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I've been forced to take some Air Units out of AI control by detaching them from their Air HQ's and giving them manual air intercept missions. It's really only where I have a specific offensive or defensive crisis to manage as I've noticed the AI is heavily supporting these with its bombers but my interceptors weren't responding with equal vigour. So, I just place them on direct intercept missions over the battle area rather than leaving the AI to do it.
 
>Normally that works, although sometimes they insist on attacking the province ahead of the bombers (which doesn't intercept them), and cannot be persuaded to do otherwise
>until I use "Air Superiority" over the target province instead.

Shooting down bombers before they get to the target rather than wait until they are over the target is historically what they did in WW2.
Are you sure it isn't an effective tactic in HOI3?

No. Planes in HoI3 "teleport" from one region to another rather than following a "flight path" and so they can't intercept en route the way things could in real life.
 
Recall that the game operates off of 1hr "ticks." If it takes the bombers more than one tick to reach a target, they "appear" to stop in a province they're not actually in. This also affects the interceptors!

So, if you leave the stance set on aggressive, and the interceptors have enough range, those interceptors can "chase" the bombers all the way back to their bases, with negative consequences.
 
What I've seen and done in several GER games is to see where the bombers normally stop on their way to the target. The AI will almost always hit the same target until it's reduced to zero, then go for the next target. If you can protect the primary target well enough, the others will almost never get hit. I have one group of INT set to intercept the bombers at that hourly stopping point, and a second group set to intercept them over target. Generally, I build an airfield in Leipzig, which is the primary target unless you build enough IC or AA to make some other place the primary target. The group at the target is given the Aggressive stance, while the first group gets Defensive. If it all works out (which is very hit-or-miss), the first group will hit the bombers before they arrive at the final destination (although they often change to attacking the province AHEAD of the bombers instead), then the bombers get hit a second time by the group covering the target. If the bombers don't break off the bombing run due to ORG loss from the two attacks, then the AA does a bit more trivial ORG damage (which can directly damage Strength if one of the bombers is already out of ORG). Since the second wave of INT is set to Aggressive, they often pursue the bombers to hit them a third time on the bombers' way home. That's usually enough to either kill one of the bombers outright, or else put the whole group down to single digits of Strength, and they won't be back for a month or more. Ideally, the first group of INT won't pursue the bombers back to base because of the Defensive setting, and the second wave doesn't have the range to reach the UK airfields. All is fine, except that you have to occasionally check BOTH groups frequently to reset them to their proper targets, otherwise they will re-target the last place they fought, and miss the next attack.

I use the Outliner to show all land and naval combats, and all air missions by both sides (all units disabled). I sometimes spot the bombing damage info in the event log at the bottom of the screen, and sometimes see the raid and intercepts as they show up in the outliner, so I usually manage to reset the air groups to their proper targets before the next raid. I STILL take a lot of IC damage, but it costs the UK at least as much in repairs as it costs me in lost IC-days, and it cuts the number of raids down to only one every month or longer. The AI simply fails at deterring such raids.

The AI is reasonably effective at supporting ground operations with TAC and/or CAS, but I never let the AI run my INT. If I see an enemy air mission or air combat in the outliner, I pause the game and dispatch an INT unit to deal with the problem, until the problem goes away. Obviously, that's not a viable method in a MP game.