People typically exhibit 'unrealistic optimism' (UO): they believe they have a lower chance of experiencing negative events and a higher chance of experiencing positive events than does the average person. UO has been found to be greater for negative than positive events. This 'valence effect' has been explained in terms of motivational processes. An alternative explanation is provided by the 'numerosity model', which views the valence effect simply as a by-product of a tendency for likelihood estimates pertaining to the average member of a group to increase with the size of the group. Predictions made by the numerosity model were tested in two studies. In each, UO for a single event was assessed. In Study 1 (n = 115 students), valence was manipulated by framing the event either negatively or positively, and participants estimated their own likelihood and that of the average student at their university. In Study 2 (n = 139 students), valence was again manipulated and participants again estimated their own likelihood; additionally, group size was manipulated by having participants estimate the likelihood of the average student in a small, medium-sized, or large group. In each study, the valence effect was found, but was due to an effect on estimates of own likelihood, not the average person's likelihood. In Study 2, valence did not interact with group size. The findings contradict the numerosity model, but are in accord with the motivational explanation. Implications for health education are discussed.