The U.S. Supreme Court decision in Exxon Shipping Co. v. Baker is a landmark that establishes an upper bound ratio of punitive damages to compensatory damages of 1:1 for maritime cases, with potential implications for other types of cases as well. This article critiques the Court’s reliance on the median ratio of punitive to compensatory damages in samples of verdicts to set an upper bound for punitive damages awards. Our critique of the approach draws on the properties of statistical distributions and a new analysis of cases with punitive damages awards. The Court’s conclusion that a 1:1 ratio establishes a fair upper bound lacks a sound scientific basis.