As the Baron points out, modeling air superiority contests in a relatively simple wargame like A&A is quite a challenge! I think there are actually several different phenomena that go by the name of ‘air superiority’ that a good house rule would pay attention to. One is that if your air force is totally unopposed, your ground units will have advantages in terms of recon, surprise, flexibility, etc. because your planes can survey the lay of the land and strike quickly at the point of maximum impact. Another is that airplanes tend to kill each other first, before killing ground units. A third factor is that when fighters intercept bombers, the bombers tend to be less effective – it’s not just that the bombers get killed accomplishing their missions; it’s also that the bombers fly at higher altitudes, fly at faster speeds, and fly on more evasive flight paths to try to minimize their risk of getting shot down. Even when the bombers survive, they do less damage if they’re being harassed by fighters.
Here’s my take on a set of rules that could capture all of those dynamics:
After all attacks are declared, the defender may scramble up to 3 fighters from anywhere on the board, plus up to 2 more fighters from each airbase. Scrambled fighters can move to an adjacent territory or sea zone to participate in a battle there, and then (if they survive) automatically return from whence they came. The same fighter cannot participate in more than one battle per turn.
Attacking and defending fighters roll their dice separately from other units. When fighters score a hit, that hit must be assigned to a plane if possible. The victim can choose which plane is killed. Even though fighter casualties are assigned separately, they are resolved at the same instant as other casualties. For example, suppose a German force of 4 inf, 1 tnk, 1 fighter, and 2 bombers attacks a French garrison of 3 inf, 1 art, 2 fighters. The Germans score a hit with their fighter, and 3 hits with their remaining forces. The French score one hit with their fighter, and 2 hits with their remaining forces. The Germans would have to lose 1 plane and 2 units of their choice – they would probably choose to lose 2 inf, 1 ftr, leaving them with 2 inf, 1 tnk, and 2 bombers. The French would have to lose 1 plane and 3 units of their choice – they would probably choose to lose 3 inf, 1 ftr, leaving them with 1 art, 1 ftr.
If at any point you have at least one plane in a territory, and your opponent has no planes or AAA guns left alive in that territory, then your infantry and mech. infantry in that territory get +1 to their dice rolls. This is cumulative with the artillery bonus. For example, if you have 2 inf, 1 mech. inf, 3 art, and 2 bombers attacking in a territory, and your opponent is defending with only 3 inf, 1 tnk, then your infantry would score hits on rolls of “3” or less – 1 for their basic offense, +1 for the artillery, +1 for the air superiority. Defending infantry can also benefit from air superiority if the defender has air superiority. For example, if your force of 4 inf, 1 fighter, 1 bomber is being attacked by 3 inf, 3 tnk, then your infantry will hit on rolls of “3” or less – 2 for their basic defense, +1 for the air superiority.
Before each combat starts, match each fighter in the combat with one enemy bomber. At the end of the first round of combat, remove that bomber from combat. It no longer rolls dice to try to score hits, and it can no longer be taken as a casualty. This represents bomber pilots’ efforts to avoid interceptors by flying high, flying fast, and then going home. The bomber can be returned to a friendly territory as normal during the non-combat move. If, in any given territory, you have more bombers than your enemy has fighters, your ‘excess’ bombers participate in the entire combat as normal.
To help adjust for the increased mobility of fighters and for their ability to preferentially target (expensive) planes, the combat value of a fighter is reduced to a “2” on offense and a “3” on defense.