Motivated by the need to predict the future biometric performance of the U.S. Visitor and Immigrant Status Indicator Technology program as it increases the size of its watchlist database, we use extreme-value theory (which is an asymptotic theory for the maximum of a large number of independent and identically distributed random variables) to analyze biometric performance as the gallery size gets very large. Due to the lack of published data for open-set fingerprint systems (where some users of the system are not on the watchlist), we assess the accuracy of our approach using the rank-one identification probability for closed-set fingerprint systems (where all users are on the watchlist). Consistent with earlier empirical observations, we find that the relationship between the rank-one identification probability and gallery size is log-linear to first-order and has a quadratic correction term, at least under our specific distributional assumptions. We also find that the probabilistic biometric model provides a good fit to empirical fingerprint data only when the genuine and impostor similarity scores are allowed to depend on the quality of the fingerprint images, which leads to genuine and impostor scores that are mixtures of distributions. Finally, we use the extreme-value approach to derive the receiver operating characteristic curve for open-set systems.