The reliability paradox has commonly been described as the observation that cognitive tasks such as the Stroop task produce robust group-level effects but unreliable individual differences. There has been much attention on increasing the reliability, either by increasing the number of trials or by changing the cognitive measure (i.e., accuracy effects rather than response time effects). Both of these approaches are based on the assumption that individual performance in these tasks is all over the place, just too noisy to learn about their latent cognitive abilities. This assumption, however, needs to be checked. To do so, I investigated individual performance over the course of one experiment, assessing how variable cognitive effects are within and across individuals. The results show surprising stability when enough trials are considered, even across experimental sessions. I argue that we therefore need to rethink the reliability paradox as not being a paradox at all: Cognitive tasks produce replicable group-level effects because these effects are consistent within and between individuals. This consistency of individual effects leads to consistently small individual variability within experiments and therefore small correlations of individual performance across experiments. Ultimately, we are not dealing with a reliability paradox but with a reliability corollary.