I'm not saying mixed compositions can/'t work better than a party of only one-type of troop, just that even in your example, infantry must have a significantly higher# of troops to be effective vs the other troops.
Most of those infantry units acted passively. blocking arrows, providing a target and such, blocking the enemy. also most of this guys weren't mine. i was in an army and we had to use them. i brought 45 guys out of 283 that is 16% of my party. anything else is either an archer, horse archer or cavalry
Let alone the fact that i only lost 24 people in that fight. That was 8% of the party and 5% where tier 4 or higher. My party wasn't even very good when it come to infantry to begin with and i had roughly 110 medicine.
Isn't the simple fact that running in an army changes the way you use troops not obvious? I used the Horse archers exactly like anyone else would. reposition, flanking. keeping them out of troubles and so on, having more Horse archers isn't even an option in that battle. you still have to deal with your vassals troops. And letting them die in order to save our HA isn't an option. you are slowing yourself down if you do that. And since the AI likes to infantry spam after defeating their parties you need the lines to hold the recruit mob. You need to upgrade depending on your surroundings.
When you run around in an army horses don't make you that much faster. you can prove that on your own by bringing 400 HA to any army outside of the Khuzait. you might gain 0.1 speed. So let's stop with this one alright. you can bring normal mounts and have half the bonus cavalry bring anyway. it's not that important. And there is also a size penalty for having a lot of troops, i think it starts from 200 and since by that time you have Stewardship, clan tier, policies and Leadership, and you might be the king. the speed bonus from cavalry gets diminishing returns.
Another thing to consider about costs is medicine. when you get to 200 you basically add 50% more survivability to any unit ( don't look at the TW mathematics in the skill screen). If you use infantry you get there faster. If you use a troop type that is so broken it doesn't get wounded you don't.
There are many more reasons to get medicine other than just survivability BTW.
So why would it be more efficient in the long run to have low medicine? Simple. it isn't, you are going to lose your High tier troops faster in a battle where your HA can't finish the enemy off with their arrows ( unless you cheese the game by retreating ) and cutting your sieging campaign short because you have to resupply on a very specific unit type that is 10 days away from where you are located.
then let's not even talk about the time we need to get them trained and the hundreds of horses we must use to upgrade and the fact that we can only get this guys in villages bounded by castles and that we need good enough relation with the notables in order to recruit from all of their slots.
meaning if we want to passively gain relation we have to take castles over towns and if we don't we have to do quests. And yeah i am not considering using very easy recruitment as that would require less than 1/10 of the tought of a nice guy.
Getting Horse archers is a very good strategy early on, later in the game you use whatever you find if you really want to be efficient. You are going to be happier if you find a unit you can build up to be a broken one, but if you don't you have to deal with it. Also if you trade, something a loot of people do early, foot troops allow you to trade more horses.
About min maxing for a specif fight sure. but all of what i stated above doesn't make it a long term strategy if efficiency is what we care about.
Troops are resources. Not using resources and piling them up for no reason in not what someone who wants to min/max does. it's something that somebody who wants an EASY button does. and if things seem too easy there is some potential missing somewhere. The good strategy players in any game min/max in using all of their resources not the other way around. Medicine and time are resources in this game.
Want to prove me wrong? Show yourself beating the game in less than 15 years without using exploits like the smithy or cheesing the battle system with retreats and reengage and such.
I think what i have been able to do in that campaign is close to the peak of efficiency you can get in this game. and i didn't even use 200 Horse archers to accomplish it.
Are we even playing the same game? this is starting to be a legitimate question for me you know? you guys are missing out so many of the things to keep in mind when talking efficiency.
Anything i state is something that i proven many times over, i don't need credibility. I have used all troops, someone else here only played with broken ones and doesn't even bother trying to make the others work. But that guy seem more than happy to call others out for lacking effort.