Hidden Measurement Error in LLM Pipelines Distorts Annotation, Evaluation, and Benchmarking

arXiv:2604.11581v4 Announce Type: replace Abstract: LLM evaluations drive which models get deployed, which safety standards get adopted, and which research conclusions get published. Yet standard confidence intervals ignore variability from prompt phrasing, model temperature, and judge model choice, producing under-coverage that worsens with more data. The omitted variance can shift results enough to reverse conclusions \citep{baumann2025llmhacking, huang2026dropping} and opens benchmarks to exploitation \citep{singh2025leaderboard}. This paper decomposes LLM pipeline uncertainty into its sources, distinguishes variance that shrinks with more data from sensitivity to researcher design choices, and uses design-study projections to reduce total evaluation error (TEE). Across the demonstrations, naive standard errors are 40 - 60\% smaller than the TEE-corrected SE. Using Chatbot Arena data, we show naive 95\% CI coverage drops as $n$ grows while TEE-corrected coverage holds at 95\%. We show further that a small pilot recovers honest CIs and projects which design changes most improve precision. Acting on those projections halves MMLU estimation error against the answer key at equivalent cost, and on a human-validated propaganda audit the TEE-recommended pipeline outperforms 73\% of single-configuration alternatives against the 9-rater human baseline.