The law of effecting targets and the function of victory in fight (battle, operations)

Having taken the law of target defeat of A. N. Kolmogorov as a basis and using the methods of probability theory, the transition from the models of application of individual and group weapons to the aggregated model of combat (battle, operation) is carried out. The victory function is one of the varieties of conflict functions, satisfies the axioms of S. Skaperdas and belongs to the class of models based on the relationship between the potentials of the parties. The scale parameter of the victory function is estimated according to the data of military statistics and substantively. It is shown that the uncertainties of the outcome of combat operations are significantly reduced when moving from the tactical level to the operational level, and from the operational level to the strategic level. The concept of a combat unit, which is basic in the theory of combat potentials, has been clarified. The justified victory function allows to analyze multi-scale combat actions from a unified position and is designed to solve the following problems: firstly, the assessment of combat capabilities of the parties in the preparation of combat actions, secondly, justification of the main elements of the commander's (commander's) plan for combat actions (determination of the directions of the main strike and concentration of the main forces as a result of solving game-theoretic problems), thirdly, justification of the composition and appearance of prospective combat formations.