  We introduce a new 'quantile' analysis strategy to study the modification of
jets as they traverse through a droplet of quark-gluon plasma. To date, most
jet modification studies have been based on comparing the jet properties
measured in heavy-ion collisions to a proton-proton baseline at the same
reconstructed jet transverse momentum ($p_T$). It is well known, however, that
the quenching of jets from their interaction with the medium leads to a
migration of jets from higher to lower $p_T$, making it challenging to directly
infer the degree and mechanism of jet energy loss. Our proposed quantile
matching procedure is inspired by (but not reliant on) the approximate
monotonicity of energy loss in the jet $p_T$. In this strategy, jets in
heavy-ion collisions ordered by $p_T$ are viewed as modified versions of the
same number of highest-energy jets in proton-proton collisions, and the
fractional energy loss as a function of jet $p_T$ is a natural observable
($Q_{\rm AA}$). Furthermore, despite non-monotonic fluctuations in the energy
loss, we use an event generator to validate the strong correlation between the
$p_T$ of the parton that initiates a heavy-ion jet and the $p_T$ of the vacuum
jet which corresponds to it via the quantile procedure ($p_T^{\rm quant}$). We
demonstrate that this strategy both provides a complementary way to study jet
modification and mitigates the effect of $p_T$ migration in heavy-ion
collisions.
