We examine how much information measured broad–line widths add to virial BH mass estimates for flux limited samples of quasars .
We do this by comparing the BH masses estimates to those derived by randomly reassigning the quasar broad–line widths to different objects and re-calculating the BH mass .

For 9000 BH masses derived from the H \beta line we find that the distributions of original and randomized BH masses in the M _ { BH } –redshift plane and the M _ { BH } –luminosity plane are formally identical .
A 2D KS test does not find a difference at > 90 % confidence .
For the Mg II line ( 32000 quasars ) we do find very significant differences between the randomized and original BH masses , but the amplitude of the difference is still small .
The difference for the C IV line ( 14000 quasars ) is 2 - 3 \sigma and again the amplitude of the difference is small .
Subdividing the data into redshift and luminosity bins we find that the median absolute difference in BH mass between the original and randomized data is 0.025 , 0.01 and 0.04 dex for H \beta , Mg II and C IV respectively .
The maximum absolute difference is always \leq 0.1 dex .

We investigate whether our results are sensitive to corrections to Mg II virial masses , such as those suggested by Onken & Kollmeier ( 2008 ) .
These corrections do not influence our results , other than to reduce the significance of the difference between original and randomized BH masses to only 1 - 2 \sigma for Mg II .
Moreover , we demonstrate that the correlation between mass residuals and Eddington ratio discussed by Onken & Kollmeier are more directly attributable to the slope of the relation between H \beta and Mg II line width .

The implication is that the measured quasar broad–line velocity widths provide little extra information , after allowing for the mean velocity width .
In this case virial estimates are equivalent to M _ { BH } \propto L ^ { \alpha } , with L / L _ { Edd } \propto L ^ { 1 - \alpha } ( with \alpha \simeq 0.5 ) .
This leaves an unanswered question of why the accretion efficiency changes with luminosity in just the right way to keep the mean broad–line widths fixed as a function of luminosity .