As the three-to-one rule of thumb appears to have evolved out of the American Civil War (although not as published in FM 6-0), then we should probably look at just our Civil War battles in our database.
Among those 243 cases are 49 cases from the American Civil War. As the three-to-one rule may have evolved from that experience, let us looking at just those cases:
Force Ratio……………………Percent Attacker Wins……………….Number of Cases
0.44 to 0.48-to-1…………………0%………………………………………………3
0.53 to 0.97-to-1………………..18……………………………………………….11
1.00 to 1.47-to-1………………..36……………………………………………….14
1.53 to 1.96-to-1………………..25……………………………………………….12
2.10 to 2.31-to-1………………..50…………………………………………………6
3.00-to-1……………………….100…………………………………………………1
5.00-to-1……………………….100…………………………………………………1
15.05-to-1……………………..100…………………………………………………1
The American Civil War is a very good test case for such an examination. Both officer corps were primarily trained at West Point (the U.S. military academy); both armies fought in the same style and doctrine; they used most of the same weapons, including the same muskets and same artillery; they were similar in culture; and they were similar in training, doctrine, background and capability. While some historical mythology has tried to make the southern Americans better fighters, it is hard to accept the argument that a farmer from North Carolina is a different, more motivated or a more capable fighter than a farmer from Pennsylvania. Most of the United States was rural. There wre also units raised to fight for the north from all of the southern states. This is about an equal comparison between two opponents that one is going to find.
The end results from these two tests are that the three-to-one rule as recorded in FM 6-0 clearly does not apply. In the case of the Civil War data at 2.10 to 2.31-to-1 odds the attacker is winning half the time. Where does one get the notion that at 3.00-to-1 odds the defender will win half the time? What historical data established that?
So the U.S. Army version of the three-to-one (meaning defender wins half the time) does not show up in the almost 400 years of history that we are examining here and does not show up in the American Civil War.