Combat Models and Historical Data: The U.S. Civil War

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Abstract
Doubt has recently been cast on the applicability of mathematical models in general and Lanchester-type equations in particular to real combat. A comparatively small amount of effort has been spent in the past in testing theory against data, and so the general validity of such modeling largely remains to be demonstrated. In this paper, combat data on the U.S. Civil War is examined to determine the extent to which it can be explained by-simple mathematical relations, and some support, as well as problems, for such modeling is developed. A model for probability of winning is developed, depending solely on the ability of each force to continue to fight after sustaining specified fractional losses. Distributions of parameters describing battles, force ratios, and loss ratios are derived. Limited applicability of Lanchester-type equations is indicated. It is concluded that although these hundred-year-old battles may have limited application to future combat, the possibilities of deriving improved combat models by analyzing real life data are essentially unlimited, and that fact differs sufficiently from theory to make it unlikely that pure conjecture will hit upon the proper form for a combat model structure.

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