Skewed Score: A statistical framework to assess autograders

Abstract: The evaluation of LLM outputs is increasingly performed by other LLMs, a setup commonly known as "LLM-as-a-judge", or autograders. While autograders offer a scalable alternative to human evaluation, they have shown mixed reliability and may exhibit systematic biases, depending on response type, scoring methodology, domain specificity, and other factors. In this paper we propose a statistical framework based on Bayesian generalised linear models (GLMs) that enables researchers to simultaneously assess their autograders while also addressing their primary research questions (e.g., LLM evaluation). Our approach models evaluation outcomes (e.g., scores or pairwise preferences) as a function of properties of the grader (e.g., human vs. autograder) and the evaluated item (e.g., response length or the LLM that generated it), allowing for explicit quantification of scoring differences and potential biases within a unified framework. In addition, our method can be used to augment traditional reliability metrics such as inter-rater agreement, by providing uncertainty estimates and clarifying the source of disagreement. Overall, this approach contributes to more robust and interpretable use of autograders in LLM evaluation, enabling both performance analysis and bias detection.