People often need to predict the outcomes of future events. We investigate the influence of order on such forecasts. Six preregistered studies (N = 7,955) show that people are more likely to forecast improbable outcomes (e.g., that an underdog will win a game) for predictions they make later versus earlier within a sequence of multiple predictions. This effect generalizes across several contexts and persists when participants are able to revise their predictions as well as when they are incentivized to make correct predictions. We propose that this effect is driven by the assumption that improbable outcomes are bound to occur at some point within small sets of independent events (i.e., belief in the law of small numbers). Accordingly, we find that the effect is attenuated when the statistical independence of events is made salient to forecasters both through the nature of the predictions themselves (i.e., when the events are from distinct domains) and through directly informing them about statistical independence. These findings have notable practical implications, as policy makers and businesses have the ability to control the order in which people evaluate and predict future events.