A statistical-mechanics analysis is used to create analytic estimates for the short-range order (SRO) parameters in FCC and BCC solid solution alloys as a function of composition and temperature. As in the classic quasi-chemical method, the analysis assumes pair interactions among atoms at different distances and partitions the entire crystal into a set of identical independent clusters that are then treated like molecules in a gas. This enables analytic development of the probabilities that govern SRO. For binary and ternary alloys, increasingly complex clusters are considered that systematically extend the range of accuracy of the analytic model relative to reference Monte Carlo simulations. The results enable fast assessment of likely SRO using estimated inputs for atom-atom interaction energies. In this record we provide our analytical solution as well as the simulation data supporting our theoretical prediction of the short-range order parameter in both FCC and BCC alloys.