Using Math to Defeat the Enemy

Preface

Many of the criticisms directed towards military simulations derive from an incorrect application of them as a predictive and analytical tool. The outcome supplied by a model relies to a greater or lesser extent on human interpretation and therefore should not be regarded as providing a ‘gospel’ truth. However, most game theorists and analysts generally understand this, it can be tempting for a layman—for example, a politician who needs to present a 'black and white' situation to his electorate—to settle on an interpretation that supports his preconceived position. Tom Clancy, in his novel Red Storm Rising, illustrated this problem when one of his characters, attempting to persuade the Soviet Politburo that the political risks of war with NATO were acceptable, used as evidence the results of a simulation carried out to model just such an event. It is revealed in the text that there were in fact three sets of results from the simulation; a best-, intermediate- and worst-case outcome. The advocate of war chose to present only the best-case outcome, thus distorting the results to support his case (Clancy, 1988).

There have been many charges over the years of computerized models being unrealistic and slanted towards a particular outcome. Critics point to the case of military contractors, seeking to sell a weapons system. For obvious reasons of cost, weapons systems (such as an air-to-air missile system for use by fighter aircraft) are modeled extensively on computers. Without testing of their own, a potential buyer must rely to a large extent on the manufacturer's own model. This might well indicate a very effective system, with a high kill probability (Pk). However, it may be the model was configured to show the weapons system under ideal conditions, and its actual operational effectiveness will be somewhat less than stated. The US Air Force quoted their AIM-9 Sidewinder missile as having a Pk of 0.98 (it will successfully destroy 98% of targets it is fired at). In operational use during the Falklands War in 1982, the British recorded its actual Pk as 0.78 (Allen T. B., 1987).

Human factors have been a constant thorn in the side of the designers of military simulations. Whereas political-military simulations are often required by their nature to grapple with what modelers refer to as "soft" problems, purely military models often seem to prefer to concentrate on hard numbers. While a warship can be regarded, from the perspective of a model, as a single entity with known parameters (speed, armor, gun power, and the like), land warfare often depends on the actions of small groups or individual soldiers where training, morale, intelligence, and personalities (leadership) come into play. For this reason, it is more taxing to model—there are many difficult-to-formulate variables. One valid criticism of some military simulations is these nebulous human factors are often ignored (partly because they are so hard to model accurately). Other perplexing issues include aggregation-disaggregation, communication networks, attrition, and end-game modeling.

“Using Math to Defeat the Enemy: Combat Modeling for Simulation” is intended to provide a foundation in the underlying combat modeling issues of military simulations. Of course, this is just a background, and a more rigorous treatment can be found in my book, Mathematical Modeling of Warfare and Combat Phenomenon (2011), Lulu.com, ISBN 978-1-4583-9255-8. Ultimately, this is a resource/reference book covering a wide gambit of military modeling issues.
This book is organized in two parts: Simulation (Part I) and Modeling (Part II). There are numerous practical applications and example models used in past and current military simulations.

This book is a result of about 25 years of use, application, research, and teaching military modeling and simulation. Much of the material in this book based on practical experience with modeling and simulation and extraction of my course notes from PowerPoint presentations.

Jeffrey S. Strickland, Ph.D.
CMSP, ASEP
President
Simulation Educators
Colorado Springs, Co
www.simulation-educators.com