Replication efforts are becoming a standard tool for assessing the knowledge production of scientific disciplines. In psychology, economics, and preclinical cancer biology, replication rates near 50% have been advanced as evidence that these disciplines have failed to reliably produce knowledge, are rife with questionable research practices, and warrant reform. Concerns over failed replications are sometimes leveraged to erode faith in science, even claiming that the majority of published research is false. Many of these claims arise from mathematical models relying on highly restrictive assumptions; for example, the effect sizes are fixed across empirical contexts, and null hypotheses of exactly zero effect are assumed to have a high probability of being true. This is stands in contrast to broader discussions of replication, where effect sizes are often acknowledged to vary across empirical contexts. Here we derive a theoretical model of the publication process that accounts for variation in observed effect sizes. We find that such variation---even if small and idiosyncratic---can lead to low rates of replications even in the absence of QRPs, large-file drawers, or a literature rife with false conclusions. Building on this model, we highlight how variation in effect sizes impact the accuracy of effect sizes in the published literature. Finally, we show that the impacts of QRPs on the quality of published science differs substantially in the presence of varying effects. Overall, our model suggests that concerns over the reliability of scientific research---and implied remedies---require reconsideration in light of varying effects.