Resolving power: A general approach to compare the distinguishing ability of threshold-free evaluation metrics

Selecting an evaluation metric is fundamental to model development, but uncertainty remains about when certain metrics are preferable and why. This paper introduces the concept of resolving power to describe the ability of an evaluation metric to distinguish between binary classifiers of similar quality. This ability depends on two attributes: 1. The metric's response to improvements in classifier quality (its signal), and 2. The metric's sampling variability (its noise). The paper defines resolving power generically as a metric's sampling uncertainty scaled by its signal. The primary application of resolving power is to assess threshold-free evaluation metrics, such as the area under the receiver operating characteristic curve (AUROC) and the area under the precision-recall curve (AUPRC). A simulation study compares the AUROC and the AUPRC in a variety of contexts. It finds that the AUROC generally has greater resolving power, but that the AUPRC is better when searching among high-quality classifiers applied to low prevalence outcomes. The paper concludes by proposing an empirical method to estimate resolving power that can be applied to any dataset and any initial classification model.