Comparison between KERRBB BH mass estimates M_BH, fit (inferred from the SED fitting procedure; each dot corresponds to the mean value computed using the extreme estimates given by the uncertainties) and the VPs calculated using the Hβ velocity dispersion σ_line (left panel) and the FWHM (right panel). We averaged all the VPs computed using data from different authors (see Table A.2; PG 1247+267 and S5 0836+71 are marked with green dots). The blue shaded area corresponds to the set of best fits between M_BH, Fit and VP after considering all possible spin values between 0 and 0.998 (equations in blue on the plot are the two extreme cases; the uncertainty on the slope is ∼20%). Assuming that Log M_BH, fit = LogVP + Log f, we found the scale factor f, labeled on the plot in red for the two extreme spin values. Uncertainty bars in both plots are ∼0.45 dex and ∼0.5 dex for M_BH, fit and VPs respectively, and the black dashed line is the 1:1 line.