  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.
