In this work, we test the assertion that the scatter in the mass of black holes which drive quasars should be luminosity dependent with less scatter in more luminous objects. To this end, we measure the width of the Mg iiλ2799 line in quasar spectra from the Sloan Digital Sky Survey (SDSS), 2df QSO Redshift survey (2QZ) and 2dF SDSS LRG And QSO (2SLAQ) surveys and, by invoking an unnormalized virial mass estimator, relate the scatter in linewidth to the scatter of mass in the underlying black hole population. We find conclusive evidence for a trend such that there is less scatter in linewidth, and hence black hole mass, in more luminous objects. However, the most luminous objects in our sample show such a low degree of scatter in linewidth that, when combined with measures for the intrinsic scatter in the radius–luminosity relation for the broad-line region (BLR) in active galaxies, an inconsistency arises in the virial technique for estimating black hole masses. This analysis implies that, at least for the most luminous quasars, either there is little-to-no intrinsic scatter in the radius–luminosity relation or the Mg ii broad emission-line region is not totally dominated by virial velocities. Finally, we exploit the measured scatter in linewidths to constrain models for the velocity field of the BLR. We show that the lack of scatter in broad-line widths for luminous quasars is inconsistent with a pure planar/disc-like geometry for the BLR. In the case of a BLR with purely polar flows, the opening angle to luminous quasars must be less than ∼55°. We then explore the effects of adding a random or spherically symmetric component to the velocities of gas clouds in the BLR. Assuming an opening angle to quasars of 45°, a planar field can be made consistent with our results if ∼ 40–50 per cent of the velocities are randomly distributed.