Best-Case Retrieval Evaluation: Improving the Sensitivity of Reciprocal Rank with Lexicographic Precision

Across a variety of ranking tasks, researchers use reciprocal rank to measure the effectiveness for users interested in exactly one relevant item. Despite its widespread use, evidence suggests that reciprocal rank is brittle when discriminating between systems. This brittleness, in turn, is compounded in modern evaluation settings where current, high-precision systems may be difficult to distinguish. We address the lack of sensitivity of reciprocal rank by introducing and connecting it to the concept of best-case retrieval, an evaluation method focusing on assessing the quality of a ranking for the most satisfied possible user across possible recall requirements. This perspective allows us to generalize reciprocal rank and define a new preference-based evaluation we call lexicographic precision or lexiprecision. By mathematical construction, we ensure that lexiprecision preserves differences detected by reciprocal rank, while empirically improving sensitivity and robustness across a broad set of retrieval and recommendation tasks.