The Stochastic Properties of Large Battle Models

This paper considers stochastic models of large battles. Such battle models are said to be stochastically determined if the gross results—for example, the casualties to each side—show low variance in repeated plays in which only the random numbers are changed. Here, low variance means a standard deviation small compared to the initial number of weapons engaged. When stochastic determinism exists in a large battle model, only a few replications of the model are needed to get good estimates of the gross results. Stochastic determinism with respect to casualties is shown to be present when the correlations between losses of individual weapons are relatively small or few in number; that is, when the fate of a given weapon has strong influence on the fates of only a limited number of other weapons. Three stochastic models—the Lanchester Linear and Square Law models and a simple missile battle model—which can be studied analytically are shown to be stochastically determined. Features of battle models that would lead to violation of stochastic determinism are discussed.