We investigate the role of major seismological (magnitude, pulse period, fault length, seismic activity, orientation of incident seismic wave with respect to fault-strike) and geometrical (fault-site geometry) parameters to understand the variations in ground-motion demands due to near-fault directivity (NFD) effects. To this end, we used a suite of probabilistic strike-slip earthquake scenarios and established the elastic spectral amplitude distributions conditioned on the above investigated parameters. The probabilistic earthquake scenarios also provided information on the sensitivity of directivity dominant near-fault (NF) ground motions to mean annual exceedance rates. We implemented different narrow-band directivity models to observe the significance of seismological modeling in the directivity dominant NF ground-motion amplitudes. The observations from these case studies suggest that each one of the above parameters have implications on the amplitude and spatial variation of directivity dominating NF ground-motion demands. The influence of each investigated parameter on NFD spectral amplitudes is dependent of the implemented directivity model. We also establish some rules to map the spatial extent of directivity dominant ground motions considering the variations in the investigated seismological parameters. The outcomes of the paper can be used to incorporate the NFD effects into design spectra representing different annual exceedance rates.