For more than two decades, researchers have been trying to explain the source of the processing cost of scalar implicature (SI). Although the computation of some SIs is associated with longer processing time (known as the delay effect), other SIs are processed cost-free. In this study, we investigated how individual differences in the rate of SI derivation modulate the delay effect across different scales. We reanalyzed four datasets from two SI verification task studies, which examined various scales. In these experiments, participants judged SI-triggering sentences as either true (literal reading) or false (SI reading). We fit a computational model to quantify the by-subject probability of computing SIs. Across datasets, we found that subjects who prefer the literal reading of the SI-triggering sentence were faster to respond true than false. However, the reading preferences modulate the verification speed differently for different scales. This suggests that the source of the delay effect might vary between scales.