Reinforcements in battle

What's the situation

If you enter combat before your armies are merged, you will do worse trades (during the time before your reinforcements arrive).

The thing is, having more numbers is an efficiency advantage. In a 2v1 for example, your 2 units do 2x damage to your enemy every fighting round, but he only does 1x damage to you. This means, if your enemy has 20hp, you will only lose 10hp to kill him (because by the time you've done 20 damage, he's only done 10). So not only do higher numbers win, they win with more efficiency, meaning you do alot more damage to the enemy than he does to you.

If you start fighting before reinforcements have arrived, you will simply trade hitpoints at a worse efficiency. By the time your numbers have arrived, you have lost some HP for a lesser reward than if you were to wait for the higher numbers to attack. Therefore, if there's no urgency to fight immediately, always wait for reinforcements to arrive before battle.

If you're sending in multiple small armies to reinforce, yes it's better to merge them first. If they get attacked, for example from air, they will atleast do some damage. Also, while entering close combat, your armies might accidentally attack too soon and enter a separate fight without merging. This is unusual, but if it happens, it is very unpleasant, because your armies will now suffer the enemy's full defensive damage twice (once for each separate army). To avoid this, order your army to move through the fight and let it go. Don't give any move/attack orders when your army is entering the combat zone (5km radius around fight, this is about twice the province center radius), let it move in on itself. This way, your army will only start fighting when it's literally on top of the enemy, and so it will merge with your other army automatically.

That answers my question. Thank you.