Abstract
Deploying LLMs raises two coupled challenges: (1) monitoring---estimating where a model underperforms as traffic drifts---and (2) prioritization---deciding where to intervene to close the largest performance gaps. We explore whether top- logprobs---cheap, consumer-accessible signals from standard inference---can serve as reliable proxies for domain-level quality of both verifiable and subjective tasks. We summarize each response's output-entropy profile into a compact vector, predict instance quality with a lightweight classifier, and then average predictions to yield a domain-level estimate. On verifiable tasks (ten STEM benchmarks, nine LLMs, exhaustive train/test compositions), estimates often track held-out accuracy, with several models showing near monotonic calibration. On subjective tasks, trained on LLM-judge scores over categorized real user conversations, several models track the judge's slice scores remarkably closely ( up to ) and detect the worst-performing categories near-perfectly, though this is not the case for all LLMs. Where coupling holds, results suggest that entropy signals can support monitoring at a fraction of the cost of judge-based evaluation.