  CMB lensing is a promising, novel way to measure galaxy cluster masses that
can be used, e.g., for mass calibration in galaxy cluster counts analyses.
Understanding the statistics of the galaxy cluster mass observable obtained
with such measurements is essential if their use in subsequent analyses is not
to lead to biased results. We study the statistics of a CMB lensing galaxy
cluster mass observable for a Planck-like experiment with mock observations
obtained from an N-body simulation. We quantify the bias and intrinsic scatter
associated with this observable following two different approaches, one in
which the signal due to the cluster and nearby correlated large-scale structure
is isolated, and another one in which the variation due to uncorrelated
large-scale structure is also taken into account. For our first approach we
also quantify deviations from log-normality in the scatter, finding them to
have a negligible impact on mass calibration for our Planck-like experiment. We
briefly discuss how some of our results change for experiments with higher
angular resolution and lower noise levels, such as the current generation of
surveys obtained with ground-based, large-aperture telescopes.
