  In the McLerran-Venugopalan model, correlators of Wilson lines are given by
an average over a Gaussian ensemble of random color sources. In numerical
implementations, these averages are approximated by a Monte-Carlo sampling. In
this paper, we study the statistical error made with such a sampling, with
emphasis on the momentum dependence of this error. Using the example of the
dipole amplitude, we consider various approximants that are all equivalent in
the limit of infinite statistics but differ with finite statistics and compare
their statistical errors. For correlation functions that are translation
invariant, we show that averaging over the barycenter coordinate drastically
reduces the statistical error and more importantly modifies its momentum
dependence.
