  The parallax effect in ground-based microlensing (ML) observations consists
of a distortion to the standard ML light curve arising from the Earth's orbital
motion. In most cases, the resolution in current ML surveys is not accurate
enough to observe this effect, but parallax could conceivably be detected with
frequent followup observations of ML events in progress. We calculate the
expected fraction of events where parallax distortions will be detected by such
observations, adopting Galactic models consistent with the observed ML
timescale ($t_0$) distributions. We study the dependence of the rates for
parallax-shifted events on the sampling frequency and on the photometric
precision. For example, we find that for hourly observations with typical
photometric errors of 0.01 mag, 6\% of events where the lens is in the bulge,
and 31\% of events where the lens is in the disk, (or $\approx 10$\% of events
overall) will give rise to a measurable parallax shift at the 95\% confidence
level. These fractions may be increased by improved photometric accuracy and
increased sampling frequency. Parallax measurements yield the reduced
transverse speed, $\tilde{v}$, which gives both the relative transverse speed
and lens mass as functions of distance. We give examples of the accuracies with
which $\tilde{v}$ may be measured in typical parallax events. Using only the 3
standard ML parameters to fit ML light curves which may be shape-distorted by
parallax or blending, can result in incorrect inferred values for these
quantities. We find that the inferred timescales from such fits tend to shift
the event duration distribution by $\approx 10$\% towards shorter $t_0$ for
events with disk lenses, but do not affect bulge lenses. In both cases, the
impact-parameter distribution is depressed slightly at the low and high ends.
