In the selection of biometrics for use in a recognition system and in the subsequent design of the system, the predicted performance is a key consideration. The realizations of the biometric signatures or vectors of features extracted from the signatures can be modeled as realizations of random processes. These random processes and the resulting distributions on the measurements determine bounds on the performance, regardless of the implementation of the recognition system. Given the underlying random processes, two techniques are applied to determine performance bounds. First, large deviation analysis is applied to bound performance in (M+1)-ary hypothesis testing problems, where the number of hypotheses is fixed as a measure of the fidelity of the measurements increases. Second, the capacity of a recognition system as a function of the desired error rate is explored. The recognition system is directly analogous to a communication problem with random coding. The recognition reliability function then determines the error rate as a function of the exponential growth rate of the number of hypotheses. Gaussian and binary examples are considered in detail. Performance prediction in the binary example is compared with performance prediction results for iris recognition systems using Daugman's IrisCode.