Why does the recently proposed simple empirical formula for the lowest excitation energies work so well?

It has recently been shown that a simple empirical formula, in terms of the mass number and the valence nucleon numbers, is able to describe the main trends of the lowest excitation energies of the natural parity even multipole states up to $10^+$ in even-even nuclei throughout the entire periodic table. In an effort to understand why such a simple formula is so capable, we investigate the possibility of associating each term of the empirical formula with the specific part of the measured excitation energy graph.