  The statistical uncertainties of 13 model parameters in the
Weizs\"acker-Skyrme (WS*) mass model are investigated for the first time with
an efficient approach, and the propagated errors in the predicted masses are
estimated. The discrepancies between the predicted masses and the experimental
data, including the new data in AME2016, are almost all smaller than the model
errors. For neutron-rich heavy nuclei, the model errors increase considerably,
and go up to a few MeV when the nucleus approaches the neutron drip line. The
most sensitive model parameter which causes the largest statistical error is
analyzed for all bound nuclei. We find that the two coefficients of symmetry
energy term significantly influence the mass predictions of extremely
neutron-rich nuclei, and the deformation energy coefficients play a key role
for well-deformed nuclei around the $\beta$-stability line.
