Identifying the optimal set of individuals to first receive information (`seeds’) in a social network is a widely-studied question in many settings, such as the diffusion of information, microfinance programs, and new technologies. Numerous studies have proposed various network-centrality based heuristics to choose seeds in a way that is likely to boost diffusion. Here we show that, for some frequently studied diffusion processes, randomly seeding s plus x individuals can prompt a larger cascade than optimally targeting the best s individuals, for a small x. We prove our results for large classes of random networks, but also show that they hold in simulations over several real-world networks. This suggests that the returns to collecting and analyzing network information to identify the optimal seeds may not be economically significant. Given these findings, practitioners interested in communicating a message to a large number of people may wish to compare the cost of network-based targeting to that of slightly expanding initial outreach.