We present new binomial models of open- and closed-set identification recognition performance, giving formulae for identification and false match rates as functions of database size, match rank and operating threshold. We compare these with previously published models and with results from face recognition trials on populations of size 4 104. We note verification to be a special case of open-set identification and relate area under the receiver operating characteristic to closed-set identification. We find the binomial model approximates performance at low false match rates but underestimates identification rates on closed sets. We implicate the binomial iid assumption, but show conditioning and score transformation methods that ameliorate this.