  The accuracy of Monte Carlo Glauber model descriptions of minimum-bias
multiplicity frequency distributions is evaluated using data from the
Relativistic Heavy Ion Collider (RHIC) within the context of a sensitive,
power-law representation introduced previously by Trainor and Prindle (TP).
Uncertainties in the Glauber model input and in the mid-rapidity multiplicity
frequency distribution data are reviewed and estimated using the TP centrality
methodology. The resulting errors in model-dependent geometrical quantities
used to characterize heavy ion collisions ({\em i.e.} impact parameter, number
of nucleon participants $N_{part}$, number of binary interactions $N_{bin}$,
and average number of binary collisions per incident participant nucleon $\nu$)
are presented for minimum-bias Au-Au collisions at $\sqrt{s_{NN}}$ = 20, 62,
130 and 200 GeV and Cu-Cu collisions at $\sqrt{s_{NN}}$ = 62 and 200 GeV.
Considerable improvement in the accuracy of collision geometry quantities is
obtained compared to previous Monte Carlo Glauber model studies, confirming the
TP conclusions. The present analysis provides a comprehensive list of the
sources of uncertainty and the resulting errors in the above geometrical
collision quantities as functions of centrality. The capability of energy
deposition data from trigger detectors to enable further improvements in the
accuracy of collision geometry quantities is also discussed.
