Distribution of relative velocities with respect to the quasar redshift for our sample of strong proximate H₂ systems (orange histograms) compared to those found in a region shifted by 5000 km s⁻¹ (blue). We here used the “zbest” provided by the DR14Q catalogue as the quasar redshift and the z_abs measurement directly from our search algorithm. Negative velocities indicate z_abs >  z_em. Note that the x-axis goes from positive velocities (blueshifted compared to the quasar) on the left to negative velocities (redshifted) to the right. Both distributions are restricted to visually-checked systems (unfilled histograms: grade A or B, filled histograms: grade A only) isolated using the outlier selection (# 2). The grey regions show the corresponding minimal search windows. Systems falling outside these regions are not considered when comparing incidence rates. The horizontal dashed line shows the mean number of intervening strong H₂ systems per velocity bin (∼1 per 500 km s⁻¹ bin). A significant excess of H₂ systems at the quasar redshift is observed and cannot be explained by intervening statistics.