Most statistical assessments of the death penalty conclude that it does not deter homicide. Scholars, however, disagree about the validity of such research and its ability to weed out the effects of extraneous factors. A central problem in this field is the lack of meaningful measures of accuracy as exist for other statistical methods like opinion polling. A mathematical model of homicide levels is a formula for estimating a locality's homicide level on the basis of its prevailing demographic, social, and economic conditions and its patterns of punishment for homicide. For the purposes of testing the model, the author first estimates the magnitude of the random components of recorded annual homicide levels and then uses this estimate to develop a reliability statistic to help measure the level of systematic error in a particular model of homicide patterns. This method is applied to three studies on the deterrent effects of capital punishment by Passell, Ehrlich, and Forst. Calculation of their level of systematic error reveal an incidence of error in all three that is far too large to allow confidence in their estimates of the deterrent effect of the death penalty. Mathematical formulas and five references are included. The appendixes contain additional information on the paper's metholology