Thanks so much for adding to this discussion. It tapered off several months ago, but the 3:1 rule is still of interest to me for a writing project I'm working on. I'd still like to see an explicit articulation of that rule by some authority current or previous to the Civil War. I think there are suggestions it existed, but I wish I could find something more concrete.
Roy B.
It is also worth noting that the 3:1 Rule for combat is not about raw numbers of troops. It is about units of combat power (which is what Lanchester is talking about in "Lanchester's Square Law" during WWI).
If 1,000 infantrymen equals one unit of combat power in all cases, life would be simple and the 3:1 Rule would be easy to apply. Unfortunately for simple rules, life is rarely simple and combat is even worse. You need an incredible amount of detail on subjects that are often not obvious or easily quantifiable to do the calculations. There are what modern military theory refers to as force multipliers to consider.
It makes a difference, for instance, if the defender is dug in to a prepared position. The saying in the days of the Civil War was roughly "one man
in a trench with a rifle is worth three in the open". As a general rule, that is a fairly practical one for
tactical infantry combat in 1864-65. If you are getting ready to make a head-on assault on an entrenched line across open ground, that is a great rule of thumb.
Now suppose you have a lot of superior artillery (say Union 3" rifles) in a good position that can enfilade the defender and shell him out of his trenches. Maybe that 3:1 Rule no longer applies. This explains why Hood and Polk argue for pulling out of the trenches at Cassville in the Atlanta Campaign (Johnston's report: "Soon after dark Lieutenant-Generals Polk and Hood together expressed to me decidedly the opinion formed upon the observation of the afternoon, that the Federal artillery would render their positions untenable the next day, and urged me to abandon the ground immediately and cross the Etowah.") Sherman has nothing like a 3:1 troop superiority, but experienced generals feel the 3:1 Rule is not applicable at Cassville.
Suppose you are in a meeting engagement, not an attack on an entrenched position? No trenches involved, just troops running into one another while on the move? Do you need a 3:1 advantage to successfully attack? Or will acting aggressively and striking first mean more?
Also, the 3:1 Rule is really all about local advantages at the point of attack. A smaller army can achieve a local advantage by moving quickly, concentrating a superior force against a fraction of the larger foe. This is an essentialJomini concept:
"There is one great principle underlying all the operations of war… It is embraced in the following maxims: (1) To throw by strategic movements the mass of an army, successively, upon the decisive points of a theater of war, and also upon the communications of the enemy as much as possible without compromising one's own. (2) To maneuver to engage fractions of the hostile army with the bulk of one's own forces. (3) On the battlefield, to throw the mass of the forces upon the decisive point, or upon that portion of the hostile line which it is of the first importance to overthrow. (4) To so arrange that these masses shall not only be thrown upon the decisive point, but that they shall engage at the proper times and with energy."
This is what Lee strove to do, and Grant, and McClellan, and many others. The skill and luck with which they did it -- as well as the skill and luck with which their opponents countered their attempts -- is what comes out in history as success and failure.