As a sanity check, we also consider the effect of host galaxy size (i.e, effective radius) on the offset distribution.  Short GRBs tend to be larger than long-duration GRBs, due to their larger stellar mass and luminosity.  In Figure 21 we plot the host-normalized offset for the same population of stellar explosions.  For long-duration GRBs and core-collapse SNe, the median normalized offset is ~ 1, as would be expected for progenitors with short delay times (as they have no time to migrate from where they are born).  Short-duration GRBs, on the other hand, have a typical host-normalized offset of ~ 1.5, with a sizable fraction of events at very large normalized offsets.