Yeah, no random number generators. Statistical averages are the only thing we can really use.
"To me, this means that each troop type should be weighed against all other troop types that can fill the same role. This is the minimum. I think that weighing every troop type against every available troop type in the game will just take too much time and generate a lot of unneeded calculations. I'd say, stick with infnatry vs. infantry, cavalry vs. cavalry, fast cavalry vs. fast cavalry, monster (40mm) vs. monster, etc. This should render some solid starting results that you can then decide if more calculations are needed."
Weighted averages are the way to go. It might be useful to attempt to "classify" every unit in the game, so that you can account for the fact that certain unit types will spend more time attacking certain other unit types. Heavy Infantry, Light Infantry, support, heavy cav, fast cav, flyers, monsters, etc. etc. I would say still "run the numbers" against each category.. but depending on the unit you are evaluating you would put a higher weight on things to reflect actual usage.
For example, say we are evaluating a heavy cav unit. You'd figure out a reasonable "heavy cav template" to be used by all heavy cavalry. So it might look something like %40 hvy inf %30 hvy cav 15% light inf 15% support. When finding a final average performance, you'd be placing more emphasis on how the cav performed against the heavy infantry, since that is a typical usage of heavy cav wheras the light infantry and support get a much lower weighting because they typically will flee combat rather than be destroyed, so those averages aren't as important. Obviously this is a cursory "template", but finding a good template for each type would be important.
"Perhaps another way to classify units is in terms of how much damage they do on the charge (average), how many casualties they are prone to take when they accept a charge (average) and how much damage/casualties they take during a round of static combat (when neither has charged). I know that I am reiterating your previous post but when doing your calculations based on the context set forth here, perhaps this gives us a better way to interpret and classify the numbers?"
I think you were misinterpreting when I was saying "combat result". Those are the three types of combats I want to evaluate using average numbers of course. But I'm not stopping at how much damage is done on the charge. You might as well evaluate the net wounds of the encounter... e.g. Heavy cav charges heavy infantry doing 2.4 wounds on average.. we will assume all infantry ranked up 5 across so 2.6 attacks back and let's say that produces .2 wounds on average. Net result is 2.2 in favor of the cav in terms of kills. This isn't really about figuring out who wins combat, but rather about evaluating the offense and defense at the same time.
Now when evaluating the 3 combat types (charging, being charged, and protracted combats) we can use weighted averages once again, based on the unit type. Heavy cav will have a lot of weight put on their "charging" combat scores, while heavy infantry will have higher percentages on being charged and protracted combat.
OR it might even be possible to just do something based on the difference in the two combatants' movement scores. M4 infantry will rarely get to charge M7 cav. So a lower "weight" would be given to the charging value of the infantry against that target.
Not sure which of the two ways I'd favor.