Characterizing a planet detected by microlensing is hard if the planetary signal is weak or the lens-source relative trajectory is far from caustics. However, statistical analyses of planet demography must include those planets to accurately determine occurrence rates. As part of a systematic modelling effort in the context of a >10-yr retrospective analysis of MOA's survey observations to build an extended MOA statistical sample, we analyse the light curve of the planetary microlensing event MOA-2014-BLG-472. This event provides weak constraints on the physical parameters of the lens, as a result of a planetary anomaly occurring at low magnification in the light curve. We use a Bayesian analysis to estimate the properties of the planet, based on a refined Galactic model and the assumption that all Milky Way's stars have an equal planet-hosting probability. We find that a lens consisting of a $1.9^{+2.2}_{-1.2}\, \mathrm{M}_\mathrm{J}$ giant planet orbiting a $0.31^{+0.36}_{-0.19}\, \mathrm{M}_\odot$ host at a projected separation of $0.75\pm 0.24\, \mathrm{au}$ is consistent with the observations and is most likely, based on the Galactic priors. The lens most probably lies in the Galactic bulge, at $7.2^{+0.6}_{-1.7}\,\mathrm{kpc}$ from Earth. The accurate measurement of the measured planet-to-host star mass ratio will be included in the next statistical analysis of cold planet demography detected by microlensing.