Strategic Combat in CoM

[Nelphine]

I think barbarians are too strong in strategic combat. Barbarian swordsmen with alchemy and heroism have 950 attack power, and with flame blade, that jumps to over 1500 (which puts it in sky drake range.)

[Nelphine]

I've realized that I had made that error of off by a factor of ten, way back when I calculated how strategic battles go.

I'm redoing this work. I believe right now, ranged are virtually useless; battles aren't 40-50 turns with 10 turns of ranged, they're potentially 100+ turns with 10 turns of ranged. I'm not sure yet though, and will post some sample battles so people can check my work.

[Nelphine]

I've made some assumptions about rounding damage in the below post. Please do not consider the below complete until these assumptions are confirmed.

Assumption 1: Every turn in strategic combat, an amount of damage is calculated. This number is a decimal number, call it 'real damage'. So a unit might take 10.15 real damage.
Assumption 2: Every turn in strategic combat, the ratio that determines how much attack strength is lost, is based on the current ratio of attack strength compared to defensive strength. Call this 'current ratio'. So if the unit had 200 attack strength and 100 defensive strength, then if it takes 2 damage in strategic combat in any turn of the combat, it will lose 4 attack strength as well; if for some strange reason due to rounding it's current ratio of attack strength to defensive strength becomes 3:2, then taking 2 damage would cause it to lose 3 attack strength.
Assumption 3: Every turn in strategic combat, based on the real damage a unit takes, the unit loses attack strength of an amount equal to the initial ratio times the real damage. Call this 'real weaken'. So based on the real damage and initial ratio examples above, the unit would take 20.3 real weaken.
Assumption 4: Every turn in strategic combat, the actual damage a unit takes is real damage rounded to the nearest integer. Call this 'damage'. So, as per example in assumption 1 above, damage taken would be 10.
Assumption 5: Every turn in strategic combat, the actual attack strength a unit loses is real weaken rounded to the nearest integer. Call this 'weaken'. As per example in assumption 3, weaken taken would be 20.

(If no rounding is done until the very end of strategic combat after one side or the other dies, it won't change much of my results, so this is just so we are all on the same page as to what I'm doing.)

Assumption 6: Due to the number of turns involved, I'm going with an average roll of 5.5 on the 1-10 roll. I'm aware battles can swing a bit if they roll particularly high or low for the first 5 turns, but I'm ignoring that in order to predict strategic battles over the course of the game, not a particular strategic battle.

1 standard Swordsmen vs 1 standard Spearmen

6 figures, 1 HP
2 attack 1 armor vs 3 attack 3 armor

Tactical:
6*0.3*3 = 5.4 damage.
-0.3 = 1 figure dead, 4.1 damage left
-0.3 = 1 figure dead, 2.8 damage left
-0.3 = 1 figure dead, 1.5 damage left
-0.3 = 1 figure dead, 0.2 damage left
-0.3 = 0 damage left.

Swordsmen kill 4 figures.

6*0.3*2 = 3.6 damage.
-0.9 = 1 figure dead, 1.5 damage left
-0.9 = 1 figure dead, 0 damage left

Spearmen kill 2 figures.

4*0.3*3 = 3.6 damage
-0.3 = 1 figure dead, 2.3 damage left
-0.3 = 1 figure dead, no spearmen left

2*0.3*2 = 1.2 damage
-0.9 = 0 figures die.

End result: 0.5 melee turns kills spearmen and does 2 damage to swordsmen.



Strategic:

Swordsmen:
Offense = 120, Defense = 168
Spearmen:
Offense = 60, Defense = 120

0.055*120 =
6.6 damage and (7)
3.3 weaken (3)

0.055*60 =
3.3 damage and (3)
2.3571428571 weaken (2)

0.055*118 =
6.49 damage (6)
3.245 weaken (3)

0.055*57 =
3.135 damage (3)
2.2392857143 weaken (2)

Note: swordsmen will continue to do 6 damage per turn until the spearmen do 20 weaken - at least 10 turns. They will do 3 weaken per turn until the spearmen do at least 29 weaken.

10 turns of swordsmen attack will cause 61 damage, 30 weaken.

Spearmen will do 3 damage until the swordsmen cause at least 15 weaken at which point they start doing 2 damage. Spearmen will do 2 weaken until the swordsmen cause 22 weaken. Spearmen will do 1 damage until the swordsmen do 51 weaken, and will do 1 weaken until the swordsmen do 47 weaken.

Spearmen will therefore do 3 damage and 2 weaken for the first 5 turns (15 and 10 total). They will then do 2 and 2 for the next 3 turns (21 and 16 total). They will do 2 and 1 for the next four turns.

So after 14 turns:
25 damage and 20 weaken dealt to swordsmen.
85 damage and 42 weaken dealt to spearmen.

For the next 2 turns the swordsmen do 5 damage and 3 weaken. The spearmen do 1 damage and 1 weaken. At that point, the spearmen start doing 1 damage, and 0 weaken. After 1 more turn, the spearmen are now doing 0 damage and 0 weaken. After 2 more turns, the spearmen die.

Total after 19 turns:
28 damage and 22 weaken dealt to sworsdmen.
Spearmen killed.

28/168 = 1/6. Therefore the swordsmen have taken 1/6 of their original hp as damage during this fight. That means they have taken 1 damage (in other words lost 1 figure).

Note: This was done based on assumption 2 working on 'initial ratio' instead of 'current ratio'. It doesn't change the end result by more than a turn, so I haven't fixed the math.



Final comparison:
In tactical combat, this fight takes 1/2 of a melee turn. The spearmen die, and the swordsmen take 2 damage. Note that on average it's actually closer to 2.1 damage that the swordsmen take, but the wonders of rounding make it likely that only 2 damage will be taken.
In strategic combat, this fight takes 19 melee turns. The spearmen die, and the swordsmen take 1 damage. Note, that on average this is exactly 1 damage, due to the rounding occuring each round during the combat.



This battle is the initial place where I believe ranged are still undervalued. 1/2 of a melee turn in tactical combat = 19 melee turns in strategic combat. Therefore 1 full melee turn in tactical (4 attacks from each side) is ~38 turns. Therefore, 1 ranged turn in tactical combat is likely to equal ~10 ranged turns in strategic combat. (Remember that in melee, both sides get to fight twice on both sides turns. So side A attacks twice, and side B counterattacks twice. Side B then attacks twice, and side A counterattacks twice. That's one turn. For ranged combat, side A attacks, then side B attacks. They end up with 1/4 the number of attacks as melee combatants get.)

That means that 10 ranged turns in strategic combat is ROUGHLY equivalent to letting them attack 1 time in tactical combat, which I believe undervalues them.

I'm also going to explore just how overpowered thrown weapons are in these sample battles, as right now barbarians are silly strong. (Alchemy + Warlod + War College + 1 common life spell = Bezerkers that are as good as Great Drakes. So, strategically, barbarians have great drakes by turn 35.)

[Nelphine]

Finally: yes, i'm planning on suggesting a new formula, which only uses the information we currently have available to strategic combat. I'm just not going to make that suggestion until I've examined 6-12 such sample battles and seen what patterns emerge.

[Nelphine]

As an example of the current problem:

Barbarian AI, whose total army strength is 3 TIMES the other 2 arcanus AI combined (on impossible difficulty), has 8 sprites in his fortress along with a hero. One of the other AI steals one of his barbarian cities, builds several bezerkers, and banishes the winning AI without any difficulty. Since that AI has around 65 spell casting skill, it's going to take him.. 16 turns to return? Even though none of the other AI can threaten any of his cities that don't have a shrine. (As soon as they get a shrine, they start building shaman and kick the bezerkers out. Which makes their strategic strength drop to about 1/5 of what it was before the shaman.)

[Seravy]

1. Not exactly, but something like that. For example if 5% damage is rolled and the army strength is 1000 total then this is 20. A doubleword is used to store it.
2-3.The damage above (200) is subtracted from the defense of the other army directly, but from the attack, the same percentage is subtracted instead of the same number.  For example if there was 1000 defense and 2000 attack then 200 defense but 400 attack is lost.

Your calculation seems correct (except for the rounding). However the spearmen dies on turn 17 - a side with less than 10 total melee attack remaining in the melee turns counts as dead, it doesn't need to reach 0.

(also, in reality, casting power would kill the spearmen way before that)

[Nelphine]

OK, so if something has 673 attack power. It rolls 10% damage. How much damage does the enemy take in that strategic combat round?

The enemy has 513 defense rating and 1011 attack rating. How much attack rating does it lose that round?

(And yes, of course spellcasting will hurt the spearmen first; but for purposes of seeing if the units are remotely balanced, I'm disregarding that.)
I didn't realize things with less than 10 attack power are considered dead in strategic combat. So, the tactic of attacking with a settler (since it has lots of HP) in order to damage with casting skill, doesn't work?

What happens if the target attacks with a settler and a swordsmen? Does the settler defense rating add to the swordsmen defense rating, or is the settler considered dead, so it doesn't add at all?

[Seravy]

OK, so if something has 673 attack power. It rolls 10% damage. How much damage does the enemy take in that strategic combat round?

It takes 67 damage in defense and 132 in attack.

So, the tactic of attacking with a settler (since it has lots of HP) in order to damage with casting skill, doesn't work?

It might if the enemy has a ranged army and there are ranged turns. Otherwise it won't.

What happens if the target attacks with a settler and a swordsmen? Does the settler defense rating add to the swordsmen defense rating, or is the settler considered dead, so it doesn't add at all?

Everything is added together first, and the total is checked for being 10 or higher. So that will work.

I don't think settlers have a good defense rating though (they have too low armor).

[Nelphine]

HP are waaaay more important to defense than armor is.

Halberdiers (2 hp, 4 armor, 6 figures) have a defense rating of 384.

Swordsmen (1 hp, 3 armor, 6 figures) have a defense rating of 168.

Settlers (10 hp, 1 armor, 1 figure) have a defense rating of 200.


On rounding: So I think the only thing 'wrong' that I did is assumption 2 - it always works on the current ratio, not the initial ratio?

[Seravy]

Yes, it works on the current ratio.