Overwhelming power
Force concentration is the practice of concentrating a military force so as to bring to bear such overwhelming force against a portion of an enemy force that the disparity between the two forces alone acts as a force multiplier in favour of the concentrated forces.
Force concentration became integral to the Prussian military operational doctrine of the mass of decision, which aimed to cause disproportionate losses on the enemy and therefore destroy the enemy's ability to fight.
From an empirical examination of past battles, the Prussian military theorist Carl von Clausewitz (1780-1831) concluded:
[...] we may infer, that it is very difficult in the present state of Europe, for the most talented General to gain a victory over an enemy double his strength. Now if we see double numbers prove such a weight in the scale against the greatest Generals, we may be sure, that in ordinary cases, in small as well as great combats, an important superiority of numbers, but which need not be over two to one, will be sufficient to ensure the victory, however disadvantageous other circumstances may be.
During the First World War Frederick W. Lanchester formulated Lanchester's laws that calculated that the combat power of a military force is the square of the number of members of that unit so that the advantage a larger force has is the difference of the squares of the two forces, i.e.
So a two to one advantage in units will quadruple the firepower and inflict four times the punishment, three times as many units will have nine times the combat ability and so on. Basically the greater the numerical superiority that one side has, the greater the damage he can inflict on the other side and the smaller the cost to himself.
There is no battlefield where battle tactics can be reduced to a pure race of delivering damage while ignoring all other circumstances. However, in some types of warfare, such as a battle for air superiority, confrontation of armoured forces in World War II or battleship-based naval battles, the ratio of armed forces could become the dominant factor. In that case, equations stated in Lanchester's laws model the potential outcome of the conflict fairly well. Balance between the two opponent forces incline to the side of superior force by the factor of . For example, two tanks against one tank are superior by a factor of four.
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