A direct relation between the first hyperpolarizability, beta, of noncentrosymmetric molecular structures and the metric centrosymmetricity content, S(i), of such structures is shown for the first time. For a series of systematic, in-plane distortions (stretch, pull, shift, and squish deformations) of the model NLO chromophore benzene, we find a convincing monotonic relationship between calculated values of beta and S(i). These results suggest that the dominant variation in beta for these structures arises from the change in oscillator strength. More striking, these comparisons demonstrate the utility of the S(i) metric in correlating observable behavior with symmetry content.