Celtic Heroes

Disclaimers:

• All testing was done in PvP with auto attacks only. There are definitely nerfs and changes to certain skills in PvP, but as far as I know the auto attack mechanic doesn't change. I asked Muldar about this, he said he was not aware of any PvP changes with respect to auto attack. Expect that the results here can be applied to NPC enemies and bosses.
• At best, these are good estimates. At worst, they could be completely off. It is very unlikely that these curves are EXACTLY right—I'll explain why later.
• If you see anything that could be proven/disproven, feel free to chip in. I'll adjust if new data comes in, or if necessary, wipe this post altogether if it turns out to be wrong.
• This does NOT account for level gap! If you are below the level of your target, you will suffer a separate damage penalty unrelated to armor/resist (unless in PvP).

Important note:
Here's an analogy—armor is to slash/crush/pierce resist as vitality is to health. Increasing your armor also increases your slash/crush/pierce resist. However, slash/crush/pierce resist can be increased by things besides armor—like wearing rare Connacht armor, or getting a druid to ward you, etc. At the end of the day it's only RESISTANCE (displayed in ability menu) that matters against the corresponding damage type. If you hypothetically had 0 armor and 1000 pierce resist, you'd still have very strong damage reduction against say, a rogue stabbing you with daggers. I mention armor in the title only because it's commonly used, but from now on I'll only refer to resists (same thing really).

Below are two graphs. CLICK FOR FULL SIZE (unless you like looking at tiny graphs)

Lower-Upper Bound Damage vs. Resist Curves (with data points marked in blue)


Average Damage vs. Resist Curve


Damage Fluctuation (and inaccuracy)
Before you can really understand the graphs, you need to realize that against an enemy with 0 resistance, any damage will do between 60% and 100% of its listed value, averaging out to 80%. So in the Lower/Upper Bound graph, you see that when X (resistance) is 0, the upper is 100% and the lower is 60%. This huge fluctuation is why it's so hard to determine an exact curve for damage vs resists! Even after hundreds of auto attacks, your average could still be too low or too high. I did curve fitting—where you draw an approximate curve through some rough data points. So a lot of stuff in this post is qualified with "about."

Graph Explanations
On the first graph you see two black curves, which represent the (approximate) maximum and minimum percent damage you can hit an enemy with a certain resistance. So suppose you're a rogue with 1000 pure pierce auto attack damage (no elemental damage). Then against a target with about 500 armor, you should do AT LEAST 30% or 300 damage and AT MOST 50% or 500 damage per swing (ignoring any level gap and assuming the graphs are correct, of course).

On the second graph you see one black curve: this is the average line. Notice how it starts at 80%. That means that even against a boss with 0 resists, you can only average 80% of your stated damage (since hits will randomly fall anywhere between 60 and 100% damage).

Notable Benchmarks (for average damage)
0 armor = 80% average damage dealt
500 armor = about 40% average damage
1000 armor = about 25% average damage
1500 armor = less than 20% average damage

The Equations
If you're reading the graphs, Y is damage you deal as a %. X is the resistance of your target. e is a mathematical constant equal to 2.71828

Upper bound damage = 80e^(-.002x)+20
Average damage = 64e^(-.002x)+16
Lower bound damage = 48e^(-.002x)+12

These are natural exponential equations. Natural—because it involves the constant e, and exponential because e gets raised by the power of the target's resistance (x).

For math junkies. Notice what happens when x = 0, we get 80+20 for the upper bound, which is where 100% comes from. Same for the rest of the equations.

Minimum damage
If x, aka the target's resistance, is a very large number (raid bosses anyone?) then we approach the asymptotes of the graph. In other words, the upper bound of damage approaches 20%, the lower bound approaches 12%, and the average damage approaches 16%. You can tell from the equations that these are the constant values.

Therefore—if these equations are right—then the baseline, rock bottom, absolute lowest hit you can do to a boss is 12% of your displayed damage.

(Of course, we're still neglecting level gap. If you are a level 60 hitting aggy for example, you will do much less than 12%)

This is where people can help improve the equations by disproving the current one. If you are above or equal to the level of an endgame boss, say Gelebron for instance, and you do LESS than 12% of your displayed damage, then let me know because that means the lower bound is definitely wrong. For this experiment you might want to take out lures/shatter and use a physical type of damage, not divine. Maybe don't try this on Gelebron since that would be too costly and/or time consuming.

An endgame warrior can easily achieve above 2k armor (slash/crush/pierce resists) with pro stance on. Probably 3k+ with lix and druid bark. So I suspect that the toughest endgame bosses might have more than that, and other lower level raid bosses likely also have thousands of resists.

As always, open to criticism/suggestions.

Thanks,very well written,nice and tidy

By the way, after hundreds of auto attacks exchanged between 2 toons, I confirmed a simple finding I made a year or 2 ago about attack vs. defense. (Also checked with Muldar, he says it looks right)

Your hit accuracy = Attack / (Attack + Defense)

Where attack is your own attack and defense is your target's defense. In PvP, if you're auto attacking a warrior with 1000 defense and you have 2000 attack, you should land 2/3 of your auto attacks and miss 1/3 of them.

With boss fights, this isn't actually useful until you determine the defense of the boss. To figure this out, estimate how many autos you land vs miss. 10k attack and missing about half your autos? The boss has somewhere around 10k defense.

By the way, after hundreds of auto attacks exchanged between 2 toons, I confirmed a simple finding I made a year or 2 ago about attack vs. defense. (Also checked with Muldar, he says it looks right)

Your hit accuracy = Attack / (Attack + Defense)

Where attack is your own attack and defense is your target's defense.

In PvP, if you're auto attacking a warrior with 1000 defense and you have 2000 attack, you should land 2/3 of your auto attacks and miss 1/3 of them.

Yep this is highly accurate and how I find to an extent boss defense. Level difference does play a role but incorporating that into it will be hard. I am interested in skill evasions though. Unless it's same as ability/ability+evasion...

Awesome work btw.

I am interested in skill evasions though. Unless it's same as ability/ability+evasion...

I haven't officially tested skill evasions but just based off what I've seen, it very likely doesn't work like that. Skills seem to have a much higher chance of landing compared to auto attacks when ability/attack and defense/evasion are roughly the same.

Skills are also much harder to test logistically. The most spammable direct damage skill is fire bolt, with a 6 second cooldown—that's still slow compared to autos, like testing auto attacks with a 6000 speed weapon and no haste! By comparison, I used a 3200 speed, 10 divine damage ceremonial dagger (which does 0 damage by itself in PvP) paired with a 300 dmg fiery conquest axe and haste ring to test resists.

Besides being time consuming, I'd also need a test dummy with either maxed or nonexistent Warding, since tests like these require at least a thousand hits in total to be accurate enough, so spell evasion could change during tests if Warding has room to improve.

Woohoo! You did it. No credit for me providing the wisdom lix though?

Outstanding work, and thank you for detailing your findings. I always appreciate learning more about the quantitative / behind-the-scenes aspect of this game.

Much appreciated, and fantastic job on putting it all together.

Welcome Back Swan aka Papi;)

fyi, the resist percentages aren't the same in pvp and pve lol

Idk why you'd ask an otm worker about the game, they know less than the players

fyi, the resist percentages aren't the same in pvp and pve lol

That's interesting, how did you manage to test in pve when the resists of enemies are unknown?

You could have a high mage lure zero out your target's resist, then lower the mage lure bit by bit until you see a drop in damage, then calculate from there. But I imagine you would need to read thousands of damage numbers and use up a lot of alt books…