I learnt from starbuck that its good to send at least 5000 archers in each attack. that way in the melee rounds when they become butter, you dont lose that much.
I don't remember telling you that
there is really no magic formulas to how any archers you must send (or not send). What matters is that you understand the specific role of archers : lowering morale
Usually you send all your phalanxes, guardians and paladins in attack to maximize your power, but it's true that archers quantities you'll put on the field are very much depending on the type and quantities of troops you see on the other side.
And the reason is because they have a support role : they can't do more than a limited specific impact, and if you don't have enough of them to reach a certain threshold, then they do almost nothing.
a few examples : if the defender has 10k elite archers, then send min 15k-20k (30k+ being better) to get the upper hand, but no need to send 100k+ unless you want to see half of them slaughtered during the following melee phases.
and if you got just 10k archers, then send 100 only ... why ? coz you don't have enough to make a difference if there is a fight,so why sacrificing 50% of 10k ? and if the defender decide to avoid the fight, then 100 archers will be enough to make a difference during the field and siege phases of the battle
have fun,