  In the era of large surveys, yielding thousands of galaxy clusters, efficient
mass proxies at all scales are necessary in order to fully utilize clusters as
cosmological probes. At the cores of strong lensing clusters, the Einstein
radius can be turned into a mass estimate. This efficient method has been
routinely used in literature, in lieu of detailed mass models; however, its
scatter, assumed to be $\sim30\%$, has not yet been quantified. Here, we assess
this method by testing it against ray-traced images of cluster-scale halos from
the Outer Rim N-body cosmological simulation. We measure a scatter of $13.9\%$
and a positive bias of $8.8\%$ in $M(<\theta_E)$, with no systematic
correlation with total cluster mass, concentration, or lens or source
redshifts. We find that increased deviation from spherical symmetry increases
the scatter; conversely, where the lens produces arcs that cover a large
fraction of its Einstein circle, both the scatter and the bias decrease. While
spectroscopic redshifts of the lensed sources are critical for accurate
magnifications and time delays, we show that for the purpose of estimating the
total enclosed mass, the scatter introduced by source redshift uncertainty is
negligible compared to other sources of error. Finally, we derive and apply an
empirical correction that eliminates the bias, and reduces the scatter to
$10.1\%$ without introducing new correlations with mass, redshifts, or
concentration. Our analysis provides the first quantitative assessment of the
uncertainties in $M(<\theta_E)$, and enables its effective use as a core mass
estimator of strong lensing galaxy clusters.
