Observers often judge agents who miss a desired outcome by a small, compared to a large, margin to be less happy. This near-miss effect has typically been examined in situations where the agents have control over outcomes (e.g., missing a flight). Here, we extend this work in three ways. First, we show that near-miss effects play into observers’ intuitive theories of emotion even for randomly-determined outcomes over which agents demonstrably have no control. Second, we find data consistent with a hypothesis in which—even in randomly determined cases—near-miss effects reflect an illusion of control over those events. Finally, we integrate near-miss effects into a broader model of affective cognition, and quantify the psychological cost of a missing a desired outcome by relatively little distance, relative to winning or losing that outcome.