AbstractConsider the following situation: Each ofNdifferent combat units is presented with a number of requirements to satisfy, each requirement being classified into one ofKmutually exclusive categories. For each unit and each category, an estimate of the probability of that unit satisfying any requirement in that category is desired. The problem can be generally stated as that of estimatingNdifferentK‐dimensional vectors of probabilities based upon a corresponding set ofK‐dimensional vectors of sample proportions. An empirical Bayes model is formulated and applied to an example from the Marine Corps Combat Readiness Evaluation System (MCCRES). The EM algorithm provides a convenient method of estimating the prior parameters. The Bayes estimates are compared to the ordinary estimates, i.e., the sample proportions, by means of cross validation, and the Bayes estimates are shown to provide considerable improvem