Moving on, we can do some math with the formula.
Take the new HCAP. How good is it? It's easy to compare to CAP because it's only different in one aspect.
An infantry unit with CAP is size 12, AP 1, damage 1, shots 6. An infantry unit with HCAP is size 20, AP 1.6, damage 1, shots 6. This means that it inflicts 2.56 as much damage to anything with (adjusted) armor of 16 or higher. Plug that into the formula and we get:
(20/12)^2 = 2.78
2.78 is more than 2.56, so this means that CAP infantry will win in a straight fight against HCAP infantry, even if they both have armor 20. This isn't the same thing as saying HCAP is useless - it may perform better on vehicles than infantry, for instance - but it does mean that HCAP infantry could be categorized as a "glass cannon", which is to say the increased firepower is overshadowed by the increased fragility. And of course the comparison goes even better for CAP against anything with an armor of 10 or even 15. I wont go as far as to say never use HCAP infantry, but I will say that CAP infantry are going to generally be better, even if your opponent never uses a unit with armor <2.
The numbers are different on a light vehicle, since a CAP light vehicle is 24 and an HCAP is 32:
(32/24)^2 = 1.78
1.78 is much lower than 2.56, so HCAP light vehicles definitely outperform the CAP version against targets with armor of 16 or more. Since light vehicles always have a base armor multiplier of 2, this means that HCAP light vehicles will definitely be at an advantage in a fight with CAP light vehicles, though the latter would still outperform them when fighting very low armor opponents, like a mass of light infantry.
How about CAP vs personal weapons for infantry? CAP has the same stats as personal weapons but gets 6 shots, so it's straight up 6 times better. They both have the same AP, so armor doesn't matter. CAP infantry is size 12 and normal infantry is size 5.
(12/5)^2 = 5.76
5.76 is slightly less than 6, so we would expect a formation of nothing but CAP infantry to (barely) beat the same size of infantry with personal weapons. This is probably a good balance point, since personal weapon infantry works better at absorbing damage and garrisoning, and therefor CAP infantry performing better in a straight fight doesn't obsolete personal weapon infantry.
Other than that, after playing around with the numbers I do want to say that I think autocannons need a buff (unless I'm missing something crucial about them). The light autocannon is still straight up worse than even the nerfed HCAP, since it's heavier, has less AP, and 3 20 damage shots are statistically worse than 6 1 damage in every situation. I'd suggest either making it AP 20, putting it in the HCAP's old role but heavier and half as effective against infantry, or possibly upping the damage to 30 and making the autocannon line specialized against high health, low armor targets (the LAC would still be weaker than the HCAP against anything with armor 16 or higher with this change, but it would be closer).
I think HCAP seem to be in a good place right now.
The fact that it is suppose to be good against high armoured units is quite clear to me.
A few very important things that you miss is the amount of space the HCAP take up in the defensive line versus an equal amount of CAP for engaging high armour target. Since these units are glass cannons it is quite important they are not hit in the first place.
The second thing is how effective they are per supply point used which as I have noticed are going to be more important than the units initial construction cost.
An HCAP will spend 6*1*1.6=9,6 SPP and do 6 damage against 1.6 armoured infantry, that is 1.6 SPP per damage.
AN CAP will spend 6*1*1=6 SPP and do 2.34 damage against 1.6 armoured infantry, that is 2.56 SPP per damage.
An HCAP will spend 6*1*1.6=9,6 SPP and do 5.20 damage against 2.0 armoured infantry, that is 1.85 SPP per damage.
AN CAP will spend 6*1*1=6 SPP and do 1.5 damage against 1.6 armoured infantry, that is 4 SPP per damage.
That supply will mount up quite allot over time in cost as will the increased chance (on equal cost) of the CAP unit to get hit as well.
So... you need to factor in more than just build cost and the units fighting in isolation not in a combined arms force.
The same goes for calculating cost of vehicles and their use of them in an army as a whole. Artillery for example will burn huge amounts of supplies as will vehicles armed with anti-vehicle cannons. A single medium artillery cannon will burn 13.5 SPP... which are the same amount of supplies as almost 14 infantry with personal weapons.
The only thing I don't fully understand with the combat model so far is if there are some limitation of how many units can be at the front and how many front units that can fight each other every turn. Can an unlimited amount of front units fight a very small enemy front line and force. Given the cost in supply and build of artillery I might sort of question their worth if there are no restriction on front units engaging each other. It might just be me that don't fully understand the combat model. But in reality artillery is a strength multiplier and there is a limitation for how much force you can bring in the front lines and pit against the enemy front lines at any given time. More is not always better, especially when there are enemy area effect weapons in play. WW2 was the first real war where formations needed to become dispersed and fight over vast areas as a result. Artillery was extremely dangerous as was tank weapons.
I think that adding some sort of bonus to front line units from bombardment units could be important. Just adding firepower will likely see them either not used or used too much based on their strength versus cost. Say that having support artillery of air cover make your attacking/defending front units harder to hit, based on the abstraction of supporting front line operation. Or something like it.
There also is the issue of hit point versus damage being a linear relationship... this makes high damage weapons just bad from a supply perspective since many targets will be extremely expensive to kill over other where a low damage weapon will never be. Sure... there are not that many high AP low damage weapons around... but that is what I would look for from a cost AND size perspective.
Perhaps a SPP formula of something like AP*Shots*((Damage+10)/2). This would not make the damage trait so overwhelmingly expensive and unbalanced for what it actually does in combat.