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:
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.
http://www.jstor.org/stable/2538771?seq=1#page_scan_tab_contents
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.
” 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.