Bin migration effects hinder a direct connection between the nuclear modification factor $R_{AA}$ and the energy lost by jets. The $R_{AA}$ compares yields of jets in pp and AA collisions that are reconstructed with the same $p_T$ and is thus biased by the steeply falling nature of the jet spectrum. To mitigate these effects, Brewer et al. [1] introduced a novel observable to directly quantify average jet energy loss ($Q_{AA}$) which is given by the ratio of the transverse momenta that correspond to the same probability quantiles in pp and AA spectra. This work reinforces the claim that $Q_{AA}$ ratio is a reliable proxy for jet energy loss and, by using it, it shows that energy loss decreases with increasing jet radius when QGP response, as implemented in the JEWEL event generator, is accounted for. Further, our results establish that, contrary to recent claims, the difference in $R_{AA}$ between inclusive and boson-jet events is dominated by differences in the spectral shape, leaving the colour charge of the jet initiating parton with a minor role to play. The experimental feasibility of a $Q_{AA}$ measurement is addressed.