  We investigate the impact of uncertainty in the velocity distribution of dark
matter on direct detection experiments. We construct an multinomial prior with
a hyperparameter $\beta$ that describes the strength of our belief in an
isotropic Maxwell-Boltzmann velocity distribution. By varying $\beta$, we
interpolate between a halo-independent and halo-dependent analysis. We present
a novel approximation for the marginalisation of this prior that is applicable
to any counting experiment. With this formula, we investigate the impact of the
uncertainty in limits from XENON1T. For dark matter masses greater than about
60 GeV, we find extremely mild sensitivity to the distribution. Below about 60
GeV, the limit weakens by less than an order of magnitude if we assume an
isotropic distribution in the galactic frame. If we permit anisotropic
distributions, the limit further weakens, but at most by about two orders of
magnitude. Lastly, we check the impact of parametric uncertainties and discuss
the possible inclusion and impact of our technique in global fits.
