Design yield is a tail functional: why distributional metrics cannot rank generative designers

Generative models for molecules, binders, and materials are commonly evaluated with distributional metrics and then deployed by drawing $N$ candidates and retaining the best. We study the mismatch between these two procedures. Best-of-$N$ yield depends on a generator only through the upper tail of its pushforward score distribution. For scores bounded in $[0,B]$, yield is Lipschitz in total variation with sharp constant $BN$, so the guarantee weakens linearly with the deployment budget. For scores unbounded above, yield has no modulus of continuity: metrics built from finitely many bounded test functions, including validity, uniqueness, novelty, FID-like scores, MMD, and precision/recall, can remain arbitrarily close while yield differs arbitrarily. The two metrics that respond to this construction, $W_1$ and forward KL to the data, penalise the same tail mass that improves design yield. We give a family with rank correlation $-1$ between distributional quality and yield, and construct generators with identical forward divergence and identical moments to any prescribed order whose sharp yield gap is determined by a linear program. We also evaluate a peaks-over-threshold estimator of $\mathbb{E}[M_N]$ and measure its calibration. Across 27 trained samplers from three architectures and five objectives, with yield held out from every predictor, the standard distribution-learning score is negatively correlated with design yield on three objectives. Two tail statistics are positively correlated with yield on all five, with bootstrap intervals excluding zero. On $\log P$, the sampler closest to the data trails the highest-yield sampler by about a hundred bootstrap standard errors. These quantities can be computed from samples that a generative benchmark already draws.