The on-top pair density P r, r gives the probability that one electron will be found on top Ž . of another at position r. We find that the local spin density LSD and generalized Ž . gradient GGA approximations for exchange and correlation predict this quantity with remarkable accuracy. We show how this fact and the usual sum-rule arguments explain the success of these approximations for real atoms, molecules, and solids, where the electron spin densities do not vary slowly over space. Self-consistent LSD or GGA Ž . calculations make realistic predictions for the total energy E, the total density n r , and Ž . Ž the on-top pair density P r, r , even in those strongly ''abnormal'' systems such as . stretched H where these approximations break symmetries and yield unrealistic spin 2 Ž . magnetization densities m r . We then suggest that ground-state ferromagnetic iron is a Ž . ''normal'' system, for which for LSD or GGA m r and the related local spin moment are trustworthy, but that iron above the Curie temperature and antiferromagnetic clusters at all temperatures are abnormal system for which the on-top pair density interpretation is more viable than the standard physical interpretation. As an example of a weakly abnormal system, we consider the four-electron ion with nuclear charge Z ª ϱ.