Balanced Accuracy: The Right Metric for Evaluating LLM Judges -- Explained through Youden's J statistic

TL;DR

This paper advocates for using Balanced Accuracy, based on Youden's J statistic, as a more reliable metric for evaluating large language models' judging capabilities, especially under class imbalance.

Contribution

It introduces Balanced Accuracy as a superior evaluation metric for LLM judges, grounded in Youden's J statistic, and demonstrates its advantages over traditional metrics.

Findings

Balanced Accuracy aligns with Youden's J statistic.

Using Balanced Accuracy improves classifier selection robustness.

Empirical results show better evaluation consistency.

Abstract

Rigorous evaluation of large language models (LLMs) relies on comparing models by the prevalence of desirable or undesirable behaviors, such as task pass rates or policy violations. These prevalence estimates are produced by a classifier, either an LLM-as-a-judge or human annotators, making the choice of classifier central to trustworthy evaluation. Common metrics used for this choice, such as Accuracy, Precision, and F1, are sensitive to class imbalance and to arbitrary choices of positive class, and can favor judges that distort prevalence estimates. We show that Youden's $J$ statistic is theoretically aligned with choosing the best judge to compare models, and that Balanced Accuracy is an equivalent linear transformation of $J$. Through both analytical arguments and empirical examples and simulations, we demonstrate how selecting judges using Balanced Accuracy leads to better, more robust classifier selection.