People calibrate future expectations to past performance when predicting transparently random events.

We report on five experiments studying people's (n > 12,000) responses to a prototypical random process: predicting the outcomes in a sequence of five fair coin tosses. "Success" rates in making predictions followed the binomial distribution, and randomly assigned participants to zero to five success experiences, capturing the entire distribution of possible performance outcomes without deception. We found that more successful predictions led to more optimistic expectations of future performance and an increased propensity for risk-taking behaviors, whereas more unsuccessful predictions led to more pessimistic expectations and risk-averse behavior, demonstrating the tendency to believe that there is a signal in performance predicting random sequences of events. Inference from performance was stronger for participants who changed their predictions more often, suggesting that it is more likely to emerge when participants detect a spurious correlation between their behavior and the experienced outcomes. The findings could not be explained by distorted beliefs about the nature of the outcome-generating process, poor knowledge of probability, or risk attitudes, and were unaffected by the presence of performance-related rewards.