Quadratic fits of the luminosity-metallicity relations M_V − [Fe/H] and M_V − [Fe/H]. The black points are BaSTI α-enhanced zero-age HB models, corrected by the calibration from Cassisi & Salaris (1997) to account a dispersion of the RRLs due to their evolution. The quadratic functions (red for canonical He, as in Eqs. (2) and (3), and dotted blue for enhanced He) were obtained via the Markov chain Monte Carlo method.