On weapons scores and force strengths

Quantitative comparisons of the combat forces on two opposing sides are virtually always formed as follows. First, all of the resources on each of the two sides are grouped into a set of categories. Each of the resources in each category is assigned a (nonnegative) value or score, where these scores are constant within categories, can vary across categories, and can be functions of the numbers and effectiveness parameters of the resources on both sides. These categories need not be the same for the two sides. Force strengths are then formed for each side by summing, over all of its categories, the product of the number of resources in each category times the score given to the resources in that category. Quantitative comparisons of the two forces are then calculated using (real-valued) functions of these strengths and, perhaps, of exogenous input parameters. Thus, such force comparisons depend on the number and effectiveness of the weapons in the forces only through these force strengths. Accordingly, if this type of quantitative comparison of the forces on two opposing sides is desired, then it is reasonable to consider the questions of how to calculate scores for the resources of each type, and of how to combine the resulting scores to form force strengths that can be used to calculate measures of the relative effectiveness of the forces involved. This article addresses these questions.