Success tends to increase and failure tends to decrease the chances of future success. We show that this impact of past outcomes can change how diagnostic success or failure are regarding the competence of an individual or a firm. Succeeding under adverse circumstances is especially impressive when initial failure reduces the chances of success more for low-quality agents than for high-quality agents. Succeeding after initial failure (being a “successful underdog”) can also indicate higher expected quality than succeeding twice if initial success increases the chances of success of all agents to a high level. In different circumstances, the outcome after success can be especially informative about quality, implying that failing after an initial success (a “one-hit wonder”) indicates lower quality than failing twice does. We find effects consistent with our model in data on Canadian professional hockey players and on data from the Music Laboratory experiment: Initial failure combined with eventual success is associated with high quality. The results help to clarify when failure should be attributed to the person in charge or to the situation, when underdogs and individuals who overcome adversity are especially impressive and when a naïve “more is better” heuristic for evaluating performance can be misleading.