This paper presents a numerical study assessing the seismic performance of steel moment‐resisting frames (SMRFs) designed with ductile exposed column‐base plate (ECBP) connections employing yielding anchor rods. For their potential use as weak bases, the proposed ECBP detail is designed to accommodate plastic deformations in the anchors. The seismic performance of 2‐ and 4‐story archetype SMRFs with ECBPs is investigated to examine the effects of various base‐connection strengths on the frame collapse mechanisms and probabilities. To this aim, the ECBP connections of each frame are designed for a set of three strength levels, ranging from reduced seismic loads to capacity‐designed forces of the adjoining columns. These designs enable the base responses to vary from highly inelastic (i.e., weak‐base design) to elastic (i.e., strong‐base design) when subjected to earthquake‐induced ground shaking. Nonlinear time history analysis (NLTHA) is extensively performed, applying a suite of assembled ground‐motion sequences (i.e., two ground motions in series) to assess the ECBP connection response and the corresponding frame behavior. Fragility analyses accounting for only the first ground motions in each considered sequence (to derive fragility curves), and the entire ground‐motion sequences (to derive fragility surfaces) are also performed to evaluate the probabilities of frame collapse and base connection failure. Finally, key findings regarding the seismic performance of ductile ECBP connections and their effects on the frame collapse are discussed. The limitations of the study are also outlined.