How to Correctly Report LLM-as-a-Judge Evaluations

Large language models (LLMs) are widely used as scalable evaluators of model responses in lieu of human annotators. However, imperfect sensitivity and specificity of LLM judgments induce bias in naive evaluation scores. We propose a simple plug-in framework that corrects this bias and constructs confidence intervals accounting for uncertainty from both the test dataset and a human-evaluated calibration dataset, enabling statistically sound and practical LLM-based evaluation. Building on this framework, we introduce an adaptive calibration strategy for constructing the calibration dataset to reduce uncertainty in the estimated score. Notably, we characterize the regimes in which LLM-based evaluation within our framework produces more reliable estimates than fully human evaluation. Moreover, our framework is more robust to distribution shift between the test and calibration datasets than existing approaches.