Most studies of medium-induced jet modification rely on the comparison of jet properties measured in heavy ion collisions with a proton-proton baseline of the same reconstructed jet $p_T$. Migration of jets from higher to lower $p_T$ due to energy loss, together with the steepness of the jet spectrum, lead to a heavy ion jet sample with a given $p_T$ range which is dominated by the jets that were least modified. We introduce a new strategy to compare heavy ion jet measurements to proton-proton baselines which views energy loss as being monotonic in $p_T$. In this strategy, the jets in a heavy ion collision ordered by $p_T$ can be viewed as modified versions of the same number of highest energy jets in proton-proton collisions. We validate, at MC level, the correlation between the $p_T$ of the parton that initiates a heavy ion jet with the $p_T$ of the vacuum jet which corresponds to it via our novel binning procedure. We show that this strategy mitigates the effect of bin migration and provides a complementary way to study jet modification in heavy ion collisions.