Strategic Combat in CoM

[Nelphine]

OK,  this thread is where I will investigate strategic combat a bit more, with examples and numbers. I'm making a new one because I play CoM, and don't want to confuse people who play insecticide or 1.51 or 1.31 with CoM numbers.

Basic formula:

(Unit melee attack - 2) x unit figures x 20 = unit melee attack rating. (if 2 rating, figures x10? if 1 rating, figures x 5? need seravy to confirm)

(Unit ranged attack -2) x unit figures x 20 = unit ranged attack rating. (if 2 rating, figures x10? if 1 rating, figures x 5? need seravy to confirm)

Unit health x unit figures x 5 x (unit defense +2) = unit defensive rating

10 rounds of ranged (or 0 if no ranged,  or in between if damage kills all the ranged rating.)

Each round both sides use melee or ranged (never both). Damage is a random roll from 1-10 multiplied by appropriate attack rating/100. Damage reduces attack rating by the same percentage as percentage of life lost.

Some things grant modifiers (will add these in later).
+to hit: +33% attack rating per plus. Note that a unit starts with standard +3 to hit, so without other to hit bonuses only gets 99% of its attack rating.
+to defend: +33% defense rating per plus
Flame breath/Lightning Breath/Thrown: as melee attack
Doom or Illusion : *2 and skip the next two lines
Armor Piercing : *1.25
Eldritch Weapon : *1.25
Poison : +60*Figures
Life Steal : +100*Figures (+to hit does not apply to this)
Destruction : +150*Figures
Stoning Touch : +200*Figures
Death Touch : +200*Figures
First Strike : *1.25
Death Gaze, Stoning Gaze : +300
Multigaze : +1200

Note: spell ward applies the appropriate penalties to hit and to defend, but does NOT affect spellcasting (below) unlike a node which does cancel spellcasting of any realm not it's own.

Spell modifiers for having a wizard:

Nature : 78 Attack, 12 PercentATK, 20 Defense
Sorcery : 30 Attack, 30 PercdntATK, 30 Defense
Chaos : 150 Attack
Life : 30 PercentATK, 40 Defense
Death : 90 Attack, 20 Defense

Each "Attack" adds 1 attack power for each (mana spent*books owned*attack for realm)/5.
Each PercentageATK adds 1% of the existing attack power for each (mana spent*books owned*attack for realm)/20/5.
Each "Defense" adds 1 defensive power for each (mana spent*books owned*attack for realm)/5/5.


Additionally, when strategic combat happens, all units offense are added together and their defense are added together, to get a single super unit.;


The goal of my work. To see if the formula can be tweaked to more closely match tactical combat as right now death and sorcery are heavily penalized, as they rely in special abilities a lot.


First example:
Demon Lord with eternal night vs 3 elite Doom Drakes with magic weapons.

Demon Lord has 25 melee (no bonus from eternal night in strategic combat) 15 ranged 10 defense 35 health +3 to hit, life steal, lots of specials.
Total ratings:
Melee 1108. Ranged 716. Defense 1680.

Doom Drakes have 2 figures, 12 melee, 7 breath weapon, 7 defense 11 health, +1 to hit, some specials.
Total ratings:
Per unit: Melee 798, ranged 0, defense 792
Total for 3 units: Melee 2396. Ranged 0. Defense 2376.


However, note that when the AI is making decisions (overland or tactical), the units don't use defense and offense separately. Instead they are boiled down to a single number.  Each unit takes offense * defense /8192, to get a final strategic rating. Then after the unit strategic rating is calculated, all the units in he stack are added together to determine the stack rating. Note that this is quite different than if all the offense were added, all defense added, then the totals multiplied by each other and then divided by 8192.

As above, the demon Lord gets a rating of (1108+716)*(1680)/8192.

The doom drakes get (798*792/8192) * 3 units.

[Nelphine]

As you can see, the demon lord, even if it rolls max on all its ranged attacks, only does 716 damage with its ranged. Then in melee it gets destroyed.

Play in tactical, and even with a wizard supporting the doom drakes, there is almost nothing they can do to beat the demon lord.

Updating with more clarity:

10 rounds of ranged attack. Since the drakes have none, only the demon lord attacks during this time. Each round it rolls 1-10, multiplies by ranged attack (716) and divides by 100. So, max is 10*716/100, or 71.6. Times 10 rounds is 716.

The drakes have now lost 716 of their 2904 health, which is a little less than 25%. Therefore they have lost the same amount of attack power. Doing horrible rounding, we call it -600 melee attack.

The drakes now have 1798 attack and 2188 defense going into the melee phase. This is about 10% more health, and more than 50% more melee attack than the unhurt demon lord.

Each round both sides roll 1-10, multiply by melee rating (1108 and 1798 in the first turn) and divide by 100. Due to the difference in attack power, the demon lord needs to roll 50% higher to do the same damage. Further, the demon lord has less defense rating, so it needs to roll even higher to match the percentage lost. If drakes roll 2, demon lord needs 4; if drakes roll 4, demon lord needs 7; if drakes roll 6, demon lord needs 10; if drakes roll 7 or more, they do more damage. Statistically, the demon lord gets destroyed - it only does more damage 20% of the time, and each round it does less, it has a lower chance the next round.

Also note I maxed the demon lord range damage. In reality it's going to average 384 damage instead of 716, which will make it nigh impossible for the demon lord to ever match the drakes in melee.

[Tiltowait]

Someone should write a program or a spreadsheet macro to simulate strategic combat, round by round. I have a hard time wrapping my head around the numbers.

[Nelphine]

Updated.

[Seravy]

I don't know enough of the numbers. Not knowing how much attack rating drops with damage is a big thing.

As many % of it as the damage was compared to the health.
So if a side took 5 damage out of their 100 health, they lose 5% of their attacks, however many that is.

Life Steal adds to attack rating, all gaze and touch attacks do. It's +100 per figure attacking. Save modifier is ignored.
The accurate attack rating is actually (melee-2)*figures*20. (and 7*figures or 13*figures for 1 or 2 melee)
Since the patch about a month ago, + To Hit also modifies attack rating by +33% for each To Hit. Formula is 33*attack rating*(3+Hit bonus)/100. Yes that means no to hit has only 99% value due to rounding, can't do 33.3333333%

So Demon Lord is (23*20+100)*198/100= 1108
Doom Drakes are, at level 0, 10 melee, 7 fire breath.
That's (8*20+5*20)*132/100*2= 686
No idea how you calculated the 2700.

Edit : Your defense calculation looks wrong too. Demon Lord has 35 health and more armor than Doom Drakes who have 22 total in the unit. There is no way higher numbers can yield a lower total rating.

[Nelphine]

There were 3 units of doom drakes. So an individual would be 1/3 of what I calculated (plus 33% attack rating due to +to hit.)

I'll redo my numbers in the original post. Sorry about life steal I missed that.

Updated post. The slight difference in attack power formula hurts multi target. It's significant. +hit is powerful, as it should be.

Also, I believe flame breath you stated was 50% stronger than standard melee. The -2 in the attack formula really hurts them here.

[Nelphine]

Updated the second post with more detailed results.

[Nelphine]

I'd like to run other examples here. At the moment I'm specifically ignoring the effects of the wizard in combat, because it shows a more accurate portrayal of the units combat ability. I'll start including wizard once it looks like we have some agreement on the unit side of things, that the current formula has significant flaws.

If you ask for other examples, preferably where you think it's obvious which side should win but strategic combat seems to give different results, or where you aren't sure how the numbers work, I'll run them.

[Seravy]

Also, I believe flame breath you stated was 50% stronger than standard melee. The -2 in the attack formula really hurts them here.

True, I keep forgetting that. Breath/thrown multiples by 30 not 20.

I think the best would be to just write a simulator or calculator. Take the unit stats and names directly from the exe, let the user select any number of any unit(s) of any level on each side and either output the total army data or even run a simulation of the battle itself.
I'm not going to do it though, don't have time for that. I can provide numbers for how much each type of touch or other attack type adds to or multiplies attack ratings. I think everything else is already known.

Demon Lord are definitely underrated because most of their power comes from the summoning, doom bolt, and immunities and not the stats. On the other hand, if they do kill something you'll get way more undead than you normally would.

[Nelphine]

Agreed. But it's not just demon lord, a lot of fantastic units have the same problem.

That's the purpose of this thread. To investigate, and see if we can come up with something better. I might run the excel sheet, but for me, showing glaring examples of problems, and then trying to find similarities in a way that will be simple to code a fix, is more important.

my next example will be the classic 'AI uses Spearman to beat sky drakes' although instead of Spearman I'm going to simply use the weakest unit that will succeed.