Oracle Gaps in Reliability Coverage: Sampling Noise or Policy Specialization?

Policies trained from the same base model can appear to solve different problems. An oracle that chooses the best policy for each problem may therefore appear much stronger than any single policy. Selecting the largest estimated success rate also selects favorable sampling errors. We study this effect through reliability coverage, the fraction of problems whose success probability reaches a chosen threshold. Our first test redistributes stored correctness outcomes across policies within each problem. A second also preserves each policy's total successes, accounting for overall quality differences under a specified statistical model. For five training seeds of a seven-billion-parameter vision-language model, redistribution reproduces 0.096 of an estimated 0.113 oracle gap at threshold 0.10. Neither test finds significant evidence at this threshold. Small advantages remain unresolved. Mixtures, routers, voting, and weight averaging show no detectable improvement over their corresponding single-policy baselines. Training policies on different datasets shows little detectable specialization under light post-training, and no router gain. A stronger recipe does create it, both tests detect it, and a router gain appears only at the high thresholds where the specialists separate. In a control with predictable specialization, a router recovers about half the oracle gap. Coverage bounds explain why even a genuine oracle advantage need not yield a deployment gain. The tests assess apparent specialization from stored responses before investment in routing. Code: https://github.com/KurbanIntelligenceLab/oracle-gaps