The distribution of blockbuster punitive damages awards has fat tails similar to the distributions of losses from natural disasters. Extremely large awards occur more often and are more difficult to predict than if blockbuster awards were distributed normally. The size and predictability of awards are important factors in the U.S. Supreme Court’s decisions on punitive damages. This article examines the effect of the Court’s decision in State Farm v. Campbell on blockbuster punitive damages awards. State Farm shifts the fat tail of the distribution of blockbuster awards down (or “thins” the tail), which is consistent with a restraining effect on award size. State Farm reduces the size of blockbuster awards in general, but this reduction is most salient in the upper half of the distribution of awards. State Farm also has a negative influence on the probability of exceeding a single digit ratio between punitive and compensatory damages. This article also examines the largest awards and considers why defendants may not pay large punitive damages awards.