One of the new lateral force resisting systems introduced to improve seismic performance of structures is rocking buckling restrained braced frame (RBRBF). This lateral force resisting system in each bay includes buckling restrained braces (BRBs) on one side and conventional braces on the other side, and vertical links between the upper ends of braces located in adjacent stories. In this system, conventional braces and adjacent columns are designed to remain elastic until near seismic collapse. In this paper, RBRBFs are designed according to a displacement-based design approach. Maximum interstory drift ratio (MIDR) and maximum residual interstory drift ratio (MRIDR) are among the most critical engineering demand parameters (EDPs) used for assessing the safety of structures after an earthquake. The primary aim of this study is to investigate the effects of utilizing RBRBFs on MIDR and MRIDR responses compared with buckling restrained braced frames (BRBFs). For this purpose, 4-, 8-, and 12-story structures with RBRBF and BRBF systems are considered, and their collapse capacity values and residual drift capacity values given different levels of MRIDR are computed using incremental dynamics analyses (IDAs). After computing the capacity values, the mean annual frequencies (MAFs) of collapse (λCol) and exceeding different MRIDR levels (λRD) are obtained. The results demonstrate that all RBRBFs have better collapse and residual drift performance than BRBFs. Based on these results, the use of RBRBFs dramatically reduces BRBF weaknesses including the concentration of damage in a single story and low post-yield stiffness.