Fire, Ice, and Lightning damage, and I think also Poison damage, is supposed to completely bypass normal defense, and should only be affected by the appropriate resistances.

Thus, while the mundane components of an attack delivers up to PierceAttack*PierceAttack/(PierceAttack + Defense) damage to the target, the magical component deals up to (FireAttack*(100 - FireResistance) + ColdAttack*(100 - ColdResistance) + LightningAttack*(100 - LightningResistance))/100 damage to the target of an attack. Normal defense is supposed to be completely useless against any form of magic damage, and since the basic magic resistance items are either 25 or 50 resistance to an element there isn't really much room for resistance bonuses there (certainly not the +1130% bonus that defense gets, though a flat bonus of 25 resistance could be appropriate). Actual damage from an attack is then supposed to be within the range (0.5*maximum_damage, maximum_damage), and the tooltip that pops up when targeting an enemy unit will show these minimum and maximum numbers (remember that damage is per-figure, and each figure provides a separate attack roll which can hit or miss, so a three-figure unit will actually deal 0, min-max, min-max + min-max2, or min-max + min-max1 + min-max2 with each attack, where min-max, min-max1, and min-max2 are random numbers between the maximum possible attack damage and one half of that). The defense rating used for the damage computation is the defense rating of an individual figure (so if you have plate on your units, you would have defense = 32 in the damage calculation, not the defense rating multiplied by the figure count or something like that).

If the attack damage range for a unit with a purely magic attack decreases when the target's defense increases, this would to my understanding be a bug.

don't think the AI gets a bonus to defense. that's the repeatable +10% defense technology at the end of the magic techtree. apparently they researched that tech about 113 times. 

pure melee weapons don't deal any real damage vs. this amount of defense. majority of the damage you do is elemental damage, since that ignores armor. don't know the design of Nick Dangers units, but i guess they are either buffed with fire/frost amulets, magic weapons (boreal blade or something) or heart of fire (or all of those items).

btw. the damage formula calculates the individual attack values of the single figures, not the combined value of the whole unit.

a plain longsword, maul or greataxe company with no elemental damage boosts will do next to nothing vs. 500+ defense

a 20 non elemental attack weapon vs. 500 defense results in 0-1 damage 

formula for max damage is in this case

20 * (20 / (500+20)) 

doesn't really matter in this case if you have 1 guy with this weapon or a company of 6.

conclusion: when the Insane AI stacks defense (repeatable +defense% tech) , forget physical damage - use elemental damage

Where is this multiplier stored? I ask, because there is nothing in the CoreDifficultyLevels.xml, but that would explain it:

I think there's a structure you can build in a Fortress that grants +2 attack to units trained there. As for why the second has a higher attack, did you at some point defeat a wildland boss whose reward included an attack modifier bonus for units trained in the city you place the trophy in?

The attack numbers for the unit "The Wall" give a damage range of roughly 20-40 damage per attack if everyone hits against a 300-defense target, or roughly 16-32 damage per attack against a 500-defense target, assuming no fire resistance is involved. If the damage calculation isn't using a per-figure attack rating for the computation, then the damage range is 42-84 against 300 defense or 33-66 against 500 defense. It should be fairly easy to test whether the damage computation is using the per-figure attack or the total unit attack at that difference in damage numbers.

Also, Nick, you posted the same attack breakdown for both units. Could you correct the second one?

There is a trait, Charge, which grants additional attack and movement at the beginning of the battle. If your units have it, that could explain it.

Looks like the damage range is greater than I thought (or at least has a higher maximum than I thought) - even with a Swarm bonus granting +8 attack you should only see up to 240 damage from how I thought the damage computation worked, regardless of which way the attack values are handled.

Edit: were your troops fighting opposite-alignment units? I just noticed that the Fortress gave your troops Enmity and that could help boost the damage number up to what you were getting.

And no swarm bonus for those attacks.

My question is does the ai not realize you are using elemental damage and trying to protect itself from that ? I mean at some point, stop researching refined defense...

I agree, it's just that with the numbers he had it should be relatively easy, since the entire damage range using the combined attack for the damage computation was completely outside of the damage range calculated using individual attacks. If you were sure you'd accounted for everything, and you saw damage either on the very low end (less than one-third the minimum damage for the combined attack rating) or very high (more than the maximum damage for the individual attack rating) you'd immediately know which formula it was using. Unfortunately, I don't know enough about how Doom Hammers work to really work them into a damage range computation, and the damage computation is something that I don't really care enough about to thoroughly test at the moment to figure out which way it works.

Plus, there are a bunch of traits you can pick up that you don't really know how they work (e.g., Enmity says it grants +25% attack against opposite-alignment units, but this only works on the mundane component of your attack, and I couldn't say if it works for custom factions using races which were supposed to be of the other alignment, such as a Mancer-blood Empire, nor do I know if the mundane attack bonus from traits like Muscle or Finesse can come into play for units using Incineration Staves, though since they don't get displayed in the attack breakdown I don't think they contribute, but it's something I'd have to test to actually know what happens).