The 3-to-1 Rule in Histories

I was reading a book this last week, The Blitzkrieg Legend: The 1940 Campaign in the West by Karl-Heinz Frieser (originally published in German in 1996). On page 54 it states:

According to a military rule of thumb, the attack should be numerically superior to the defender at a ratio of 3:1. That ratio goes up if the defender can fight from well developed fortification, such as the Maginot Line.

This “rule” never seems to go away. Trevor Dupuy had a chapter on it in Understanding War, published in 1987. It was Chapter 4: The Three-to-One Theory of Combat. I didn’t really bother discussing the 3-to-1 rule in my book, War by Numbers: Understanding Conventional Combat. I do have a chapter on force ratios: Chapter 2: Force Ratios. In that chapter I show a number of force ratios based on history. Here is my chart from the European Theater of Operations, 1944 (page 10):

Force Ratio…………………..Result……………..Percentage of Failure………Number of Cases

0.55 to 1.01-to-1.00…………Attack Fails………………………….100……………………………………5

1.15 to 1.88-to-1.00…………Attack usually succeeds………21…………………………………..48

1.95 to 2.56-to-1.00…………Attack usually succeeds………10…………………………………..21

2.71 to 1.00 and higher….Attack advances……………………..0…………………………………..42

 

We have also done a number of blog posts on the subject (click on our category “Force Ratios”), primarily:

Trevor Dupuy and the 3-1 Rule

You will also see in that blog post another similar chart showing the odds of success at various force ratios.

Anyhow, I kind of think that people should probably quit referencing the 3-to-1 rule. It gives it far more weight and attention than it deserves.

 

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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.
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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.
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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).
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Mr. Lawrence lives in northern Virginia, near Washington, D.C., with his wife and son.

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3 Comments

  1. I think the 3-1 rule is one of the most strange “rules” I have ever encountered.
    That kind of “rule” could potentially be true if it was formulated as “if everything else is equal, the side with a 3-1 superiority wins”. However, in war “everything else” is hardly ever equal, which would make the rule hard to apply.
    But even if it would be more common, success can often not be judged as “winning” or “losing”. Rather, we are better served by regarding outcome in battles and operations as continuous variables.
    From a philosophical point of view, it is easy to refute the “rule”. Of course it could be argued that with a 3-1 superiority, success will usually follow. To twist this into claiming that 3-1 is required for success is plainly wrong.

  2. ” Of course it could be argued that with a 3-1 superiority, success will usually follow. To twist this into claiming that 3-1 is required for success is plainly wrong.”

    This is a perfect short summary of why the 3-to-1 rule is a problem. Almost tempted to make these two sentences their own blog post.

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