In Lanchester’s Law: Too Few American Soldiers?, Temple math professor, John Allen Paulos, author of Innumeracy, gives a brief explanation of Lanchester’s Law:
Lanchester’s Law can be paraphrased as follows: “The strength of a military unit — planes, artillery, tanks, or just soldiers with rifles — is proportional not to the size of the unit, but to the square of its size.”
You see, if you double the size of your force, not only do you deal out twice as many casualties, but you only take, in relative terms, half as many; your firepower gets reduced by casualties just half as quickly.
Poulos then goes on to explain that if you improve the quality of your forces — he defined this in terms of improving the accuracy of your artillery — it doesn’t scale the same way. If you’re twice as accurate and deal out twice as many casualties, that’s merely twice as good.
Of course, quality isn’t as valuable as quantity, in this case, because he defined quality in purely offensive terms. If quality took both offensive quality and defensive quality into account, it would be mathematically indistinguishable from quantity.