When economic agents have access to both a continuous variable and a discrete signal based on that variable, theory suggests that the signal should have no bearing on behavior conditional on the variable itself.  Numerous empirical studies, many based on the regression discontinuity design, have contradicted this basic prediction.  We examine one such scenario, involving the educational accountability system implemented in North Carolina public schools until 2009.  We show that schools that barely missed eligibility for salary bonuses displayed a significant improvement in performance the following year, relative to schools that barely qualified.  While these results make sense from an intuitive perspective, rational models of behavior suggest that personnel in both sets of schools should have realized that the marginal returns to effort in the following year would be significant.  Results are instead consistent with a model of learning and imperfect information.  Importantly, seemingly irrational responses are least common in schools led by highly experienced principals.  Data suggest that inexperienced leaders and personnel under-appreciate the role of random chance in the determination of performance metrics.