Predicted cutoff energy (E_c, left) and γ-ray efficiency (right) distributions for one realization of the disk population (S1), showing three regimes. The orange points indicate the direct application of the relation to the synthesized P and ﹩\dot{P}﹩, and the blue points indicate the introduction of scatter on both E_c and ﹩{{ \mathcal L }}_{\gamma }﹩. The former captures the observed observational spread in E_c, and the latter captures beaming and other neglected physical influences on the luminosity/flux (e.g., magnetic inclination).