It is observed that the even-even nuclei having identical NpNn/Δ values exhibit identical excitation energies and/or energy ratios (EJ/E2,EJ/E4) in their ground-state bands (g.s.b.). Np (Nn) is the valence proton (neutron) number and Δ is the average pairing gap, (Δp+Δn)/2. It is shown that this correlation is a manifestation of a very simple but uniform dependence of the excitation energies of the g.s.b. of even-even nuclei, spanning a wide mass region (70≤A≤244), on the ratio of their pairing and n-p interaction energies. An explicit form of this dependence is phenomenologically deduced and subsequently used to study the development of collectivity, existence of subshell closures and some other nuclear systematics.