Quantitative Division Design and number of brigades in each division. TFH.
Hi
In Their Finest Hour (TFH) with the new armor level and piercing rating system it is probably even more important whether you choose to build few large divisions or build more but smaller divisions. I can't prove this point though. It is just a hunch.
I can think of six major effects that is influenced by the division sizes - "concentration of fire", "overwhelmed defenses", "armor level and piercing rating", "unified command", "flexibility" and "cannon fodder".
Concentration of fire
One large division will concentrate its fire on one target, where two smaller divisions might choose to fire at two targets.
Note that if the enemy is a single division this effect won't matter as both smaller divisions will have only one target to choose from anyway.
Overwhelmed defenses
In the case when the enemy doesn't fire evenly at your divisions some smaller divisions risk getting overwhelmed by enemy fire while other divisions have remaining "unspent" defensive capability.
This effect is probably most noticeable when the enemy has few but large divisions that might benefit from the "concentration of fire" advantage.
Division statistics (armor level and piercing rating in particular)
By the nature of armor level and piercing rating rules large divisions get their armor level and piercing rating as the maximum formed over more brigades than smaller divisions do. There will thus be a tendency for large divisions to have better armor level and piercing rating and higher combined arms bonus.
Unified command
The more brigades you can cram into each division the more brigades are under the command of your top generals. Large divisions tends to have better leadership this way.
Flexibility
On the other hand smaller divisions means more divisions which gives greater flexibility, for instance to perform flanking attacks.
Cannon fodder
Also important is the opportunity to vary division sizes to employ cannon fodder. Suppose you have two divisions each made up of one expensive brigade and two inexpensive brigades. Every shot fired at one of the divisions will cause about one third of the damage to the expensive brigade and two third to the inexpensive brigades. If the inexpensive brigades are really inexpensive you might instead split your divisions into four, two divisions each made up of one expensive and one inexpensive brigade and two divisions simply made up by one inexpensive brigade each. When the enemy targets your divisions at random half of the divisions don't even contain expensive brigades and for the two that do only half of the damage will be dealt to the expensive brigade (and the other half of the damage to the inexpensive brigade).
Let us label the configurations "EII + EII" and "EI + EI + I + I" respectively. By rule of thumb we get, in the first case the expensive (E) brigades take 1/3 of the damage and the inexpensive (I) brigades 2/3, in the second case the expensive (E) brigades take 1/4 of the damage and the inexpensive (I) brigades 3/4.
It is quite important, I think, to be aware of the cannon fodder effect so that you don't inadvertently use your expensive reconnaissance units as cannon fodder.
I've typed in some formulas in (programming language) F Sharp that I think can supplement the Division Designer spread sheet. The calculator example is here
http://www.act-consult.net/rodhern/hoicalc/ . I will add some notes regarding the calculations / source code later.
Best regards
Rodhern
P.S. I have really very little idea if my formulas are correct. I am mostly just rambling.