Procedures which classify individuals into discrete categories are often evaluated by the fraction of individuals correctly classified. If the individual behavior is truly stochastic rather than deterministic, the expected fraction of correct classifications would be less than one, even when the procedure is based upon perfect estimates of every individual's probability of belonging to a category. For the binary case of two categories, the expected fraction which is correctly classified is between 50 and 100 percent. The exact value depends upon the mixing distribution of probabilities in the population.