The nonlinear response of an irregular base-isolated building depends on the angle of seismic incidence (ASI). The variation in the structural response caused by the ASI depends on whether the horizontal ground motion set considered as the seismic input has a notable directivity effect. In a previous study by the author, the ratio of the equivalent velocities of the cumulative energy input along the major and minor axes (REI) was considered to select ground motion sets with a notable directivity effect. A question of interest concerns the relationship between the ratio REI and the variation in the structural response parameters. In this study, nonlinear time-history analyses of two five-story irregular base-isolated building models are performed using 15 long-period pulse-like ground motion records considering various ASIs. Then, the relationships between the ratio REI and the variation in the peak and cumulative response parameters are investigated. The main findings of this study are that (i) the variation in the response parameter generally becomes larger when the ratio REI is close to zero and (ii) the variation in the total input energy resulting from ASI is negligibly small and independent of the ratio REI.