@CWO:
In my opinion, it should make no difference whether you pair a carrier with a cruiser alone, with a battleship alone, with a cruiser and a battleship together, with two cruisers, with two battleships, or any other such combination. The type of anti-aircraft defensive bonus given to the carrier should remain the same in all cases. Why? Because cruisers and battleships both have the same type and roughly the same quantity of anti-aircraft firepower. Cruisers don’t have any special anti-aircraft ability that battleships don’t have. Battleships don’t have any special anti-aircraft ability that cruisers don’t have. Neither therefore brings to the carrier any unique bonus, so I disagree with the notion that cruisers should be treated any differently from battleships in that regard. If you want to treat them differently anyway, that’s up to you. I’m just giving you my personal view of what I think is historically realistic.
I was almost sure that neither BB or CA should have a different treatment. So it would be a breaking point between an in-game incentive and balance of units vs historical realism.
My above opinion is based on the premise that, for A&A OOB rule purposes, all units represent a single generic type with a common set of abilities for all nations. In other words, “cruiser” in A&A OOB terms means a generic cruiser. A cruiser is a cruiser, with a single set of combat abilities, and with no distinction made between heavy cruisers, light cruisers, anti-aircraft cruisers, early-war cruisers, late-war cruisers, American cruisers, Japanese cruisers, or whatever.
If the house rule system you’re creating makes such distinctions, that introduces a potentially huge jump in the level of complication for a game which (in its Global 1940 version) is already pushing the limits of practicality. You’re free to do so if you wish, but I’m not going to offer any opinions about combat bonuses at that level of detail because I think it’s excessive to fracture units into too many sub-types in a strategic-level game.
Regarding your question “Is there many occasions in which Carriers and Battleship were without Cruiser warships?”, the question is too broad to answer definitively for the entire sweep of WWII. All I can say for certain is that the USN’s standard and most effective configuration for a carrier-based naval task force was the put the carriers in the middle of the formation, to dispose the battleships around the carriers, to dispose the cruisers around the battleships, and to dispose the destroyers around the cruisers, similarly to the concentric rings of an archery target, so that as you go further out from the bull’s eye (the carriers) the surrounding ships become smaller in size but greater in number.
You have a gift to clearly formulate overall principles of depiction of game units.
I made a kick search about US Cruisers and Battleships to see what was their respective function.
All that I could find was about the introduction of the fast BB (Iowa-class?, I can’t remember.) which have 2 purposes: shorebombardment and AAA air cover.
Based on this someone may prefer give AAA combined arms only for BB and CV since it their is no sign of a Navy doctrine which specified the AAA purpose for Cruiser, right?
But, in one of your post above you showed that Cruisers and BB have similars weapons against aircrafts and the main difference is the sheer numbers, am I right? Hence, both can give AAA cover in combined arms with CV.
An other aspect is about the kind or degree of AAA cover provided by BB and Cruiser.
You said this:
it should make no difference whether you pair a carrier with a cruiser alone, with a battleship alone, with a cruiser and a battleship together, with two cruisers, with two battleships, or any other such combination. The type of anti-aircraft defensive bonus given to the carrier should remain the same in all cases.
And that the best defensive formation was the concentric ring of an archery target, from outside to inside: DDs, Cruisers, Battleships then Carriers.
My intuitive impression based on this historical defensive formation was that, keeping the same ratio number of real warships / game unit, a ring with DDs & CVs was weaker agains aircrafts than DDs, CAs & CVs or DDs, BBs & CVs, and both were weaker than the full Carriers group Task Force: DDs, CAs, BBs & CVs.
And because of this, it was more accurate to give a better AAA cover to the full Carriers group TF.
To provide HR illustrations:
**A- “When 1 Cruiser or 1 BB is paired to a CV, give them an AAA cover @1 against up to 3 planes, as a regular AAA fire.”
vs
B-
- Give 1 Carrier unit 1 preemptive AA@1 on defense when paired with 1 Cruiser or 1 BB.
- Give 1 Carrier unit 2 preemptives AA@1 on defense when paired with 1 Cruiser and 1 BB.**
Another question, does this concentrated ring formation would have been as much efficient if there was no smaller warships such as cruisers in the outer perimeter but another group of Battleships?
Because in the doc mentioned above Battle 360 E8 D-Day in the Pacific Part 3/6, they suffer a lot about friendly cross-fire.
Does the problem would have become worse with double the number of BBs?
If not, then there is no compelling historical reason to not provide this:
**C-
- Give 1 Carrier unit 1 preemptive AA@1 on defense when paired with 1 Cruiser or 1 BB.
- Give 1 Carrier unit 2 preemptives AA@1 on defense when paired with 2 Cruisers or 2 BBs or 1 CA & 1 BB unit.**
In other words, does the combined arms of Cruiser unit and Battleship with CVs could have provided a better AAA defensive cover?