ABSTRACT In active galactic nuclei, the relationship between UV and X-ray luminosity is well studied (often characterised by αox) but often with heterogeneous samples. We have parametrized the intrinsic distribution of X-ray luminosity, LX, for the optically selected sample of SDSS quasars in the Stripe 82 and XXL fields across redshifts 0.5–3.5. We make use of the available XMM observations and a custom pipeline to produce Bayesian sensitivity curves that are used to derive the intrinsic X-ray distribution in a hierarchical Bayesian framework. We find that the X-ray luminosity distribution is well described by a Gaussian function in log10 LX space with a mean that is dependent on the monochromatic 2500 Å UV luminosity, L2500. We also observe some redshift dependence of the distribution. The mean of the LX distribution increases with redshift while the width decreases. This weak but significant redshift dependence leads to L2500–LX and L2500–αox relations that evolve with redshift, and we produce a redshift- and L2500-dependent αox equation. Neither black hole mass nor Eddington ratio appear to be potential drivers of the redshift evolution.