Armour Effectiveness Modifier

[Lien Leposh]

The text below is copied directly from the manual and its got me puzzled. See at bottom.

The fire modifier for the two cases are shown below where the hard attack value is H and an armored unit defense value is D.

• Case 1. If H < D, then the modifier is H / D.
• Case 2. If H > D, then the modifier is 1 / Square Root (H / D).

For example, suppose a unit with a hard attack value of 4 fires on an armored unit with a defense value of 8. Then an armor effectiveness modifier of 1/2 is applied to the fire value. Also, if a unit with a hard attack value of 8 fires on an armored unit with a defense value of 2, then an armor effectiveness modifier of 1/SquareRoot(4) = 1/2 is applied to the fire value. In the first example, the modifier represents the effect of non-penetration by the firing unit. In the second example, the modifier represents the fact that once penetration is achieved, then fire values do not increase linearly. That is to say, if you are firing a large caliber anti-tank gun at a weaker target and you get a hit then you don’t get two kills. This would be like a big AT gun killing two halftracks with a single shot.

How is the modifier applied? As it stands in the above examples my logic has it that the weak units have a modifier of 1/2 and the strong unit have a modifier of 1/2.
Take an example of 10 Shermans (average gun and average armour) vs 10 King Tigers (Thick armour and BIG guns) with all other factors being equal. Common sense tells you that King Tiger wins.
However my logic tells me that according to the above calculations the King Tiger would do better if its Gun was equal to the armour of the sherman as the ratio would be nearer 1 and there would be a modifier of 1, and not a fraction of 1.
Yes I can see the argument of not killing 2 birds with one stone, but over the course of 2 hours fighting I will be flinging lots of stones and I would expect my big stones to be more effective than my opponants small ones.

So, how is the modifier actually applied ?
My thoughts are that if H>D then why isnt the modifier just "square root (H/D)" given my argument above?
Or have I missed something?

Thanks