Damage functions and estimates of fratricide and collateral damage

There are multiple damage functions in the literature to estimate the probability that a single weapon detonation destroys a point target. This paper addresses differences in the tails of four of the more popular damage functions. These four cover the asymptotic tail behaviours of all monotonically decreasing damage functions with well-behaved hazard functions. The differences in estimates of probability of kill are quite dramatic for large aim-point offsets. This is particularly important when balancing the number of threats that can be engaged with the chances of fratricide and collateral damage. In general, analysts substituting one damage function for another may badly estimate kill probabilities in a offset-aiming, which could result in poor doctrine.