<p>Notation primer.</p>

Studies comparing emergency department (ED) patient prioritization rules often use single averages, which can hide important clinical trade-offs. This paper presents and demonstrates a three-part evaluation framework designed for clear, multi-faceted comparisons of prioritization policies. The framework includes: (1) statistics that account for extreme outcomes, (2) profiles showing how well time targets are met, and (3) analysis based on stakeholder priorities. We illustrate the framework in a unified discrete-event simulation of a 30-bed mixed-acuity ED to show how conclusions can change across tails, thresholds, and stakeholder preferences; the numerical results are for illustration only and are not recommendations for any specific hospital. Our main contribution is the method itself: a consistent and repeatable way to reveal different but complementary information, helping decision-makers match policies to their local goals, limits, and risk tolerance. Before implementation, future work should apply this framework using data from specific hospitals and gathering input from their stakeholders.