contest is more likely to be optimal to a contest organizer than what Terwiesch and Xu (2008) and other prior literature asserted. The e-companion is available at https://doi.org/10.1287/mnsc.2017.2738 . This paper was accepted by Gad Allon, operations management.