The random phase approximation (RPA) builds in correlations left out by mean-field theory. In full 0ħω shell-model spaces we calculate the Hartree-Fock (HF)+RPA binding energy, and compare it to exact diagonalization. We find that often, but not always, the HF+RPA gives a good approximation to the “exact” ground state energy. In those cases where the RPA is less satisfactory, however, there is no obvious correlation with properties of the HF state, such as deformation or overlap with the exact ground state wave function. This weakens the reliability of the RPA for computing binding energies.