Standard tests designed to identify mutual funds with non-zero alphas are problematic, in that they do not adequatly account for the presence of lucky funds. Lucky funds have significant estimated alphas, while their true alphas are equal to zero. To address this issue, this paper quantifies the impact of luck with new measures built on the False Discovery Rate (FDR). These FDR measures provide a simple way to compute the proportion of funds with genuine positive or negative performance as well as their location in the cross-sectional alpha distribution. Using a large cross-section of U.S. domestic-equity funds, we find that about one fifth of the funds in the population truly yield negative alphas. These funds are dispersed in the left tail of the alpha distribution. We also find a small proportion of funds with truly positive performance, which are concentrated in the extreme right tail of the alpha distribution.