Recent studies of neutral atomic hydrogen (H I) in nearby galaxies found that all field disc galaxies are H I saturated, in that they carry roughly as much H I as permitted before this gas becomes gravitationally unstable. By taking this H I saturation for granted, the atomic gas fraction fatm of galactic discs can be predicted as a function of the stability parameter q = jσ/(GM), where Mand jare the baryonic mass and specific angular momentum of the disc and σ is the H I velocity dispersion (Obreschkow et al. 2016). The log-ratio Δfq between this predictor and the observed atomic fraction can be seen as a physically motivated ‘H I deficiency’. While field disc galaxies have Δfq ≈ 0, objects subject to environmental removal of H I are expected to have Δfq > 0. Within this framework, we revisit the H I deficiencies of satellite galaxies in the Virgo cluster and in clusters of the EAGLE simulation. We find that observed and simulated cluster galaxies are H I deficient and that Δfq slightly increases when getting closer to the cluster centres. The Δfq values are similar to traditional H I deficiency estimators, but Δfq is more directly comparable between observations and simulations than morphology-based–deficiency estimators. By tracking the simulated H I deficient cluster galaxies back in time, we confirm that Δfq ≈ 0 until the galaxies first enter a halo with Mhalo > 1013M☉, at which moment they quickly lose H I by environmental effects. Finally, we use the simulation to investigate the links between Δfq and quenching of star formation.