#RockyReads for #Wargame – War by Numbers: Understanding Conventional Combat (Potomac Books, 2017)


War by Numbers is a book on modeling warfare. It is a summary of the work of The Dupuy Institute (TDI) and a call out to the wild that their studies of large-scale, conventional, attritional warfare is still relevant even in the age of “Small Wars.”


If you’ve been playing wargames as long as I have then you are undoubtably familiar with a Combat Results Table (CRT). You are also likely familiar with the classic 3:1 combat odds wherein if, as the attacker, you want to guarantee success in combat you always attack with odds of 3:1 or better.

Combat Results Table in Battle for Moscow (C3i Magazine Nr. 25) [Free download]

Where did this CRT come from? Well, you can thank an ORSA.

ORSA Defined

Operations research (also called operational research) began in World War II but really picked up steam in the 1960s under then-Defense Secretary Robert McNamara. He wanted to use systems analysis to make Pentagon decisions on force requirements, weapons systems, etc. This work built upon computerized combat models that had been introduced in the early 1950’s. The need for hard data to build the combat models upon yielded the need for somebody to collect this data. This is where Trevor Dupuy got started, and why today we have an ORSA.

ORSA is the acronym for the scientific field “Operations Research/Systems Analysis,” but ORSA is what many an “ORSA Analyst” simply call themselves. Here is how the US Army defines what an ORSA does:

ORSAs use analytical methods and mathematically based procedures to enable leadership decisions in a constantly changing global environment. [ORSAs] introduce quantitative and qualitative analysis to the military’s decision-making processes by developing an applying probability models, statistical inference, optimization, and economic models.


ORSAs integrate military knowledge and experience with the scientific and managerial fields. They serve as subject matter experts in designing forces, allocating resources, analyzing effects, performing course of action and trade off analysis, and they effectively communicate potential solutions to complex problems to decision makers.

The Deployed Analyst Handbook, CAA-2015094, p. 1-2

Wargamers, especially those engaged in professional wargaming through the design of analytic wargames, certainly sound like ORSAs. I’m sure there are ORSA who are wargamers. Don’t be fooled, however, for ORSAs thrive on building qualitative analysis on the back of a huge body of quantitative analysis. That quantitative analysis is the focus of War by Numbers.

War By the Numbers

War by Numbers is a look at historical conventional combat using the work of Trevor Dupuy (Col. USA (Ret.)) and The Dupuy Institute (TDI). The book showcases TDI’s quantitative analytical efforts by attempting to tie that work to a comprehensive theory of war. Although you will find studies on Force Ratio here that statistically bear out the 3:1 attacker-victorious thinking, the deeper studies look at what Dupuy termed “Human Factors” and how they contribute to the ultimate goal of a combat model; casualty estimation:

What are human factors? Trevor Dupuy listed them as morale, training, experience, leadership, motivation, cohesion, intelligence (including interpretation), momentum, initiative, doctrine, the effects of surprise, logistical systems, organizational habits, and even cultural differences. Human factors are hard to measure, and as such the analytical community often ignores them.

These factors, added together, made up what Dupuy called the combat effectiveness value (CEV). He could add this value to his combat model to try and represent the differences in relative performance of two opposing armies. For example, he used a force multiplier of 1.2 for instances when the German army faced the US Army in World War II in 1943-44. This indicated the German army (which, when lowercased here, indicates a combination of forces and not only the German Army proper) was 20 percent more effective, given that all other factors were equal. For the Eastern Front in World War II, we have tended to use a combat force multiplier of 3.0 to represent the difference between the German army and the Soviet Army in 1943. This is the same combat force multiplier Dupuy used to represent the differences between the Israeli Army in 1967 and 1973 and the various armies opposing it.

For any student of military history, to state that human factors are really important in warfare is stating the obvious. It is what enables attackers to win when outnumbered. It is what allowed the German army in 1943 to succeed in attacks at or greater than 1.91 to 1 while the Soviet Army still failed 44 percent of the time at those odds.

War by Numbers, p. 17

War by Numbers also takes a look at combat models by providing a historical overview and a bit of a deeper dive into TDI’s own QJM (Quantifiable Judgement Model) and TNDM (Tactical Numerical Deterministic Model).

Wargame Applications

War by Numbers is useful to wargamers, both professional and hobby, to better understand models of warfare, and especially to gain a better understanding of the mathematical foundations of combat adjudication models. Beware though, some designers might try to use the Dupuy’s TNDM, or what they see as the outputs of TNDM, as combat results. without fully understanding all the factors that go into the model. Further, there is a danger here in that too much dependence on the combat models advocated by TDI could push your wargames into the Modeling & Simulation arena. At the end of day what do you want to play, a simulation or a war game?


Lawrence, Christopher A., War by Numbers: Understanding Conventional Combat, Lincoln: Potomac Books, 2017

3 thoughts on “#RockyReads for #Wargame – War by Numbers: Understanding Conventional Combat (Potomac Books, 2017)

  1. This reminds me of the story about Charles Roberts, his invention of the “classic Avalon Hill CRT”, and a summons from the RAND corporation.
    Lance McMillan on BGG tells it better (https://boardgamegeek.com/thread/1762462/article/25709069#25709069)

    “The way I heard it (from Alan Emrich, who knew Charles Roberts and heard him speak on this subject) is that sometime in the early ’60s Roberts was “invited” by the FBI to come for an interview at RAND headquarters; they didn’t tell him the subject they wanted to discuss. When he got there he was grilled intensively for over an hour about how he’d come up with his now (in)famous 3:1 CRT. Apparently RAND had been working on a classified project for the Department of Defense and had spent (allegedly) over a million dollars coming up with a very detailed “scientific algorithm” to determine the outcome of various hypothetical combat scenarios. After roughly a year of secretive work, their hush-hush project had yielded a formula that produced results remarkably similar to those found on Robert’s 3:1 CRT. The “interview” was to find out who the “spy” was that had leaked that sensitive information to Roberts (remember, this was in the early ’60s and we were still deep in the depths of the Cold War — many were convinced there were commie agents hiding behind every shrub). Roberts was able to convince them that he’d simply extrapolated his CRT based off his reading military history. Then, while being escorted out of the building, Roberts glanced through a couple of open office doors and saw maps with hex grids super-imposed on them, which is where he said he got the idea to use hex grids for commercial wargames.

    The key here is that RAND wasn’t creating “wargames” for competitive play: they were designing them to fill a specific DoD requirement for a military analysis tool. Hobby/recreational wargames were a different creature entirely.”

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