Category Dupuy’s Theory of Combat

AI and the 3-to-1 rule (AI issue #4)

My friend, affectionally known as Mr. Spock, decided to look at a little further. He asked Microsoft’s Copilot: “What evidence is there about Dupuy Institute claims concerning the relevance of a 3:1 ratio’s usefulness in military warfare?”

The short answer: The Dupuy Institute’s own research does not support the idea that the 3:1 ratio is a universally valid or predictive rule of warfare. Their empirical battle databases show that attackers often win with less than 3:1, that 3:1 is rarely achieved, and that the rule itself is conceptually ambiguous. The Institute’s founder, Trevor N. Dupuy, explicitly criticized the rule’s usefulness.

Now this does contradict the previous AI answer on the subject: Another AI issue (#3) – The Dupuy Institute

It did provide a “structured, evidence-driven breakdown”

Core Evidence From Dupuy Institute Sources

1. Dupuy’s empirical critique of the 3:1 rule

Trevor Dupuy argued that the 3:1 rule is ambiguouspoorly defined, and unsupported as a universal planning factor. He questioned what “3:1” even refers to—men, weapons, firepower, or some other measure—and emphasized that context matters more than raw numbersdupuyinstitute.dreamhosters.com

He wrote that neither numbers nor firepower “tells us much unless we know the circumstances under which these numbers face each other and the manner in which the firepower is applied.” dupuyinstitute.dreamhosters.com

2. Historical battle database results (HERO/CAA study)

Dupuy’s Historical Evaluation Research Organization (HERO) compiled 598 battles (1600–1973). The U.S. Army Concepts Analysis Agency analyzed these data and found:

  • Attackers with ≥3:1 manpower succeeded 74% of the time.
  • Attackers with between 1.5:1 disadvantage and <3:1 advantage still won 58–63% of the time.
  • Only 17.7% of battles** even achieved a 3:1 manpower advantage.** dupuyinstitute.dreamhosters.com

Implication:
3:1 improves odds but is not required for success, and most real battles do not meet it.

3. Dupuy’s own clarification in Understanding War

In a 1989 correspondence responding to critics, Dupuy clarified that he did not endorse the 3:1 rule as a reliable predictor. He called it a “crude rule of thumb” used by planners, not a validated law of combat. JSTOR

He emphasized that the rule’s basis is only that “in historical instances an attacker with such an advantage has usually been successful”—a generalization, not a principle. JSTOR

4. Modern Dupuy Institute commentary (Christopher A. Lawrence)

Current TDI leadership continues to stress that:

  • The 3:1 rule is frequently misunderstood.
  • Their data shows wide variation in outcomes at all force ratios.
  • Human factors, posture, terrain, and operational conditions often outweigh raw ratios. The Dupuy Institute

Lawrence points readers to Understanding War and War by Numbers, both of which show that force ratios alone are weak predictors of outcomes.


🧭 External scholarly reinforcement

5. U.S. Army monograph: An Examination of Force Ratios

A 2019 Army thesis reviewing Dupuy and others concludes that force ratios are often invalid as planning heuristics and may create “unwanted mental constraints.” apps.dtic.mil

This aligns with Dupuy’s own empirical findings.


🎯 Synthesis: What the Evidence Shows

What is supported?

  • A 3:1 manpower advantage does correlate with higher attacker success rates.
  • It is a useful very rough heuristic for planners.

What is not supported?

  • That 3:1 is necessary for success.
  • That 3:1 is a universal predictor across eras, terrains, or force types.
  • That 3:1 is meaningful without specifying what is being measured (men, firepower, combat power).
  • That 3:1 is commonly achievable in real operations.

Dupuy Institute’s bottom line:

The 3:1 rule is not a validated law of combat, but a simplistic planning rule whose predictive value collapses under empirical scrutiny.


 

In the end its sources are two articles on this blog, a response Trevor Dupuy wrote in 1989 in response to a question about his 1987 book Understanding War, and a masters-degree-level thesis prepared at C&GS. It interestingly and somewhat significantly did not reference Trevor Dupuy’s book Understanding War which has a chapter on the subject or my book War by Numbers which has a chapter on force ratios.

Now, why isn’t it referencing these sources, which are probably where I would start if I was researching this subject? Well, they are published books and still under the 70 year copyright rule.  So you can look at a copy at your local library, but AI cannot reference or read it. It is not available as a download file on the internet, therefore they appear to not exist. This means that AI has a 70-year blind spot, in that it cannot reference or review anything written in the last 70-years unless someone re-posts elements to the internet. This is what is did with Trevor Dupuy’s book Understanding War.  In this effort (which was fine), it mostly used blog posts written by me or Shawn Woodford.

I am not sure how this works, but if I get hit by a bus, and am no longer able to pay the annual fees to maintain this blog, then I gather this knowledge will disappear from the internet and from AI’s access.  

This is now the fourth issue I have had with AI (not that I am using it much). I have blogged about them:

1. Khrushchev Quote and AI – The Dupuy Institute
2. Yahoo AI and order of battle for operations near Chernihiv in 2022 – The Dupuy Institute
3. Another AI issue (#3) – The Dupuy Institute
4. This blog post (AI Issue #4)

Report #81: Soldier Capability

We have had report number #81 available on our website for a while. It is on “Soldier Capability: Army Combat Effectiveness (SCACE): Historical Combat Data and Analysis (1980) (Battelle). See: HERO/TNDA Reports – The Dupuy Institute

The link to the report is here: 081.pdf

It is also available on line through DTIC. It is the same report with a different cover: Soldier Capability – Army Combat Effectiveness (SCACE). Volume 3. Historical Combat Data and Analysis.

Not sure I have anything else other to say about this other than to note that some (but not all) of our reports are available through DTIC or NTIS.

Europe’s Choice: Military and Economic Scenarios for the War in Ukraine

This paper just released by CORISK and the Norwegian Institute of International Affairs (NUPI) is definitely worth taking a look at.

English language version: 2025 Europes choice_FINAL_251125_174147

There are eight references to Dupuy’s work and one to War by Numbers, so it definitely holds our interest. The chapters in the report are:

  1. Military Scenarios and their costs
  2. Introduction
  3. Political analysis
  4. The Scenario
  5. Humanitarian analysis
  6. Military analysis
  7. Economic analysis
  8. Costs and conclusions
  9. Sources
  10. Appendix A – Extended model for calculating combat power
  11. Appendix B – Method for calculating average loss of Russian material

Definitely take a look at this. 

 

P.S. Official link: Publikasjoner

And in Norwegian: To scenarier for krigen i Ukraina: Hva betyr de for Europa – og hva vil det koste? | NUPI

Books and public sources that describe the QJM and TNDM

The QJM (Quantified Judgment Model) and TNDM (Tactical Numerical Deterministic Model are two combat models that Trevor Dupuy developed first in 1977 as the QJM, and then heavily revised and released in 1990 at the TNDM. We do sell a computerized version of the TNDM along with manuals and training courses but at a price out of reach for most individuals. See: TNDM & QJM – The Dupuy Institute

Now, I do regularly get enquiries about the model. The combat models are described in a half-dozen books.

1.  The first version of the combat model, the QJM, is fully described in Trevor Dupuy’s book Numbers, Predictions and War (1977). You may have to fish around for it, it is not in print. I see a used version for sale on Amazon.com for $77.59 and $89.95.
2. The theoretical discussions that come from his work is described in his book Understanding War (1987). This is the most significant book written by Trevor Dupuy and should be in every serious military analyst’s library. Amazon.com has a used copy for $15.89. We have new copies for $24.95: Understanding War: History and Theory of Combat – The Dupuy Institute and Ordering Information – The Dupuy Institute. An earlier theoretical book, Evolution of Weapons and Warfare (1980) is available on Amazon.com for $19.96.
3. The new model, the TNDM, was created in 1990. It is described in two books, Attrition (1990) and If War Comes (1991). Both are out of print. Attrition is for sale on Amazon.com for $123.10. I tried to warn you:  We our down to our last 16 copies of Attrition – The Dupuy Institute. If War Comes is not on Amazon.com (even though it was on the Times best-sellers list).  His father’s books, written in 1938 is available for $15.55 paperback and $30.00 hardcover. Trevor Dupuy’s book is available on Ebay for $45.95.
4. Some quantitative analysis of combat and a little on the TNDM is described in my book War by Numbers (2017). That book is still in print and available in Amazon.com for $37.15 (list price 39.95). It is rated at 4.7 out of 5 on Amazon.
5. Now there were a lot of reports and studies does to develop these combat models. They include:
6. There were also a dozen “International TNDM Newsletters” prepared when we were working various support contracts for the TNDM. They are here:  TNDM Newsletter – The Dupuy Institute
7. Finally, it is discussed in our blog: Mystics & Statistics – The Dupuy Institute. Specifically if you search on our blog categories “TNDM”: TNDM – The Dupuy Institute or “Modeling, Simulation & Wargaming”: Modeling, Simulation & Wargaming – The Dupuy Institute or “casualty estimation”:  Casualty estimation – The Dupuy Institute or “Dupuy’s Theory of Combat”: Dupuy’s Theory of Combat – The Dupuy Institute
8. Finally, it was discussed in our now inactive Forum: The Dupuy Institute Forum – powered by Infopop
 
Hopefully, that should answer a lot of enquiries.
 

Dupuy’s Verities vs the Russo-Ukrainian War

So, we have had almost three full years of conventional war in and around Ukraine. Back in the 1970s- 1980s Trevor Dupuy assembled a list of factors (or verities) that influence and describe conventional combat. They covered combat in three different areas. They were 1) The Timeless Verities of Combat (13 verities), 2) Combat Attrition Verities (29 verities), and 3) Combat Advance Rates (15 verities).

They are listed below in these three posts:

The Timeless Verities of Combat – The Dupuy Institute

Trevor N. Dupuy’s Combat Attrition Verities – The Dupuy Institute

Trevor Dupuy’s Combat Advance Rate Verities – The Dupuy Institute

They are listed in detail in my book War by Numbers, although I edited a few for brevity.

They are listed in detail in Trevor Dupuy’s 1987 book Understanding War. They are also listed in his 1980 book Evolution of Weapons and Warfare.

They have been around for a while. I think they are a significant list and of course have been coded into his combat models the QJM and TNDM, which actually have proven track record of making good predictions. I do think they have been underutilized and underappreciated by the wider defense community.

Anyhow, my questions for the community that reads our blog is:

1. Which of these verities have been re-confirmed by war in Ukraine?, and
2. Which of these verities have been called in doubt by the war in Ukraine?

Interested to see the responses.

 

 

 

P.S. Some related links:

TDI Friday Read: Principles Of War & Verities Of Combat – The Dupuy Institute

Dupuy’s Verities: Offensive Action – The Dupuy Institute

Dupuy’s Verities: The Power Of Defense – The Dupuy Institute

The Combat Value of Surprise – The Dupuy Institute

Dupuy’s Verities: The Utility Of Defense – The Dupuy Institute

Dupuy’s Verities: Initiative – The Dupuy Institute

Dupuy’s Verities: Fortification – The Dupuy Institute

Dupuy’s Verities: The Advantage Of The Offensive – The Dupuy Institute

Dupuy’s Verities: The Requirements For Successful Defense – The Dupuy Institute

A Comment On The Importance Of Reserves In Combat – The Dupuy Institute

Dupuy’s Verities: Surprise – The Dupuy Institute

Dupuy’s Verities: The Effects of Firepower in Combat – The Dupuy Institute

Dupuy’s Verities: The Inefficiency of Combat – The Dupuy Institute

Dupuy’s Verities: Combat Power =/= Firepower – The Dupuy Institute

Dupuy’s Verities: The Complexities of Combat – The Dupuy Institute

Response to Question on Dupuy’s Combat Attrition Verities – The Dupuy Institute

Average Losses per Day in Division-level Engagements on the Eastern Front in 1943 – The Dupuy Institute

People keep referencing us on the 3-to-1 Rule – The Dupuy Institute

Last Six Blog Posts – The Dupuy Institute

Shout out to Echoes of Past – The Dupuy Institute

These are all the posts you get if you click on the category “Dupuy’ Verities”:  Dupuy’s Verities – The Dupuy Institute

Shout out to Echoes of Past

I do want to make a shout out to Echoes of Past who keeps posting quotes by my book War by Numbers and from Trevor Dupuy’s books. His twitter account is here: Echoes of Past (@EchoesofpastX) / X

This includes: Echoes of Past on X: “4/5 “We can still lose this war. . . . The Germans are colder and hungrier than we are, but they fight better. —GEN. GEORGE S. PATTON, January 4, 1945, in Dupuy et al., Hitler’s Last Gamble” (Christopher A. Lawrence, War by Numbers) @dupuyinstitute https://t.co/fcgMxVkEV0″ / X

and: Echoes of Past on X: “”#Combat is too complex to be described in a single, simple #aphorism.” (Christopher A. Lawrence, #War by Numbers) https://t.co/kioG46QbI2″ / X

and from our blog: Echoes of Past on X: “#Ukraine #Kursk operation does three things for them: 1. Propaganda value. 2. Ukraine 🇺🇦 captured over 100 Russian prisoners which they can later exchange. Ukraine had thousands captured in 2022 & have never held enough Russian prisoners to exchange for people Russia holds. https://t.co/SWHSFkoSLn” / X

and: Echoes of Past on X: “War by Numbers assesses the nature of conventional warfare through the analysis of historical combat. Christopher A. Lawrence establishes what we know about conventional combat and why we know it. ⁦@dupuyinstitute⁩ https://t.co/Gryxkdtvho” / X

and: Echoes of Past on X: “Depressing insight for Tank Enthusiasts from book “War by Numbers” by Christopher A. Lawrence. Tank loss rates are 5-7 times higher than personnel casualties in combined arms engagements. #WarByNumbers #ArmoredForces #MilitaryStrategy @dupuyinstitute https://t.co/d5WWTuH3bT” / X

and: Echoes of Past on X: “@AmosFox6 @dupuyinstitute Hi Amos, it will be an excellent opportunity to hear him. I just finished one of his classics “War by Numbers”. Sharing few insights and I will be building it further. You may bookmark 🔖 it.👇” / X

and: Echoes of Past on X: “According to Christopher A. Lawrence in War by Numbers, the expenditure of artillery ammunition in urban operations is not significantly greater than in nonurban operations. 🏙️ #UrbanLogistics #MilitaryOperations #WarfareStudies https://t.co/mXBHvEHFDr” / X

and: Echoes of Past on X: “@vtchakarova 5/n Casualty rates are higher for small forces vs. large forces. Theodore Dodge noted this trend nearly 100 years ago. Size matters in battle 🛡️ #militaryhistory #warfare #smallvslargeforces https://t.co/jjLil3rKbM” / X

and: Echoes of Past on X: “@vtchakarova 4/n According to Christopher A. Lawrence in War by Numbers, the expenditure of artillery ammunition in urban operations is not significantly greater than in nonurban operations. 🏙️ #UrbanLogistics #MilitaryOperations #WarfareStudies https://t.co/NrINYgN5qd” / X

and: Echoes of Past on X: “3️⃣/n In warfare, combat effectiveness plays a crucial role in inflicting casualties. The Germans in WWI and WWII, as well as the Israelis in the Arab-Israeli wars, showcased higher casualty-inflicting rates. 💥 #warfare #combat #effectiveness Pic 2 :@vtchakarova https://t.co/WQR8JwwPfU” / X

and: Echoes of Past on X: “2/n Historical fortifications like Maginot Line, Mannerheim Line, Siegfried Line, & Bar Lev Line were overcome not due to their failure, but because of a powerful relentless effort. It’s important to recognize context, rather than jumping to conclusions. https://t.co/nV3bxn1KSD https://t.co/ywrGBhFvNP” / X

and: Echoes of Past on X: “1️⃣st thought from “War by Numbers” by Christopher A Lawrence Tank loss rates are 5 to 7 times higher than personnel casualty rates. This applies to combined arms engagements in which armored forces make up a substantial proportion of fighting strength on one or both sides. https://t.co/Dshm8nopA4” / X

and: Echoes of Past on X: “Casualty rates are higher for small forces vs. large forces. Theodore Dodge noted this trend nearly 100 years ago. Size matters in battle 🛡️ #militaryhistory #warfare #smallvslargeforces @dupuyinstitute @WarMonitors @WarintheFuture @AmosFox6 @VertigoWarrior @warmatters https://t.co/IJHwBVdcrO” / X

 

Also a shout out to Mountain Navy: Mountain Navy 🎲🗺⚔️ on X: “Usually think of Lawrence @dupuyinstitute as Mr. “Tanks at Kursk” so this new #militaryhistory #book looks to be an interesting adjacent read. https://t.co/v7XyyGT6tc” / X

and Robert Gilbey: Robert Gilbey on X: “‘The Battle for Kyiv’ by Christopher A. Lawrence from the @dupuyinstitute This is a very insightful & indifferent analysis of the opening invasion of Ukraine, leveraging metrics from OSINT & official sources it breaks down the context, actions & effects of combat ops around Kyiv https://t.co/OMX5C6kYL6” / X

and Amos Fox: Amos Fox on X: “Part I of my conversation with Chris Lawrence from the @dupuyinstitute. Part II drops tomorrow. After that the Revolution in Military Affairs podcast will take a 4 week break. https://t.co/fTCrKkoes6” / X

and Mark Galeotti: Mark Galeotti on X: “I then look at 4 books to help explain Russian adaptation: 1. Christopher Lawrence of @dupuyinstitute, The Battle for Kyiv (@Frontline_Books), useful for insights into the various forms of military capability 2/” / X

and Paul Poast: Paul Poast on X: “To identify war outcomes, Stam’s study drew on military histories, notably the encyclopedic volume by Dupuy & Dupuy (cc @dupuyinstitute). https://t.co/oGJR4ZZuNQ” / X

 

I am sure there are a few I missed this year. Only two of these people are known to me. Sorry for anyone I have missed.

 

We have sold out of Attrition

Attrition: Forecasting Battle Casualties and Equipment Losses in Modern War is no longer for sale by The Dupuy Institute. We sent out our last two copies last week. We still hold copies of everything else listed here: Books – The Dupuy Institute

If you want Attrition, it is available on Amazon.com, but at a hefty price of $180: Attrition: Forecasting Battle Casualties and Equipment Losses in Modern War: Dupuy, Trevor N.: 9780963869234: Amazon.com: Books. We sold our copies for $19.95.

There is little chance we will publish it again. The rights are held by the Dupuy family, not us. We sold 54 copies over the course of 9 years. This hardly justifies a new print run.

You were warned: We our down to our last 16 copies of Attrition – The Dupuy Institute. We did sell those 16 copies in 9 months.

Definition of Limited War

Just for the record, here is the definition of a “limited war” from The Dictionary of Military Terms, by Trevor N. Dupuy, Curt Johnson and Grace P. Hayes (1986). page 137.

Limited war – 1) A war looked upon by one or more of its contestants as not involving its own sovereignty or most vital interests, and as being limited in at least one respect, as, for example, to a particular geographic area, to the employment of certain resources, or to the number of contestants. 2) A war considered by a detached observer as relatively limited in some key respect, especially with regard to political objectives. 
 

This is still the best dictionary of military terms out there. Vastly superior to what is published by the Pentagon.  

People keep referencing us on the 3-to-1 Rule

Several people in their articles have referenced a 3-to-1 rule and then reference us as the source. The latest example is in a German article on Taiwan: Storming Taiwan by force of arms? | Telepolis

Of course, we are the people who are saying the 3-to-1 rule is really not correct. They obviously do not read that far.

This is the reference they use: The Source of the U.S. Army Three-to-One Rule – The Dupuy Institute. My final sentence in that article is “Are we training the next generation of George B. McCellans?”

 

Various links related to the 3-to-1 rule:

Trevor Dupuy and the 3-1 Rule – The Dupuy Institute

The U.S. Army Three-to-One Rule – The Dupuy Institute

The 3-to-1 Rule in Histories – The Dupuy Institute

The 3-to-1 Rule in Recent History Books – The Dupuy Institute

The U.S. Army Three-to-One Rule versus 243 Battles 1600-1900 – The Dupuy Institute

The U.S. Army Three-to-One Rule versus 49 U.S. Civil War battles – The Dupuy Institute

The U.S. Army Three-to-One Rule versus the 752 Case Division-level Data Base 1904-1991 – The Dupuy Institute

Summation of Force Ratio Posts – The Dupuy Institute

JSTOR, Trevor Dupuy, Combat Data and the 3:1 Rule – The Dupuy Institute

The 3:1 Ratio – The Dupuy Institute

Army- and Division-level force ratio posts – The Dupuy Institute

The 3-to-1 rule and the War in Ukraine – The Dupuy Institute

We have been talking about this for a while. It appears that some people are not listening.