The Wiener Path Integral Interpretation of the 3:1 Combat Rule

TL;DR

This paper introduces a Wiener path integral approach to model combat dynamics, incorporating stochastic effects to evaluate the empirical 3:1 combat rule and identify conditions affecting its validity.

Contribution

It develops a novel physics-inspired stochastic framework for combat modeling, extending Lanchester's law with probabilistic analysis and semi-analytical methods.

Findings

The 3:1 rule's validity depends on specific parameter regimes.

Numerical results highlight the importance of combat effectiveness ratios.

The framework bridges statistical mechanics and military operations research.

Abstract

The Wiener path integral framework is proposed to model military combat dynamics by incorporating the neglected stochastic effects to the Lanchester's square law. This framework is applied to evaluate the empirical 3:1 combat rule, which posits that an attacker requires a threefold force superiority to achieve victory. Specifically, the attacker's winning probability is computed utilizing a semi-analytical Rayleigh-Ritz method. Numerical results demonstrate that the validity of the rule critically depends on specific parameter regimes, primarily contingent upon the relative combat effectiveness ratio between the opposing forces and the tolerance for attrition. This work establishes a physics-informed theoretical bridge between statistical mechanics and military operations research for analyzing uncertain combat systems.