  Cluster expansion (CE) is effective in modeling the stability of metallic
alloys, but sometimes cluster expansions fail. Failures are often attributed to
atomic relaxation in the DFT-calculated data, but there is no metric for
quantifying the degree of relaxation. Additionally, numerical errors can also
be responsible for slow CE convergence. We studied over one hundred different
Hamiltonians and identified a heuristic, based on a normalized mean-squared
displacement of atomic positions in a crystal, to determine if the effects of
relaxation in CE data are too severe to build a reliable CE model. Using this
heuristic, CE practitioners can determine a priori whether or not an alloy
system can be reliably expanded in the cluster basis. We also examined the
error distributions of the fitting data. We find no clear relationship between
the type of error distribution and CE prediction ability, but there are clear
correlations between CE formalism reliability, model complexity, and the number
of significant terms in the model. Our results show that the \emph{size} of the
errors is much more important than their distribution.
