I have a spreadsheet set up to guide me in exactly that, I just don't have enough combat experience in game to really judge how well the spreadsheet model matches the combat model. I'll clean it up, send it to you, and open the assumptions and results up for discussion.
So I'm late with this, but I did finally get to it. Force composition analysis, or who's worth what in combat.
A man leaves combat in one of two ways: he dies (which his defense rating protects against) or he flees in terror (which his morale rating protects against). He causes those effects in the enemy by attacking them. So the basic measure of worth in combat I call the ADAM rating: Attack, Defense, Attack, Morale, multiplied together.
But there are multiple phases of combat, and each unit has different attack and defense ratings for each phase, so different ADAM ratings. It's easy enough to compute those different ADAM ratings, but how do we combine them so that we can meaningfully compare archers (strong in skirmish) to heavy infantry (strong in melee)?
Short answer: I guessed. I made skirmish count twice as much as the other two phases in the overall ratings. My reasoning was that every battle is guaranteed to have a skirmish phase. A strong skirmishing force can win a battle outright, or seriously bias the outcome of melee in favor of its side. Every battle is also guaranteed to have a pursuit phase once one side has won. While this last phase is irrelevant for determining the winner of the battle, it matters quite a bit in winning wars, as this is where you do the bulk of your killing.
So the formula I use is 2*Skirmish ADAM + Melee ADAM + Pursuit ADAM. I then divide each unit's rating by the rating of light infantry (the lowest overall value unit) to get a relative scale shown below in order of increasing power
Unit RBV
Light Infantry 1.0
Archers 1.7
Heavy Infantry 3.3
Pikemen 5.1
Light Cavalry 14.8
Horse Archers 23.1
Heavy Cavalry 48.5
That's why Holy Orders and their heavy cavalry are so frightening: the knights alone can take on up to 50:1 odds depending on how bad their opponent's force composition is. Note that Mongol horse archers are no laughing matter either. With this in mind, it may be more useful to compare units to the heavy cavalry. This is how many of each unit it takes to make a fair fight for one knight. Also useful for comparing the value of different types of castle buildings to your levies.
Unit R HC
LI 48.5
Archer 28.5
HI 14.7
Pike 9.4
LC 3.3
HA 2.1
HC 1.0
The raw ADAM numbers for each phase, for those who wish to weight the phases differently in search of more accurate results
Unit Skirmish Melee Pursuit
LI 36 81 81
HI 6.25 720 40
Pike 1.2 1200 0.48
LC 80 108 3200
HC 80 8000 3200
Arch 192 2 12
HA 1372 252 2401
It's important to note that this is all based on the base stats for each unit. Technology, leader skill, tactics, terrain, etc can all alter these relationships. As far as technologies, since attack strength counts twice in the ADAM rating (once for killing, once for breaking morale), a 10% increase in attack rating is a 21% increase in combat power (1.1 x 1.1 = 1.21). So prioritize offensive technology whenever it makes sense to do so, especially for your most numerous troops.
Summary:
- Knights > Horse Archers > Light Cavalry > Pikes > Heavy Infantry > Archers > Peasant light infantry
- Improving offensive technology gives roughly twice the benefit of improving defensive or morale technology
Next time I'll use these unit ratings to rank the buildings in order of combat power per gold to determine build order.
