Automatic speaker verification (ASV) vendors and corpus providers would both benefit from tools to reliably extrapolate performance metrics for large speaker populations without collecting new speakers. We address false alarm rate extrapolation under a worst-case model whereby an adversary identifies the closest impostor for a given target speaker from a large population. Our models are generative and allow sampling new speakers. The models are formulated in the ASV detection score space to facilitate analysis of arbitrary ASV systems.