Large language models (LLMs) are increasingly used as automated evaluators of AI systems, including in high-stakes applications. In this role, LLMs are used to generate judgments about the quality, appropriateness, or even safety of model outputs. This approach is motivated by practical constraints. Expert human ratings are costly and difficult to scale, whereas LLM ratings can be produced quickly at low cost. However, current approaches to deploying LLM evaluators are ad hoc, typically limited to reporting agreement metrics between human and LLM judges as a justification for substitution of human ratings, and lack a formal basis for study design. This paper (1) shifts the role of the LLM judge from substitutive to auxiliary, and (2) formulates the LLM-as-a-judge paradigm as one of augmenting human evaluation through a two-stage sampling design, where LLM evaluations are measured for all observations at the first stage and human ratings are partially observed for a subsample at the second stage. We propose to use a doubly robust estimator from the missing data literature, which takes advantage of the robustness property against the prediction model, since the missingness model is known by design. Using the asymptotic variance of this estimator, we propose how sample sizes of human and LLM ratings can be determined to achieve a targeted level of power. We also show that a study can be efficiently designed by allocating more human ratings for types of evaluations where the predictability of LLM ratings is not high. To the best of our knowledge, there is very little guidance on how much human oversight should be retained when validating benchmarks.