Talking Force Ratios Once Again

I guess we need to talk about force ratios once again. Not sure why. This has been discussed in depth by us. It was discussed in Trevor Dupuy’s Understanding War and was discussed in my book War by Numbers. But let me start first with some Clausewitz quotes:

In tactics, as in strategy, superiority of numbers is the most common element in victory.


If we thus strip the engagement of all the variables arising from its purpose and circumstance, and disregard the fighting value of the troops involved (which is a given quantity), we are left with the bare concept of the engagement, a shapeless battle in which the only distinguishing factors is the number of troops on either side.

These numbers, therefore, will determine victory. It is, of course, evident from the mass of abstractions I have made to reach this point that superiority of numbers in a given engagement is only one of the factors that determines victory. Superior numbers, far from contributing everything, or even a substantial part, to victory, may actually be contributing very little, depending on the circumstances.

But superiority varies in degree. It can be two to one, or three or four to one, and so on; it can obviously reach the point where it is overwhelming.

In this sense superiority of numbers admittedly is the most important factor in the outcome of an engagement, as long as it is great enough to counterbalance all other contributing circumstance. It thus follows that as many troops as possible should be brought into the engagement at the decisive point.

and also:

Numerical superiority was a material factor. It was chosen from all elements that make up victory because, by using combinations of time and space, it could be fitted into a mathematical system of laws. It was thought that all other factors could be ignored if they were assumed to be equal on both sides and thus cancelled one another out. That might have been acceptable as a temporary device for the study of the characteristics of this single factor; but to make the device permanent, to accept superiority of numbers as the one and only rule, and to reduce the whole secret of the art of war to a formula of numerical superiority at a certain time and a certain place was an oversimplification that would not have stood up for a moment against the realities of life.

OK…in its most basic form, combat power is numbers x equipment x human factors x conditions of combat (including posture, terrain, weather, surprise, etc.). Nothing earthshaking here, but this often gets lost in the discussion. 

In Trevor Dupuy’s Understanding War, which is his most significant work, he has Chapter 3: Clausewitz’s Theory of Combat, which has a section on “The Law of Numbers.” and Chapter 4: “The Three-to-one Theory of Combat.” These are worth reading.

My book War by Numbers covered some of the same ground. Chapter Two is called “Force Ratios.”

An article from the Wall Street Journal was published on Friday that addressed this subject, somewhat incompletely: The author did reach out to me by email on 27 April, but I don’t check that mail box that often, so never got back to him in time for the article.

I am not going to discuss or debate this article, but instead point out that this has been discussed before. So not sure why we are back drinking from the same well using the same tables that we know are not correct. In particular I am talking about the table from the U.S. Army’s COFM (Correlation of Forces and Means).

This is discussed in this blog post: How Does the U.S. Army Calculate Combat Power? ¯\_(ツ)_/¯ | Mystics & Statistics (

Table in question is here:

A copy of the COFM is here: COFM. Do not know if this is the most current or recent version, nor do I care, because it is flawed.

We have discussed this many times before. See: How Does the U.S. Army Calculate Combat Power? ¯\_(ツ)_/¯ | Mystics & Statistics ( and TDI Friday Read: The Validity Of The 3-1 Rule Of Combat | Mystics & Statistics ( and Summation of Human Factors and Force Ratio posts | Mystics & Statistics ( and Summation of Force Ratio Posts | Mystics & Statistics (

The COFM is called out five times in the ATP 5-0.2-1 Staff Reference Guide. The guide is discussed here: Staff Reference Guide | Mystics & Statistics (

Other people have also discussed this:  

1993: Correlation of Forces: The Quest for a Standardized Model by Major David Hogg: Correlation of Forces. Note that the COFM table is quote in figure 1 in this paper.

2007 or later: Demystifying the Correlation of Forces Calculator: They reference the paper above by LTG (then Major) David Hogg.

2019: An Examination of Force Ratios: This last paper actually references my book War by Numbers.

This entry was posted in Modeling, Simulation & Wargaming, War by Numbers by Christopher A. Lawrence. Bookmark the permalink.

About Christopher A. Lawrence

Christopher A. Lawrence is a professional historian and military analyst. He is the Executive Director and President of The Dupuy Institute, an organization dedicated to scholarly research and objective analysis of historical data related to armed conflict and the resolution of armed conflict. The Dupuy Institute provides independent, historically-based analyses of lessons learned from modern military experience. ... Mr. Lawrence was the program manager for the Ardennes Campaign Simulation Data Base, the Kursk Data Base, the Modern Insurgency Spread Sheets and for a number of other smaller combat data bases. He has participated in casualty estimation studies (including estimates for Bosnia and Iraq) and studies of air campaign modeling, enemy prisoner of war capture rates, medium weight armor, urban warfare, situational awareness, counterinsurgency and other subjects for the U.S. Army, the Defense Department, the Joint Staff and the U.S. Air Force. He has also directed a number of studies related to the military impact of banning antipersonnel mines for the Joint Staff, Los Alamos National Laboratories and the Vietnam Veterans of American Foundation. ... His published works include papers and monographs for the Congressional Office of Technology Assessment and the Vietnam Veterans of American Foundation, in addition to over 40 articles written for limited-distribution newsletters and over 60 analytical reports prepared for the Defense Department. He is the author of Kursk: The Battle of Prokhorovka (Aberdeen Books, Sheridan, CO., 2015), America’s Modern Wars: Understanding Iraq, Afghanistan and Vietnam (Casemate Publishers, Philadelphia & Oxford, 2015), War by Numbers: Understanding Conventional Combat (Potomac Books, Lincoln, NE., 2017) , The Battle of Prokhorovka (Stackpole Books, Guilford, CT., 2019), The Battle for Kyiv (Frontline Books, Yorkshire, UK, 2023), Aces at Kursk (Air World, Yorkshire, UK, 2024), Hunting Falcon: The Story of WWI German Ace Hans-Joachim Buddecke (Air World, Yorkshire, UK, 2024) and The Siege of Mariupol (Frontline Books, Yorkshire, UK, 2024). ... Mr. Lawrence lives in northern Virginia, near Washington, D.C., with his wife and son.

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