Static, thermodynamic, and rheological data of polymerically stabilized colloidal dispersions are usually predicted on the basis of ad hoc hard sphere models. Here, the specific effects of the grafted polymers are explicitly taken into account through a hard core plus a soft tail potential. A systematic analysis of structural and thermodynamic quantities is performed by using the thermodynamically self-consistent integral equation scheme of Rogers and Young. Criteria to construct reference hard sphere systems, showing quantitative agreement with the true systems, are presented. It is shown that there are regions of the potential parameter space where the hard sphere modelization is not possible and where the true potential has to be used.