  We have performed magnetohydrodynamic simulations in general relativity of
binary neutron star and binary black hole-neutron star mergers, as well as the
magnetorotational collapse of supermassive stars. In many cases the outcome is
a spinnng black hole (BH) immersed in a magnetized disk, with a jet emanating
from the poles of the BH. While their formation scenarios differ and their BH
masses, as well as their disk masses, densities, and magnetic field strengths,
vary by orders of magnitude, these features conspire to generate jet Poynting
luminosities that all lie in the same, narrow range of $\sim 10^{52\pm1}~{\rm
erg ~s^{-1}}$. A similar result applies to their BH accretion rates upon jet
launch, which is $\sim 0.1-10~{\rm M_{\odot}~s^{-1}}$. We provide a simple
model that explains these unanticipated findings. Interestingly, these
luminosities reside in the same narrow range characterizing the observed
luminosity distributions of over 400 short and long GRBs with distances
inferred from spectroscopic redshifts or host galaxies. This result, together
with the GRB lifetimes predicted by the model, supports the belief that a
compact binary merger is the progenitor of an SGRB, while a massive, stellar
magnetorotational collapse is the progenitor of an LGRB.
