LLM evaluations drive model deployment, safety standards, research conclusions, and future projections, for example, about AI's impact on the labor market. Yet the way we often estimate noise from autoraters (LLM-as-judge) ignores variability from factors like judge model choice and prompt phrasing, which means we're underestimating error in a way that worsens with more data. This unmeasured variance can affect results enough to reverse conclusions. And judge-pipelines that fail to average this variation are more vulnerable to "benchmark hacking". This paper introduces a framework we call "total evaluation error (TEE)," which decomposes LLM pipeline uncertainty and uses design-study projections to reduce total error. In our safety and ideology applications, naive standard errors are 53-70% smaller than the corrected SE under our TEE framework. Using Chatbot Arena data, we show naive 95% CI coverage drops as n grows, while TEE-corrected coverage holds at 95%, and TEE-guided pipelines restrict the potential range of benchmark gaming by roughly 43%. We show further that a small pilot allows for the estimation of proper CIs, with the added benefit of projecting which design changes most improve precision. Using those projections to allocate API calls cut MMLU estimation error roughly in half against the answer key at the same budget, and increased per-match agreement with human voters on Chatbot Arena by 7.9 percentage points.

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