Can a lower Brier score prove better calibration?

Question: Classifier M1 has a lower Brier score than classifier M2 on the same test set. Which conclusion is the most defensible? A) M1 has better overall probabilistic accuracy, but the result alone does not prove that M1 is better calibrated B) M1 must have a smaller expected calibration error under every possible binning scheme C) M1 must have a better ROC-AUC because the Brier score is rank-based D) M1 is necessarily both more calibrated and more discriminative than M2 Correct: A Explanation: The Brier score is a strictly proper scoring rule measuring squared probabilistic error. Its value reflects more than calibration alone, including the model's ability to separate outcomes. A lower Brier score therefore does not isolate calibration quality. Topic: advanced ML / probabilistic classification / Brier score