  Galaxy cluster masses, rich with cosmological information, can be estimated
from internal dark matter (DM) velocity dispersions, which in turn can be
observationally inferred from satellite galaxy velocities. However, galaxies
are biased tracers of the DM, and the bias can vary over host halo and galaxy
properties as well as time. We precisely calibrate the velocity bias, b_v --
defined as the ratio of galaxy and DM velocity dispersions -- as a function of
redshift, host halo mass, and galaxy stellar mass threshold (Mstarsat), for
massive halos (M200c > 1e13.5 msun) from five cosmological simulations:
IllustrisTNG, Magneticum, Bahamas + Macsis, The Three Hundred Project, and
MultiDark Planck-2. We first compare scaling relations for galaxy and DM
velocity dispersion across simulations; the former is estimated using a new
ensemble velocity likelihood method that is unbiased for low galaxy counts per
halo, while the latter uses a local linear regression. The simulations show
consistent trends of b_v increasing with M200c and decreasing with redshift and
Mstarsat. The ensemble-estimated theoretical uncertainty in b_v is 2-3% but
becomes percent-level when considering only the three highest resolution
simulations. We update the mass-richness normalization previously estimated by
Farahi et al. (2016) for an SDSS redMaPPer cluster sample. The improved
accuracy of our b_v estimates reduces the mass normalization uncertainty from
22% to 8%, demonstrating that dynamical estimation techniques can be
competitive with weak lensing in calibrating population mean masses. We discuss
necessary steps for further improving this precision. Our estimates for
b_v(M200c, Mstarsat, z) are made publicly available.
