okay, i just tested this 10 times for both sides. scenario: 15 hittite HHA vs 30 phoe compies. whichever side i was controller, i put a wall around the other side to force a battle. range made no difference, as i put the two armies close together (still seperated, just close enough together so that any one unit from one side could still shoot at the farthest unit from the other side without taking a single step.
Results:
a) me controlling the HHA's. i had no trouble winning all 10 battles. i just let the horse archers do their thing rather than use doctrine of concentrated fire, as the comps have so little hps it's not worth concentrating fire. in all battles, i had at LEAST 5 hha's left, about 8 on the average. in one test, i had 10 left, although i must say that there were only about 3 left with full life, most were around the 10-20 hp range. nonetheless, all the comps were dead. score HHA's:10, compies:0.
b)me controlling the comps. i used concentrated fire in 5 tests, let the compies do their own in 5 tests. i split my comp army into two numbered groups (i didn't move them, only numbered them into two groups) and concentrated my fire on two horse archers, and when my composite armies got too small, i regrouped all of them together. i won once, lost 4 times. there were about 4 horsies left on the average though for the other tests, usually a bit hurt. i once got it down to 3, where 2 had full life, one was almost dead, but i died. score: HHA's:14, compies:1. now i left all the compies to try their own thing. theoretically, this should produce the same results as the first test, since both armies are left to do their own thing, but we know that the computer likes to move stuff around rather than shoot. thus, in the end, rather than having an average of 8 HHA's left, the average dropped to 6. all the compies still died. final score, HHA's:19, compies:1.
I suppose i could try it with minoan comps, but then the defensive side would win, since it's kinda hard to make the horse archers stay in one place while i maneuvered my comps into range, but have them be able to counter attack when attacked. my guess is maybe an average of 4 horse archers left when on defense, but they might die when attacking, due to need to jockey for position. it would take some real skills to get them to all line up at the same time.
conclusion: i will take my 15 hittite heavy horse archers up against your 30 composite bowmen (not minoan) anyday, but i'd rather see them go splat with cat blasts. a dead army is still a dead army even if you spent a tad bit less resources on it. what the heck, i'd take my hittite CHARIOT archers against your comps, assuming equal numbers.