Recent studies have revealed the impact of ground motion loading history on performance limit states of reinforced concrete (RC) bridge columns such as reinforcement bar-buckling and residual drift ratio. Conventional hazard characterizations such as peak ground acceleration, spectral acceleration, and spectral displacement only capture peak values of ground motion hazard and, therefore, fall short of providing the necessary information to account for these limit states. In this study, a parameter termed as the opposite peak ratio (Rop) is defined, explored, and shown to be useful in reproducing loading history characteristics of ground motions for displacement-based design. Several past ground motion records were analyzed to develop empirical models that can estimate Rop. These models provide the mean and confidence intervals of Rop as a function of earthquake magnitude, epicentral distance, structural period, hysteretic model, and displacement ductility. To motivate practitioners to make use of Rop, a design scenario and two case studies are discussed. In an RC bridge column design scenario, it is shown that having prior information about the expected Rop at the site could reduce the structural cost of the bridge. Next, case studies designed to investigate correlations between Rop and the performance limit states of RC bridge columns are discussed. By analyzing the results of nonlinear time-history analyses of numerical RC column models, it is established that Rop could potentially be a significant variable in generating fragility models for these limit-states.