Currently, the courts, primarily appellate courts, treat excessiveness in determining the death sentence in murder cases in an intuitive and unsystematic manner. Excessiveness as used here means the probability that a defendant would not receive a death sentence in a similar situation elsewhere. The legal support for such a claim may be the eighth amendment, and to date the courts have not specified the level of probability at which a defendant's death penalty becomes excessive. Applied social science was used to analyze excessiveness in capital sentences from a study of 239 murder convictions given by California juries from 1958 to 1966. Three quantitative measures of excessiveness were developed: the salient features measure and two main determinants measures. A discussion of six principles in the construction of the quantitative measures is given. It is recommended that quantitative arguments in an excessiveness review proceeding establish a threshold and perform a burden-shifting function. If the numbers in the aggregate suggest that the defendants receive a death sentence less than a certain percentage of the time (i.e., 50 percent), then the burden of proof on the excessiveness issue should shift to the State. Tabular data are included.