In ordering alloy systems, the overall long-range order parameter does not distinguish the degree to which the component structures are delocalized for different configurations of equal randomness. We define a new parameter, which is sensitive to such differences, by considering the short-range order parameters as a set of statistical moments for geometric variation in the crystal. A computer model has been developed which uses this parameter to analyze finite alloy systems for configurational preferences by a Monte Carlo method. Initial studies have established the parametric range as a function of LRO and nonstoichiometry. Qualitative results correspond well to predictions for ideal systems.