Dwarf spheroidal galaxies that form in halo substructures provide stringent
constraints on dark matter annihilation. Many ultrafaint dwarfs discovered with
modern surveys contribute significantly to these constraints. At present,
because of the lack of abundant stellar kinematic data for the ultrafaints,
non-informative prior assumptions are usually made for the parameters of the
density profiles. Based on semi-analytic models of dark matter subhalos and
their connection to satellite galaxies, we present more informative and
realistic satellite priors. We show that our satellite priors lead to
constraints on the annihilation rate that are between a factor of 2 and a
factor of 7 weaker than under non-informative priors. As a result, the thermal
relic cross section can at best only be excluded (with 95% probability) for
dark matter masses of $\lesssim 40$ GeV from dwarf spheroidal data, assuming
annihilation into $b\bar{b}$.