An Examination of Force Ratios

A friend just pointed me to a recent 2019 paper done out at C&GSC at Leavenworth. It is called “An Examination of Force Ratios” and is by Major Joshua T. Christian. It is 37 pages. It is here: AD1083211.pdf (

A few notes

  1. “The nature of the inputs required for models such as the QJM or COFM mean that they are backwards looking, require numerous inputs, effort, and time to develop which limited their effectiveness to operational planners.”

Now, don’t know what he really means by the perjorative phrase ‘backwards looking,” but I will point out the TNDM (the upgraded version of the QJM) was used to predict the Gulf War, and these predictions were presented in testimony to the U.S. Congress and published in the book If War Comes, How to Defeat Saddam Hussien.” See: Assessing the TNDA 1990-91 Gulf War Forecast | Mystics & Statistics ( and Forecasting the 1990-1991 Gulf War | Mystics & Statistics (

2. The second section of the paper, “Origins of Force Ratios,” focuses on Lanchester equations. We have discussed this before: Lanchester equations have been weighed…. | Mystics & Statistics ( and TDI Friday Read: The Lanchester Equations | Mystics & Statistics ( and The Lanchester Equations and Historical Warfare | Mystics & Statistics ( and Presentations from HAAC – Fitting Lanchester Equations | Mystics & Statistics (

3. Page 13: Hate to nit pick, but peak strength in Vietnam was higher and earlier than what he states. There are a number of other such statements in this paper I could argue with, but will avoid doing that. See Vietnam War chart drawn from page 274 of America’s Modern Wars: Insurgency & Counterinsurgency | Mystics & Statistics | Page 4 ( 

4. Page 13: I also note the discussion on the 10-to-1 counterinsurgent versus insurgent ratio. Also see: Presentations from HAAC – Iraq, Data, Hypotheses and Afghanistan | Mystics & Statistics ( and Force Ratios and Counterinsurgency II | Mystics & Statistics ( and A Force Ratio Model Applied to Afghanistan | Mystics & Statistics ( Also, I do have a chapter on Vietnam in my book Modern American Wars.

5. Page 14: “This section highlights the work of operations research analysts, particularly those produced by the Historical Evaluation and Research Program (HERO), ad how it contributed to the Army’s transformation of the 1960s and 1970s.”

This is an odd statement. HERO was mostly historians. There were no OR people on staff, although people like Dr. Janice Fain, Robert McQuie and Dr. James Taylor were friends of Trevor Dupuy and provided independent inputs as friends and consultants. I was the first employee with some background in quantitative analysis of historical data (primarily from econometrics). It is part of the reason I was hired in 1987.

The idea that HERO “contributed to the Army’s transformation of the 1960s and 1970s” is jolting to me. All my experience is that in general, we tended to be ignored, downplayed or just dismissed. The Army’s support for what we do is clearly demonstrated by the low levels of funding that have been provided over the decades.

6. Page 15: “…establishing Dupuy as a prominent figure in the operational research field by the 1970s.”

There is little chance that MORS (Military Operations Research Society) will give him an award. See: Vance R. Wanner Memorial Award (

7. Page 26: Now he gets to discussing me. I will try to withhold commenting too much.

8. Page 27: “Lawrence utilized the Tactical Numerical Deterministic Model (TNDM), which succeeded the QJM, to conduct his analysis, and more specifically to determine the winner and loser of an engagement, assess personnel and equipment losses, and determine the rate of advance.

No, I did not.  I did not use the TNDM or any combat model for any of my analysis in the book. I did due a few simple statistical comparisons but did no combat modeling. He is not the first person to have made such mistake, which can only have come about by skimming my book (vice reading the whole thing) and then making false assumptions. I do have a chapter towards the end of the book that discuss some of the validation tests we ran using the TNDM, which is what seems to confuse people, but the TNDM was not used for any of the analysis in the book. He does correctly describe the validation tests of the model.

9. “As a result, the TNDM is more frequently used by companies to develop requirements that drive the development of hypothetical weapons more so than operation planners.”

Uh, no. We have done one report for Boeing on FCS that could be considered as such, but that is all, ever. See: Insurgency & Counterinsurgency | Mystics & Statistics | Page 4 (

10. Pages 31-32: In his discussion of insurgencies, it is clear has not seen my book America’s Modern Wars, or Dr. Andrew Hossack’s work or the work done by CAA on this using our databases (see pages 70-77 in America’s Modern Wars). He probably needs to. 

11. Page 33: I will not comment on his conclusions. A few relevant blog posts: Summation of Force Ratio Posts | Mystics & Statistics (


There are 34 references to Dupuy in the paper, 11 references to The Dupuy Institute, 8 references to me (I know, very vain of me), 8 references to Dr. Janice Fain, 15 references to HERO, 17 references to the QJM and 15 references to the TNDM.

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Christopher A. Lawrence
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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