  We investigate the impact of dynamical streams and substructure on estimates
of the local escape speed and total mass of Milky Way-mass galaxies from
modelling the high velocity tail of local halo stars. We use a suite of
high-resolution, magneto-hydrodynamical cosmological zoom-in simulations, which
resolve phase space substructure in local volumes around solar-like positions.
We show that phase space structure varies significantly between positions in
individual galaxies and across the suite. Substructure populates the high
velocity tail unevenly and leads to discrepancies in the mass estimates. We
show that a combination of streams, sample noise and truncation of the high
velocity tail below the escape speed leads to a distribution of mass estimates
with a median that falls below the true value by $\sim 20 \%$, and a spread of
a factor of 2 across the suite. Correcting for these biases, we derive a
revised value for the Milky Way mass presented in Deason et al. of $1.29
^{+0.37}_{-0.47} \times 10^{12}$ $\rm M_{\odot}$.
