Using GaAs as a test material, we investigated the redshift between emission and the optical bandgap. The knowledge of the energy difference, referred to as the Stokes shift, is of considerable importance for solid-state light sources because its magnitude defines the centered monochromaticity of the emission. Employing Fan's theory, we reveal the basic parameters, which determine the Stokes shift, and provide an uncertainty analysis, considering both uncorrelated and correlated variables. We disclose that the considerable scatter of the dielectric constants in the literature causes uncertainties comparable to or even exceeding the mean. The work stresses that the high-frequency and static dielectric constants might be closer than the currently promoted numbers.