Mass action models of Falklands War battles

Brandon Malcolm Pincombe, Adrian Hall Pincombe


We develop a dataset describing variables associated with six Falklands War battles: combatant numbers; deaths; temporal aspects; and offensive support. Linear relationships between battle duration and deaths necessitate using force and loss ratios to remove temporal variation. Mass action models of battle attrition fit this dataset poorly (at best coefficient of determination \(R^{2}=0.10\)). The low level rules in simulations used by military force designers frequently share assumptions with, or are, mass action models. Errors in force balance or constitution are dangerous so exposing problems with and exploring improvements on existing combat models is important. While six data points are too few for a thorough analysis, our results are consistent with: a linear relationship between time in danger and number killed; different times in danger for the two sides, dependent on detection and lethality ranges; and data substructure, even when temporal aspects are removed through ratio models. This data substructure indicates at least one extra variable needs to be considered. We contend that this variable is related to suppression, and this contention is not falsified by the high use of offensive support in the most successful attacks. Mathematical modellers should consider cancelling out temporal variation in combat datasets through ratio models and/or exploring the effects of mutable detection and lethality ranges. Suppression is an attempt to manage exposure to death, to introduce non-stationarity and irregularity into the dataset to benefit the suppressor, to change the bounds of the system using a soft controller; we should investigate how to model it. Force designers should ask simulation modellers whether the mathematical models underlying their simulations represent suppression accurately (or at all) and rethink reductions of simultaneously delivered offensive support available on demand based on models ignoring suppression.

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mass action models; model testing; combat modelling; combat data

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