Category War by Numbers

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 ambiguous, poorly 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 numbers. dupuyinstitute.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)

Another AI issue (#3)

My biggest issue with AI is not that it is going to take over the world (i.e. Terminator V?), it is that it makes mistake. AI makes simple factual errors because it lacks the ability to question and crosscheck. Now, granted a lot of people make the same type of mistakes, but if these “machines” are going to be better than us, they kind of need to quit making simple mistakes.

I have blogged about these mistakes before. here Khrushchev Quote and AI – The Dupuy Institute  and here Yahoo AI and order of battle for operations near Chernihiv in 2022 – The Dupuy Institute. It messed up a citation in the first case and it made an error in the order of battle in the second. The problem was that these mistakes were on the web (and AI does not seem to be able to do original research) and it picked up those errors. It does not appear to have the ability to weigh and discern the difference between contradictory data or look deeper into data that does not look right. It seems to have no ability to tell if the data does not look right. It does provide entertaining art though:  War by Numbers by AI – The Dupuy Institute.

Now an old friend of mind has found another error. In this case he was using AI to help with a wargame design. It provided the following note:

  • Even overwhelming invasions (e.g., the Great Heathen Army) suffered setbacks.

Your probability curve (14% at 1:1, 28% at 2:1, 42% at 3:1, etc.) mirrors the historical pattern that 3:1 is the threshold of likely success, a principle echoed in modern military theory (e.g., Dupuy, Numbers, Predictions, and War).

It actually referenced Numbers, Predictions, and War. Not sure if the AI could actually read it as it is not supposed to be available on the web (copyright is still active). But NPW does not actually address the 3-to-1 rule. Doesn’t even mention it (I do have a .pdf version I can search). Now, Trevor Dupuy does have a chapter on it in Understanding War, but it doesn’t really say that. We have blogged about this before:

  1. The U.S. Army Three-to-One Rule – The Dupuy Institute
  2. The Source of the U.S. Army Three-to-One Rule – The Dupuy Institute
  3. The U.S. Army Three-to-One Rule versus the 752 Case Division-level Data Base 1904-1991 – The Dupuy Institute
  4. The U.S. Army Three-to-One Rule versus 49 U.S. Civil War battles – The Dupuy Institute
  5. The U.S. Army Three-to-One Rule versus 243 Battles 1600-1900 – The Dupuy Institute
  6. People keep referencing us on the 3-to-1 Rule – The Dupuy Institute which references another eight links to the blog on the subject, including:
  7. Trevor Dupuy and the 3-1 Rule – The Dupuy Institute

Anyhow, we have talked about it a lot. It never seems to go away even though I think the military analytical community would be better served to never reference it again. I also have a chapter on force ratios in my book War by Numbers.

So, AI pulls up a rule that does not have much validity and then proceeds to give an incorrect reference to a book that never discusses it. Not encouraging.

E. B. Vandiver, long serving head of CAA, has passed away

E. B. Vandiver, known to everyone as “Van”, passed away this last week at the age of 87. He became the director of the Concepts Analysis Agency in 1984. I first briefed him in 1987 when I was leading the Ardennes Campaign Simulation Data Base (ACSDB). He retired from full-time work in 2012, promoted up to being “Director Emeritus.” CAA had now become the Center for Army Analysis and had moved to its own building in Fort Belvoir.

A bio: Edgar Bishop Vandiver III (born September 19, 1938), American operations research analyst | World Biographical Encyclopedia

I gather there will be services in Fairfax, VA on Wednesday, March 25.

Obituary: Edgar Bishop Vandiver III Obituary (1938-2026) | Fairfax, VA

As he was the head of the Army’s premier analytical office for almost 30 years, he had an impact on the army and its development from the 1980s, through the collapse of the Soviet Union, through the Iraq and Afghanistan wars and after. The head of CAA started as a major general slot back in 1973. Vandiver filled that role for 28 years. 

Past Directors:

  • MG Hal Hallgren January 1973 – February 1976
  • MG Ennis C. Whitehead Jr. April 1976 – May 1980
  • MG Edward B. Atkenson July 1980 – February 1982
  • Mr. David C. Hardison February 1982 – September 1984
  • Mr. E. B. Vandiver III September 1984 – November 2012
  • Dr. William Forrest Crain November 2012 – May 2020

Current Director: Dr. Steven Alexander Stoddard

Wikipeida article on CAA: Center for Army Analysis – Wikipedia

In his almost 30 years at CAA, he tended to make his impact through his management and direct conversation, as opposed to issuing papers and reports. I always found this oral history project done in 2005 to be of interest:

Military Operations Research Society (MORS) Oral History Project Interview of E.B. Vandiver, III, FS on JSTOR

Anyhow, we crossed paths a lot over the decades, although we did not know each other personally. The first major project I worked on, the ACSDB, was funded by CAA and regularly briefed to Van starting in 1987. The Kursk Data Base project I worked on was funded by CAA and was the source for four of my books (my fourth book on Kursk is coming out this fall). We were asked by him to do the Enemy Prisoner of Wars (EPW) studies and the three Urban Warfare studies among other projects. We ended up do the Iraq Casualty Estimate for him in 2004. That work is summarized in my book America’s Modern Wars. Certainly, half of my book War by Numbers was as a result of CAA funding. It was a productive relationship that lasted 22 years. Certainly his willingness to take me seriously when I first started working in this industry in 1987 and his willingness to continue taking me seriously after Trevor Dupuy passed away in 1995, went a long way in being able to do the work that I desired and in keeping The Dupuy Institute alive. 

My last conversation with him was in 2009 or so as the budget was in decline and there was little funding left. I did acknowledge him in several of my books. In the end, without Vandiver at CAA, I would not have had the career I had and could not have done the explorations that I did. He tended to provide budget and let us work the projects as we best felt. He always supported the value of historical research and historical analysis. He had a very significant impact on the community.

9 Books

Finally here is a picture of all nine of my published books. It includes two copies of The Battle for Kyiv, as one is the hardback and one is the paperback version. The paperback version does have some revisions and an expanded photo section.

We are looking to add two more books to that collection in the next six months. An additional book on the Russo-Ukrainian War should be out in the next 2 to 3 months, and The Battle of Tolstoye Woods should be out hopefully this spring. The editing process on all my books is slow, primarily because the large amount of charts, tables and tabular data in them that are a pain to edit and proof.

Two books

These two books are my two analytical books. Both quantitative in approach. Notice the use of the word “Understanding” in both titles.

American’s Modern Wars cover our analysis of insurgencies and counterinsurgencies based upon an analysis of 89 post-WWII cases. There has been very little quantitative analysis of insurgencies. This is the most extensive effort I am aware of. We were blessed with budget and a staff that at one point included ten people. It is amazing what you can do when you have manpower (read $$$).

War by Numbers is our analysis of conventional warfare. It was built from a series of studies we did over the years for the DOD and other contractors. Probably the most extensive qualitative analysis of aspects of conventional war that has been done in the last few decades. Again, helps to have budget.

These are my two “theoretical” books. I am halfway through a book called More War by Numbers. I have stopped work on it to concentrate on other tasks. May get back to in 2027.

The analysis for America’s Modern Wars was based upon 89 post-WWII insurgencies, interventions and peacekeeping operations. We did expand the database to well over 100 cases but never went back and re-shot the analysis due to budget cuts. It would be my desire to expand the database up to around 120 cases, update the 20 or so that were on-going (our data collection stopped in 2008). and then re-shoot and expand the analysis. This would be a good time to do this instead of again waiting until we are in another insurgency and yet again chasing our tail. Our track record on these have not been good, we lost Vietnam, we lost Afghanistan and Iraq was touch-and-go for a while. While we are not in the middle of another insurgency is a good time to study and learn about them based upon real world experience (AKA history).

Sorry to get preachy, but I really don’t like losing wars.

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

Leavenworth Master’s Thesis on “Forecasting Approaches in Operations Desert Sheild and Desert Storm

In 2020 Major Aaron F. Anderson, a student at the U.S. Army Command and General Staff College in Fort Leavenworth Kansas, published a master’s thesis called “Forecasting Approaches in Operations Desert Sheild and Desert Storm.” It was just sent to me.  I was not aware of it even though the author quoted my book War by Numbers extensively. It is referenced 19 times in the paper, so of course, I have a bias towards it.  Anyhow a link to the 45-page paper is here: Forecasting Approaches in Operations Desert Shield and Desert Storm

Paper’s abstract: 

The Closing of OSD Net Assessment

Turns out that OSD Net Assessment is being closed down. Pete Hegseth shutters Pentagon office that helped military leaders plan for possible future wars and Hegseth ‘disestablishing’ Office of Net Assessment, Pentagon’s strategic analysis specialists – Breaking Defense. Hegseth has instructed DOD to come up with a replacement organization “within 30 days.”

This was a small office in OSD (Office of the Secretary of Defense) that developed legendary status over the years: Andrew Marshall (foreign policy strategist) – Wikipedia

The Dupuy Institute did a number of contracts for Andy Marshall, specifically (see: TDI Reports – The Dupuy Institute)

1. SR-1 Soviet/Russian Influence on Chinese Military Doctrine (Jul. 2003).

2. SA-1: Measuring the Value of Situational Awareness (May 2004)

3. OSD-1: The Applicability of Classical Counterinsurgency Theory to Counterinsurgency Operations (Jan. 2008).

The original Iraq Casualty Estimate (Chapter 1 of America’s Modern Wars) that we did in 2004 was primarily funded by Andy Marshall. He contributed $75K based upon a phone call from Vandiver (CAA) and then CAA chipped in $20K, although CAA ran the project. I did brief Andy Marshall.

The office was funded with about $20 million a year. This supported maybe a dozen people and a budget of $12 or $13 million that he used to pay for various contracts (I accidently saw one of his big omnibus contracts). 

He retired in 2015 and an Air Force colonel that I did not know took over. They then issued out a giant omnibus contract which we bid on. They did not contract us.

OSD Net Assessment did an annual “net assessment” of the Soviet Union and Warsaw Pact. Apparently, his last net assessment was done in 1991. After that he focused on a range of issues, including orienting towards China and the RMA (Revolution in Military Affairs). Note that he funded our Situational Awareness report in 2004, which really did not provide overwhelming support for the RMA. It is two chapters in my book War by Numbers and I will be doing a briefing on it on 8 April at the Virtual Connections Conference.

That he was doing lots of analysis but no net assessments became an issue and at some point in the last decade, there were rumors that some of the JCS staff took over the net assessment function. I gather after he retired (he was in his 90s), the new guy was supposed to direct the department back to net assessment. So, I am not sure, but I gather there is now no real department in OSD that is doing net assessment. 

 

The Current Ukrainian Offensive

Ukrainian offensives do get my attention because I believe that to negotiate a peace settlement that does not permanently surrender 20% of their country Ukraine will probably need to start retaking some of that ground. They really have not reclaimed any more of their own territory since November 2022.

But they are on the offensive again. Curiously, just before the Trump inauguration. To quote twitter account @timkmak from yesterday (bolding is mine): (1) Tim Mak on X: “Here’s what we are reading today: Ukraine has launched a new offensive in Kursk region, the Russian Defence Ministry said. Ukrainian officials have indicated this is part of a larger operation. This follows territorial setbacks for Ukraine in the Kursk region in recent months. https://t.co/CEMHisnLqv” / X

“Ukraine has launched a new offensive in Kursk region, the Russian Defence Ministry said. 

Ukrainian officials have indicated this is part of a larger operation.

The follows territorial setbacks in Ukraine in the Kursk region in recent months.”

Other people are reporting that Ukraine has taken Berdin and has gone 2.7 kilometers past the Russian zero line (Def Mon on X: “Ukrainian forces likely went about 2.7km past the Russian zero line. https://t.co/WDFs2bGxZU” / X and Def Mon on X: “The developments in Kursk oblast looks something like this. We do not know if Ukraine managed to consolidate positions. We think we have geolocated UA units inside Berdin and Novosotnitskii. Geos: https://t.co/RNty0eKLQL https://t.co/ouerMmm9y4” / X).

Reports that this is a significant attack (“AT LEAST a 6 brigade attack): david D. on X: “im tracking about 10 “attacks” by ukr forces around kursk and north Belgorod. keep in mind that some will be real attacks, and some will be feints to draw in russian forces. russians are saying this is AT LEAST a 6 brigade attack… things will be clear later today expect” / X

There are reports of significant Russian losses (which must always be taken with a grain of salt): Chuck Pfarrer | Indications & Warnings | on X: “BURN RATE: In the last 48 hours in Kursk Oblast, the Russian army lost up a battalion of North Korean infantry and VDV paratroopers. Since AUG, Moscow has deployed 50K troops to Kursk Oblast: approximately 38K are assessed as killed, wounded, missing or surrendered.” / X. 

Some maps of the area:  Chuck Pfarrer | Indications & Warnings | on X: “UKRAINE’S KURSK OFFENSIVE: Latest from the BBC. https://t.co/QLSOk09HmP https://t.co/8xx9goK4kl” / X and Aurora Borealis 🤫 on X: “katsaps report the loss of the village of #Berdin, #Kursk region. https://t.co/QBeVLm9C81” / X and david D. (@secretsqrl123) / X and MAKS 24 🇺🇦👀 on X: “🔼🇺🇦 AFU managed to advance 8 km in the Kursk region, according to Russian voenkors. Map from ISW 🗺️👇👀 https://t.co/ebSfskuV9p” / X.

Anyhow, more to come, but all these reports must be taken with a grain of salt.

The Kursk offensive in August of 2024 was an interesting exercise but fundamentally did not retake any of their own territory and did not take enough of Kursk province to give them a lot they could trade off. It did not fundamentally change the situation on the ground, which is what was needed to give them advantage at the negotiation table. Unconditional surrender is very rare. Most wars end in a negotiated settlement.

The strength and loss figures being reported represent some fraction of reality. I do not know what that is (is it 1/10th or is it 9/10s?). I seriously doubt that the people posting these figures know that either, although some may indicate otherwise.

I was very disappointed in the failed Ukrainian offensive in early June 2023. For the sake of negotiating a positive resolution to the conflict, they really needed to take ground. I thought the Kursk offensive was a good stunt, but only that. Still, they have turned it into an extended fight that may yet yield dividends. If this offensive in Kursk is the start of a series of offensive that extend to Zaporizhzhia, Donetsk and Lugansk provinces, then this could become very significant. We shall see.

A key element in warfare is surprise (I do have a chapter on that in my book War by Numbers). If I can predict what Ukraine is going to do, that is not a good sign, as so to can the Russians. Therefore, if the Ukraine General Staff is doing their job right, they should be taking both Russian and me by surprise. That they appear to be doing.