A Combat Equation Derived from Stochastic Modeling of Attrition Data

摘要

A macroscopic combat equation is derived with stochastic methods. Variables of the equation are the force sizes of the attacker and the defender at the beginning and at the end of the battle. The calculation is based on a combination of force strengths and breakpoints are implied by a win/lose decision methodology. All model parameters of the combat equation have a real world interpretation. Attrition processes are modeled as geometric Brow-nian motion and stopping rules of battles are modeled as decision boundaries. The theoretical combat equation is compared with historical combat attrition data from an ensemble of different battles and for the evolution of three single battles. The combat equation, with appropriate values of model parameters, agrees with the attrition data. The comparison is accomplished by calculating the probability of victory from the theory and from the empirical data.