Balanced Accuracy: The Right Metric for Evaluating LLM Judges -- Explained through Youden's J statistic
This addresses the need for more trustworthy evaluation metrics in AI research, particularly for comparing LLMs, though it is incremental as it refines existing statistical methods rather than introducing a new paradigm.
The paper tackles the problem of selecting reliable classifiers (LLM or human judges) for evaluating large language models by showing that common metrics like Accuracy and F1 are flawed due to sensitivity to class imbalance, and proposes using Balanced Accuracy (equivalent to Youden's J statistic) to improve robustness in classifier selection.
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.