Decision boundaries used to model probability of victory and duration of combats

Received 30 October 2016 Accepted 15 December 2017 Abstract—Geometric Brownian motion with decision boundaries is used in modelling combat effects such as probability of winning a battle and duration of a battle. We verify that it is possible to construct a model and analytical mathematical formulas for these quantities. Variables of the model are force sizes at the beginning and at end of a battle, and decision boundaries for the two opposing forces. The model with different model parameters is compared with empirical attrition data. New results can be uncovered when outcomes and expected durations of empirical battles are studied with the model. We conclude that battles, where the attacker is superior to the defender, and battles with comparable force strengths on the two opposing sides, are described with different model parameter values. This can indicate an extra advantage for attackers that cannot be explained by other factors of the model. We show how asymmetrical decision boundaries are used to model this kind of effects. These general conclusions are made on an aggregate level from the modelling results of individual battles.