[2511.22442] What Is the Optimal Ranking Score Between Precision and Recall? We Can Always Find It and It Is Rarely $F_1$

Computer Science > Performance arXiv:2511.22442 (cs) [Submitted on 27 Nov 2025 (v1), last revised 30 Mar 2026 (this version, v2)] Title:What Is the Optimal Ranking Score Between Precision and Recall? We Can Always Find It and It Is Rarely $F_1$ Authors:Sébastien Piérard, Adrien Deliège, Marc Van Droogenbroeck View a PDF of the paper titled What Is the Optimal Ranking Score Between Precision and Recall? We Can Always Find It and It Is Rarely $F_1$, by S\'ebastien Pi\'erard and 2 other authors View PDF HTML (experimental) Abstract:Ranking methods or models based on their performance is of prime importance but is tricky because performance is fundamentally multidimensional. In the case of classification, precision and recall are scores with probabilistic interpretations that are both important to consider and complementary. The rankings induced by these two scores are often in partial contradiction. In practice, therefore, it is extremely useful to establish a compromise between the two views to obtain a single, global ranking. Over the last fifty years or so, it has been proposed to take a weighted harmonic mean, known as the F-score, F-measure, or $F_\beta$. Generally speaking, by averaging basic scores, we obtain a score that is intermediate in terms of values. However, there is no guarantee that these scores lead to meaningful rankings and no guarantee that the rankings are good tradeoffs between these base scores. Given the ubiquity of $F_\beta$ scores in the literature,...