Improviser said:
For army promotions the animations for an army attack will show when the unit attacking in the army changes. For an army say of 3 veteran swords, the top unit may promote if the army wins with 9-12 hp's, the 2nd unit if 5-8 hp's and the 3rd unit if 1-4 hp's.
I'm not sure if the first unit loaded in the army goes in at the top or the bottom though.
The units attack in the order of their base attack factor, and in case of ties, in order of their base hit points. (Same for defending, using the defense factor). So for example, let's say you're Carthage, and you made an army with a Vet sword, a regular sword, and 1 regular Numidian Merc. You would have 10 hp (4+3+3). If attacking, the vet sword would be the top unit, since it has the best base attack factor (3), and most base hit points (4). It would fight for the first 4 hits of that battle. If the enemy wasn't defeated, the second sword would step up, and fight for 3 hp worth. Finally the NM would fight the last 3 hp if needed. On defense, the reg. Numidian would defend first, since it has the better defense factor, then the vet sword, then the regular sword.
AFAIK, the hit points, when the army is full, are apportioned to the units according to their level, so the Vet fights for 4hp, then the regulars fight for 3 each. It's when the army is at less than full hp that it gets trickier, I think they are allocated to each of the units in proportion, but I'll have to check.
Since (as was mentioned) only the unit fighting at the time of victory can be promoted, and since the top unit, with the Army's attack bonus, is often enough to defeat a single enemy, the top unit tends to promote more quickly. Note that even in a second attack that same turn, the same unit will be the first attacker, and fight for the first 1/3 or so of the hps.
Because a lot of people put a *'d elite (one that's already generated a leader) in their armies, that means that the unit that sees the most action, is probably already elite, and therefore can't be promoted. In the example army, once the vet sword gets promoted to elite (bringing the army up to 11 hp), he will still fight first every battle, and fight with up to the first 5 hps of the army. The only way for the reg sword to be promoted, is if a battle lasts past the first 5 hps, so the (original vet) sword is done, then he steps up, and wins it within his 3 hp. The Merc in this case would likely only get a chance at promotion if the army is attacked, as it's the top defender, or if it fights a single fight down to the last 2-3 hps, when the Merc will step forward.
Another Note: One ability not mentioned is that an army comprised of all fast units (horse/knights/cav, etc) CAN retreat when it gets down to the last hp. An army of move-1 units will not, even though the army itself has a move of 2, it's based on the fast unit flag, not just the movememt allowance.