  Predicting the ground state of alloy systems is challenging due to the large
number of possible configurations. We identify an easily computed descriptor
for the stability of binary surface alloys, the effective coordination number
$\mathscr{E}$. We show that $\mathscr{E}(M)$ correlates well with the enthalpy
of mixing, from density functional theory (DFT) calculations on
$M_x$Au$_{1-x}$/Ru [$M$ = Mn or Fe]. At each $x$, the most favored structure
has the highest [lowest] value of $\mathscr{E}(M)$ if the system is
non-magnetic [ferromagnetic]. Importantly, little accuracy is lost upon
replacing $\mathscr{E}(M)$ by $\mathscr{E}^*(M)$, which can be quickly computed
without performing a DFT calculation, possibly offering a simple alternative to
the frequently used cluster expansion method.
