The preponderance-of-the-evidence standard usually is understood to mean that the plaintiff must show that the probability that the defendant is in fact liable exceeds 1/2. Several commentators and at least one court have suggested that in some situations it may be preferable to make each defendant pay plaintiff's damages discounted by the probability that the defendant in question is in fact liable. This article analyzes these and other decision rules from the standpoint of statistical decision theory. It argues that in most cases involving only one potential defendant, the conventional interpretation of the preponderance standard is appropriate, but it notes an important exception. The article also considers cases involving many defendants, only one of whom could have caused the injury to plaintiff. It argues that ordinarily the single defendant most likely to have been responsible should be liable for all the damages, even when the probability associated with this defendant is less than 1/2. At the same time, it identifies certain multiple-defendant cases in which the rule that weights each defendant's damages by the probability of that defendant's liability should apply.