The likelihood ratio (LR) is an optimal approach for deciding which of two alternate hypotheses best describes a given situation. We adopted this formalism for predicting whether biopsy results of mammographic masses will be benign or malignant, aiming to reduce the number of biopsies performed on benign lesions. We compared the performance of this LR-based algorithm (LRb) to a case-based reasoning (CBR) classifier, which provides a solution to a new problem using past similiar cases. Each classifier used mammographers' BI-RADS descriptions of mammographic masses as input. The database consisted of 646 biopsy-proven mammography cases. Performance was evaluated using Receiver Operating Characteristic (ROC) analysis, Round Robin sampling, and bootstrap. The ROC areas (AUC) for the LRb and CBR were 0.91+/- 0.01 and 0.92 +/- 0.01, respectively. The partial ROC area index (0.90AUC) was the same for both classifiers, 0.59 +/- 0.05. At a sensitivity of 98%, the CBR would spare 204 (49%) of benign lesions from biopsy; the LRb would spare 209 (51%) benign lesions. The performance of the two classifiers was very similar, with no statistical differences in AUC or 0.90AUC. Although the CBR and LRb originate from different fields of study, their implementations differ only in the estimation of the probability density functions (PDFs) of the feature distributions. The CBR performs this estimation implicitly, while using various similarity metrics. On the other hand, the estimation of the PDFs is specified explicitly in the LRb implementation. This difference in the estimation of the PDFs results in the very small difference in performance, and at 98% sensitivity, both classifiers would spare about half of the benign mammographic masses from biopsy. The CBR and LRb are equivalent methods in implementation and performance.