[How Stuff Works] Damage

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[How Stuff Works] Damage

Postby armis » Thu Oct 25, 2012 2:09 am

This is a compilation of things I’ve either read on these boards or tested myself, but mostly tested myself because I have trust issues :P. All credit to those whose work I'm using here.

While I think people mostly understand now the major points of how the game calculates damage, I think it’d be useful to have a central reference for this. First, to encourage discussion on the things I may have gotten wrong, obviously, and second so that you don’t have to search the boards for an hour to find the tiniest bit of accurate information. Comments in orange are those that I still have to test whenever I get a minute, which might not be for the next few days.


The Principles

Before we start crunching numbers, there are a few rules that one should understand about how damage works:
1) Virtually all bonus damage is additive. If you find an item with +20% melee damage, for instance, or +10% all damage, it’s not going to multiply your current damage output by 1.2 or 1.1, respectively. The damage bonus will add to all the other bonus sources you may have, and only then will the resulting total be applied to your base damage.
2) Fumbles only happen on auto-attacks, not on skills.
3) Fumbles never crit.
4) DoTs don’t crit. Nope.
5) Weapon-based critical hits always deal maximum damage. Surprisingly, I haven’t seen anyone mention this here yet though it’s both rather huge in terms of optimization, and pretty glaring when you look at the combat log. This holds true for auto-attacks and all skills wased on weapon DPS.
6) There are hard caps you can’t go over, no matter how much stuff you stack:
  • Fumble chance: minimum of 0% (duh)
  • Fumble damage recovery: maximum of -0% (duh again)
  • Execute chance: maximum of 100% (you don’t say?)
  • Critical chance: maximum of 100% (yes, this is Captain Obvious speaking)
  • Critical damage: maximum of 500%
  • Dodge chance: maximum of 75%
  • Block chance: maximum of 75%

The Fake Formula

The formula below describes how damage works, but incorrectly. I want to make that very clear. However, it’s simple enough to give you a basic understanding of how things work, and then I’ll go on to post the actual full formula.

(1)
Code: Select all
DPS = base_dps * (1+bonus_damage) * (1+speed_bonus) * (1+crit%*crit_dmg) * (1+u*fumble%*fumble_dmg)


There.

1) The bonus damage is, like I mentioned above, the sum of all sources of applicable bonus damage. This includes:
- strength bonus for weapons (equal to Str/2 and uncapped)
- focus bonus for elemental damage (equal to Foc/2 and also uncapped)
- sources of direct applicable bonuses like +10% all damage, +35% fire damage, +20% ranged weapon damage, etc.
In very few cases, a source of bonus damage will apply directly to the base damage (instead of being added to all the others), thus making it extremely valuable. This is the case, for example, with Prismatic Bolt’s tier bonuses.

2) The speed bonus is either attack speed bonus (if it’s a weapon attack) or a cast speed bonus (if it’s a skill). Some skills have a cooldown, and as far as I know they never benefit from casting speed bonuses in terms of damage per second. Others are channeled (their mana cost is expressed in mana per second): some of them do benefit (Arc Beam, Shocking Burst for instance) from cast speed bonuses, but others don't (Magma Spear); at this point I'm not sure why, and I don't have a full list. In all cases, however, cast speed does accelerate the wind-up animation, so the spells do come out a bit quicker. Attack speed does benefit skills based on weapon DPS indirectly, in that increasing attack speed increases weapon DPS.

3) Critical hit chance for skills is actually often not the one you see in the Arcane Statistics panel. For skills dealing a percentage of weapon DPS, it is usually your normal crit chance multiplied by this factor. For other skills it's a different hidden value that needs to be figured out (or fished from game data files). For instance, each pillar of Ice Prison has a ~75% adjustment to its crit chance when shattering.

4) The next expression is the increased damage from critical hits, assuming critical hits are based off the normal base damage range. Since weapon-based crits always deal max damage, this expression is in fact wrong for thos type of attacks but it's just simpler to visualize like this anyway.

5) The last expression is fumbles. Fumbles only happen on auto-attacks, so u is a special variable equal to 1 for auto-attacks, and equal to 0 with skills. Since fumbles and crits are separate events, this expression is technically wrong too - again, it's simpler to explain the concepts this way.

6) Base dps here can be a great many things.

  • With auto-attacks, your base dps is your weapon DPS. But wait! That’s straightforward enough with one-handed and shield or with two-handed weapons, but with dual weapons it becomes more complicated.
  • Dual weapons alternate their attacks depending on their speed, which works out to a sort of averaging of their DPS values. That’s lame, because it makes them strictly inferior to one-handed weapons. Their saving grace is Execute. Execute means both fire at once, so your damage is the sum of the two.
    The DPS formula for dual wield has been found to be the following (I take no credit for that one – in fact I haven’t even tested it, so take that with a pinch of salt):
    Code: Select all
    Base_dps = (A+B)/(a+b) * (1+execute%)

    A and B are the average damage per hit values of the two weapons, a and b are their respective speeds.

  • With skills based on weapon damage (those that say “X% of weapon DPS”) in the tooltip, the base dps is:
    Code: Select all
    Base_dps = WDPS * X% / CS

    where X% is the skill’s damage multiplier and CS is the cycle speed of the skill, i.e. the time between two consecutive castings of the skill.

    Cycle speed isn't listed anywhere and must be figured out for each skill (though it is equal to the cooldown on skills that have those). It is only relevant if you want an absolute measure of DPS, or want to compare two skills in terms of damage over time. If you're just figuring out the optimal gear/stats for one skill, then you can actually do your comparisons without this variable.
    Do note that when dual-wielding, skill damage is always, and only, based on the weapon in your right hand (i.e. the one in the box on the left side of the inventory screen) (edit: except Arc Beam, apparently - credit to Baron).
    If the skill deals elemental damage (“X% of weapon DPS as Fire,” for instance) then you get to add both Strength and Focus as sources of bonus damage in (1).
  • With skills based on flat damage values, such as say Hailstorm, the base dps is the damage range listed in the tooltip divided by the cycle speed. Easy. For those skills, Strength does not factor at all and it’s all about the Focus.

The Actual Formula

Now that we understand the basics, let’s dig into the details. The actual accurate formula is the following (hang on, it’s a bit long):

(2)
Code: Select all
DPS = (1+bonus_damage) * (1+speed_bonus) * [(1- u * fumble%) * [(1-crit%) * base_dps + crit% * crit_dmg * crit_dps] + u * fumble% * fumble_dmg * base_dps]


Yay for science. Pay attention to the nested parentheses, it’s a bit hard to read on screen.
Crit_dps is basically the same as base_dps for flat-damage skills (e.g. Hailstorm), and is the maximum damage in the range for weapon-based skills (e.g. Flame Hammer) and auto-attacks.

The idea is basically that:
- if you fumble, you deal your fumble damage (if it’s an auto-attack, obviously)
- if you don’t, you have a chance to crit and deal crit damage (plus your crit damage bonus)
- otherwise you deal normal damage
- whatever happens, it’s all augmented by bonus damage and the appropriate speed bonuses

But it gets worse, because sometimes base_dps is actually made of different things: physical and elemental damage. In this case, I won’t type out the whole equation but basically you need to split the physical and elemental damage, calculate DPS separately, then add them up again, all because elemental damage is increased by Focus (and some specific bonus sources, like +15% ice damage) while physical isn’t.


Gear: As If It Weren’t Confusing Enough

There are many affixes on gear that can impact the equation above (poetically named “(2)”).
- increases to attack or cast speed add to the speed_bonus variable
- damage increases, when relevant (and including Strength and Focus, or Melee/Ranged bonuses), add to the damage_bonus variable
- affixes modifying crit chance, crit damage, fumble chance and fumble recovery add to their respective variables
- here’s where it gets neat: what happens with stuff that adds fixed damage?

Well, thanks for asking. It depends on whether it’s a weapon socketable (or a weapon enchantment) or not. If it is, the added damage value gets added to the base weapon damage per hit. This is huge, because if you add a Skull of Vellinque (+199 physical damage) to a weapon that deals 100 damage per hit, you’re essentially tripling the total DPS (give or take). Bear in mind that if you add elemental damage such as from Embers, it gets bonus damage from Strength AND Focus (and all other applicable bonus sources). The flip side is that if you’re using a flat-damage skill, your weapon is irrelevant and so is this socketable.

If it’s not a weapon socketable/enchantment, then it sucks. Not that I’m judging. The fact is, it gets no bonus damage whatsoever. That +173 ice damage necklace basically adds 173 ice damage to your final damage number before fumbles and crits, but that’s it. You could have 2000 Focus and you’d still only get +173 ice damage, even with skills. Note that the bonus damage from Sword and Board works like this too, making it IMO the most useless skill in the game.

Adding to the confusion is how the game calculates it: all elemental damages are actually calculated and applied separately, which means that enemy armor will apply separately to each of them. In addition, when socketing a physical damage gem (or enchant, etc.) in a weapon dealing physical damage, the game will count it separately. In other words, any addition of physical damage applies separately from the weapon's base physical damage. Yes, it's a bit confusing so here's a screenshot:
Spoiler: show
Image
Notice in the combat log the +Physical line, which is separate from the first line (that corresponds to base damage of the gun), and is the result of a +27 physical enchant and +199 physical skull (226*(1+5% from Str) = 237).



Weapon affixes and skills
(largely copied from my Embermage Handbook but has general applications)

There's a lot of confusion around which skill applies which weapon affix. Like I said above, skills based on weapon DPS transmit some effects, but not all of them. Let me refine that a bit.

1) Skills that are NOT based on weapon DPS do not transmit any active effect (i.e. DoTs, % chance to cast spells, armor debuffs, etc.).
2) Skills based on weapon DPS may transmit some, but it depends on the effect and on the skill.

On stacking:

DoTs from skills never stack with themselves: you can cast Magma Spear as many times as you like, but the target isn't going to get more damage per second (however, the duration will be refreshed each time). Do note that the number in the icon that tells you how much damage the target is taking does change for some skills, as some DoTs have a damage range and a new application can roll a different number in that range. DoTs from skills usually scale with focus and the appropriate +% damage modifiers.

DoTs from weapons (as a native affix, not as a socket - enchantments not tested at this time) DO stack with themselves [edit: apparently so do DoTs from enchantments - thanks lminith]. Two hits from Endgame will result in the target taking twice the damage over time, with the game keeping track of each duration separately (the icon will only show the longest time remaining). In addition, those DoTs scale with your character's Focus, but not his strength (even though technically they're physical damage - go figure). In other words, they can be a source of massive damage if you have a fast-attacking weapon or a fast-casting skill, and lots of Focus.

DoTs from socketables stack with themselves too, both from multiple weapon hits or from having multiple socketables in one weapon. However, they don't scale with Focus (nor Strength), so their damage ends up rather piddly. Not worth the socket IMO. (edit: apparently fixed to scale with Focus in 1.22 - according to patch notes - but I haven't tested it)

Also, as a miscellaneous bit of information: DoTs don't build charge, whether from a skill, weapon or socketable.

Armor debuffs from weapons or socketables do stack with themselves too. More interestingly, the "% chance to flee" debuff (which I assume works like other "chance to inflict X" affixes) seems to stack too, though I have no idea how that works: if you hit the dummy with a "10% chance to flee" weapon, once every few hits it'll get a little icon that says "10% chance to flee". If it gets that effect applied again, the icon will be upgraded to 20%, then 30, etc. At face value it's like you have a chance to inflict a debuff that has a chance to cause the target to flee; my guess is that the game is just acting up a bit and the 20/30/40% chances just mean the "fleeing" debuff was applied while it was still active from a previous hit.


What About Attributes?

Attributes define a lot of the damage variables. What often happens is you take an attribute, derive the base value of, say, crit chance, and then add to that all the fixed bonuses you have (usually from gear).

Crit% = Dex * (0.2002 – 0.0002 * Dex), capped at 50.1% at 500 Dex (Dodge also follows this relationship)
Crit_dmg = 50 + Str * 0.4, capped at 450% (technically 449.6%; basically Str above 999 doesn’t give you anything. Total crit damage from all sources caps at 500% in the Arcane Statistics screen though)
Fumble% = 21%, and no amount of stats will change that number, only gear will improve it
Fumble_dmg = 25 + Dex * (0.3003 – 0.0003 * Dex), capped at 100% at 476 Dex
Execute% = 9.8 + Foc * (0.2002 – 0.0002 * Foc), capped at 60% at 500 Focus (technically 498)
Block% = Vit * (0.2002 - 0.0002 * Vit), capped at 50.1% at 500 Vit


How the Character and Arcane Statistics panels report things

Have you ever wondered what the Character and AS panels reported exactly? I know I have. Let’s find out with Serguei, my trusty consoled character.

Spoiler: show
Image

Spoiler: show
Image


Serguei's equipped with two Corbucci's rings, a pair of Steam-Tech Nines, and 6 pieces of the Labarinto set (which is, incidentally, ugly as hell).

Let's take a look at some numbers:

1) Physical Damage: 531-1069
The Steam-Tech Nine (which I'll call Tec9 as it's shorter) deals 79-159 physical damage. Serguei has 1000 Str, and his gears give him +72% ranged weapon damage. 79 * (1+1000/200+72/100) = 530.88; 159 * (1+1000/200+72/100) = 1068.48

2) Elemental damages: 1077 ice and poison
This field only seems to report the maximum value, not the average. The Tec9 deals 80-159 ice and poison damage. Serguei has 1000 Str and 10 Focus, and his gear gives him +72% ranged weapon damage. 159 * (1+1000/200+10/200) = 1076.43

3) Critical Damage: 19338
Serguei has +500% critical hit damage. Adding up the maximum physical, ice and poison damages above and boosting them by +500% gives (1069+1077+1077)*(1+500%) = 19338

4) Damage per second: 3995
The Tec9 deals 119 average physical damage, 119.5 average ice and poison damage, and has an attack speed of 0.64. Serguei has 6% increased attack speed.
DPS(physical) = 119/0.64 * (1+6%) * (1+1000/200+72/100) = 1324.47
DPS(ice) = 119.5/0.64 * (1+6%) * (1+1000/200+10/200+72/100) = 1339.93
DPS(poison) = 119.5/0.64 * (1+6%) * (1+1000/200+10/200+72/100) = 1339.93
DPS(total) = 1324.47+1339.93+1339.93 = 4004.33
That's an extra 10 points compared to the stats screen, which I'm attributing to rounding error. Note that this number doesn't take crits into account, and further testing shows it doesn't take fumbles into account either.

5) Magic Damage (from character screen): 1070-2154
2154 is simply twice (ice + poison) the 1077 number we've seen above. Repeating that calculation with the minimum damage of 80 gives you 541.6 minimum ice and poison damage, or 1081.2 total. I'm going to call rounding error again, but I can't help but notice that if you use 79 instead of 80 as the minimum elemental damage, all the calculations end up yielding exactly the reported numbers. I'm guessing the minimum damage is misreported in the tooltip.

6. Weapon Damage: 1601-3223
Easy enough: 531-1069 physical, 541-1077 ice and poison, total 1613-3223. Again this weird thing with the minimum value, see above.

7. Further testing reveals that none of the numbers above, including DPS, take fumbles into account.

So we now know what the reported numbers correspond to.


Armor

So we know that armor is basically a direct reduction to damage taken, and that a random amount between 50 and 100% of the armor value is applied to each hit. Beyond that not much has been done to figure out how armor works, which is why Chthon's work was so interesting. Lifted straight from his post a couple pages down:
Chthon wrote:A brief report on how monster armor works:

1. Testing methodology
Testing monster armor is a flying pain the ass for a couple of reasons. First, there's a range of damage reduction, so instead of straight numbers, you've got to deal with averages and mins and maxes that you're never sure you've hit yet. Second, the practice dummy has such absurdly high armor values that testing against it often results in damage being reduced to zero (for which the game gives you a consolation prize of 1 damage).

The best method I could come up with was this: I started a new character a made my way to the path of the honored dead where monsters are level 4 (at least for me). The low level results in a low armor, which in turn results in a narrow range of damage reduction, which allows testing to proceed without requiring a huge number of samples. Console "levelup 99" to get access to any skill I want to mess with and to equip any item. Console "aifreeze" to make the monsters hold still. Console "unit bandit_assassin" to spawn a bandit assassin to spawn an unlimited supply of guys to hit. I picked the assassin because he's supposed to have flat 100% armor across all types. Use console to spawn weapons as desired. Axes are preferred because they have no damage range to muddy up the picture. Start with a plain no-mods physical axe, then work up to more complicated weapons. For each sample, look at the combat log and subtract the "post" value from the (bonus modified) damage roll (the number on the right of the arrow).

2. Getting from .dat to actual damage reduction.
This one is a bit of a head-scratcher. ARMOR_MONSTER_BYLEVEL_VERYHARD.DAT says that level 4 monsters are supposed to have 15.14 armor. BANDIT_ASSASSIN.DAT says that bandit assassins are supposed to have 100% normal armor for all armor types. The observed range of damage reduction against the plain axe was 9-17. I don't really have a good theory for this discrepancy. (Uh... the monsters are really level 4.5?) If anyone is able to figure out where that extra 2 points of armor came from, please let me know.

3. Really unexpected result: Monster armor scales with skill WDPS!
For weapon-DPS-based skills that do less than 100% weapon DPS, monster armor is scaled by the same percentage. To replicate: While equipped with your plain axe, use a skill with really low WDPS at early ranks (rank 1 Chain Snare is a good example) and compare the average damage reduction to the average reduction from normal hits with the plain axe.
This is BIG NEWS since it means that a lot of skills everyone thought would get absolutely clobbered by armor to the point of uselessness are actually viable. (And Ravage fans should be doing a happy dance.)

4. Another unexpected result: Monster armor scales on secondary targets.
The armor on monsters taking splash damage from non-claw melee weapons (i.e., secondary targets) is getting scaled down by something -- presumably your damage-to-secondary-targets percentage. To replicate: Spawn two bandit assassins on top of each other; whack with plain axe.

5. Multi-type damage gets pro-rated... with one major anomaly
When you hit with a weapon that does multiple damage types, the monster's armor gets pro rated across the various damage sources. The pro rating is done in proportion to the post-roll, fully modified damage for each type (rather than the pre-modifier roll, or the pre-roll min/max/avg).
To replicate: This is best tested by using wands/staves with equal bases for all four elements. Each element will be reduced by 1/4 as much as your plain axe hits were. The Beast with a Million Eyes demonstrates that the base physical damage is also subject to pro rating (but see below). Adding items like 2x Ratchet Ring to boost one particular element will show that the pro rating cares about the final, post modifier roll.

Now for the anomaly:
If the weapon does base physical damage, this gets reduced by more than it should. To be precise, it looks like double. This appears to result in more than 100% of the monster's armor getting applied.
Example: A Four-Bearded Axe socketed with 3x Iron Ember Chip does 114 base physical and 105 +physical (yes, they get separate lines in the console even though they're both physical). That was as close as I could get to what should be a 50/50 pro rating. It's not. The base physical is subject to the exact same reduction range as the the plain axe (double what was expected), while the reduction applied to the +dmg from the socketables is about half what the plain axe had (as expected). The sum result is that ~150% of the monster's armor gets applied!
Another example: Mountain of the Cannibal God. One would expect the reduction applied to the poison to be ~1.5x bigger than the reduction to the base physical, but the reduction to the base physical is actually slightly larger. Adding points to focus and/or poison_dmg% gear can eventually flip this over, but the reduction applied to the base physical stays higher than the ratio between the damage types would indicate.
My best theory to explain this is that it's a BUG.

6. Degrading Armor
These effects stack with each other and themselves. Unless otherwise stated, they have a 5 sec duration. They are not scaled down (or up) by WDPS% on skills (at least not for the skills I tested with). Ordinarily, these effects apply after the hit does its damage. One exception I saw was Ravage, where each hit does its armor degrade effect before it does its damage (degrade, hit, degrade, hit, degrade, hit). (Yet another reason for Ravage fans to do a happy dance.)

7. "Monsters takes X% more damage" effects (like Howl)
These effects are applied after the monster's armor is applied.

8. Frost Breath
Applies its "monsters takes X% more damage" effect before it does its damage.

9. Multi-component skills (like Wolfpack)
I only tested Wolfpack, but I assume the others (like Emberquake) work the same. It's hard to tell because the console reports poorly on flat damage skills, but it looks like the two components are treated as separate hits that are each subject to the monster's full armor. Also, if the flat component (against, just tested Wolfpack) is sufficient to kill a monster, the WDPS component doesn't happen at all.
Last edited by armis on Wed Apr 03, 2013 2:21 am, edited 25 times in total.
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Re: [How Stuff Works] Damage

Postby jdean300 » Thu Oct 25, 2012 2:16 am

Okay.... didn't read everything because I'm itching to go farm, but this is awesome! I have bookmarked it. Good work and thanks for this :)
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Re: [How Stuff Works] Damage

Postby grasida » Thu Oct 25, 2012 3:11 am

There's a very simple way to test whether or not the screens take fumble rate into account. That is, increase your dexterity and see if the numbers change. Now put on a piece of fumble chance reduction gear and see whether the numbers change. I haven't specifically tested for this myself, but I have never noticed those numbers changing as a result of a dexterity increase or a reduction in fumble chance, so I believe that the screens don't take those into account.

I knew almost all of this already, but I really appreciate how thorough and clear your post is. The forum needs more posts like this. I do have one question. You mention all sources of extra damage not attached, either as base affixes or from embers, to your weapon are not modified by anything at all. They are a flat number added to each attack after the damage calculation is complete (this is the part that I didn't know). Now, I assume those bonuses are added to weapon damage, not weapon DPS, meaning they benefit high speed weapons much more than slow weapons. If so, 100 poison damage on an amulet is 200 DPS assuming .5 second attack speed. In that case, is the number added to skills that use weapon DPS for the purposes of their damage calculation 200 or 100? And, for skills, is it also applied at the end of the calculation just as it is with normal attack? If so, then all those affixes do indeed, as you said, suck.
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Re: [How Stuff Works] Damage

Postby armis » Thu Oct 25, 2012 4:08 am

grasida wrote:There's a very simple way to test whether or not the screens take fumble rate into account. That is, increase your dexterity and see if the numbers change.

Of course there is, it's just that I didn't think to do it yesterday and I'm not going to be able to play until like this weekend at best :). Just figured I'd put this out and fill in the blanks when I get around to it.

You mention all sources of extra damage not attached, either as base affixes or from embers, to your weapon are not modified by anything at all. They are a flat number added to each attack after the damage calculation is complete (this is the part that I didn't know). Now, I assume those bonuses are added to weapon damage, not weapon DPS, meaning they benefit high speed weapons much more than slow weapons. If so, 100 poison damage on an amulet is 200 DPS assuming .5 second attack speed. In that case, is the number added to skills that use weapon DPS for the purposes of their damage calculation 200 or 100? And, for skills, is it also applied at the end of the calculation just as it is with normal attack? If so, then all those affixes do indeed, as you said, suck.

Correct, they're added to weapon damage, not DPS. In the example above, slotting a +173 ice damage amulet makes the listed ice damage go from 1077 to 1250, and modifies the DPS accordingly. As far as I could tell from a few pot-shots with Rapid Fire, the amulet provided no significant upgrade to damage, which makes me infer that it's also added to the end of the calculation for skills (which makes sense since that's how it works for normal attacks) even though I haven't run the precise calculations numbers. I could probably grab the damage range of Rapid Fire from the combat log and check it next time if you like.
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Re: [How Stuff Works] Damage

Postby beastmodeengaged » Thu Oct 25, 2012 6:57 am

This is an awesome post. I've used some data from this post as well as other sources including my own research to create a gdocs spreadsheet. My research corroborates yours on every place where they intersect. Right now this spreadsheet is a bit customized on Engineer/Emberquake, but could easily be extended for more classes and skills.

Link: https://docs.google.com/spreadsheet/ccc ... U5sb3U3dEE

Tell me your gdoc name if you want to collaborate on making the ultimate spreadsheet.

Edit: I'm extending it now to account for the max crit thing. I didn't know that, I'm just going to take your word for it.
Last edited by beastmodeengaged on Thu Oct 25, 2012 7:46 am, edited 1 time in total.
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Re: [How Stuff Works] Damage

Postby Sogetsu » Thu Oct 25, 2012 7:25 am

Oh gosh, this is sooo good, thanks a lot for the compilation, I will surely ask some stupid things later, but after I take the time to slowly read all and clear few doubts I have right now.

Ok, I want to add something about Weapon DPS and ASPD... like you pointed before, it is said that "More ASPD on the Weapon = Better Weapon DPS" for auto attacks and skills as well.

This is true, because when you increase your Weapon ASPD, it has got the same Base_Damage as before, but it deals it in less time, so the Weapon_DPS increases
For AutoAttacks it is usually better to achieve high ASPD, but for skills you are mostly going for more Base_Damage on your weapon, because it also increase the Weapon_DPS, I mean, if you increase the Base_Damage of your Weapon, and the ASPD of it remains the same, you are rising your Weapon_DPS

Now the problem about it in some part, which is saddening me with a Weapon I don't want to let it go for other is this:
Because the damage reduction is based on flat numbers, there is one point where it is best to increase your Weapon_Base_Damage instead your Weapon_ASPD for more Weapon_DPS unless you are trying to abuse proc of something.
Why is this? Simple, because let's say your Sword has 0.64 ASPD, and it's base Damage is not super high, but with that ASPD you surely can achieve nice DPS, like 3 hits every 2 seconds. When the mobs start to get more DEF, every single hit you do is reduced a LOT, they are fast, but every one of them is getting a huge reduction on the rest Monster_Armor - Your_Weapon_Base_Damage
At that point you are surely going to do more damage with a Weapon with same Weapon_DPS but based on less ASPD and more Weapon_Base_Damage, not only on skills, also in auto-attacks unless you are using the high ASPD to trigger many good effects

TL:DR , Increasing your Weapon_ASPD or incresing your Weapon_Base_Damage as well, you increase your Weapon_DPS, but it is always better to increase your Weapon_Base_Damage (specially for Skills) unless you are trying to constantly proc something based on your Weapon_ASPD while Auto-Attacking

trevallion wrote:Unless something has changed very recently, +physical damage affixes and gems get their own calculation in the combat log, separate from the main attack. They all get added together and corrected by attack speed, then modified by strength and other appropriate modifiers. I can't remember if sword and board gets its own as well, but I think it's just added to the gems and affixes and not modified by strength. It doesn't really matter for potential damage because it adds up to the same thing either way you handle it, but the important part is that it has to penetrate armor separately from the main attack. I haven't tested with +flat elemental damage types but I assume they work the same way. My guess is that it was easier to calculate it separately than to check if the weapon has that damage type already and then add it in.



If that is true ^
Then you should try to obtain more Weapon_Base_Damage from Weapon instead Gems on the same you are using IMO

EDIT 1:

I firstly thought it was like Arlian said about the "% of Weapon DPS", but then I read somewhere that it was the Arcane Statistics one, can't remember if I tested it or not at the end...

There are many things on these forums that people claim on some point they work in one fashion, and the other half affirms they work in a different way :?

One of those is the FireSpark apply to SpiderMines DoT, other is the Weapon_DPS in which the skills are based, ArcaneStatistics or WeaponTooltip

IMHO is the one from ArcaneStatistics, because there are many bonuses, some from skills included, that increase your WeaponDamage/ASPD, so the final Weapon_DPS is not showed really on the tooltip

It's is easy to test however, simply take a Zerker, with Cold_Steel_ Mastery in high value, then use two different weapons
One with a half Ice/Physical Weapon and other only Physical and with Higher DPS
On Auto-Attacks, the "lower DPS" weapon will deal more Damage or the same as the other with higher DPS, because it has the bonus of Cold_Steel_Mastery
Then, use ANY skill based on "% Weapon DPS" and check if the numbers are similar or not... then you will realize if the value is the one from WeaponTooltip or ArcaneStatistics

Actually I am using Reaper of Spiders because I LOVE that weapon and it's ASPD with my Lancerker, and even with better weapons, it deals the same damage on AutoAttacks because the bonus of Cold_Steel_Mastery
But as I pointed before, there will be some point where I will need to use a Weapon with higher Base_Damage and try to rise it's ASPD because the high Armor of the mobs will do obsolete my fast hits with lower Raw_Damage even with the bonus of the skill

A better and clear example using an Engi
Code: Select all
1) Take 2 weapons, 1H-Axe and 2H-Axe with almost the same WeaponDPS on the WeaponTooltip, if possible, same BaseDamage and same ASPD
2) Rise HeavyLifting to a high value
3) The WeaponDPS from WeaponTooltip should remains the same without change on both Weapons
4) The WeaponDPS from the ArcaneStatistics should change and show the 2H-Axe with a HIGHER WeaponDPS because it gets the bonus from HeavyLifting, which means that you hit FASTER with it (NOT HARDER), and then the WeaponDPS is better thanks to the ASPD_Bonus from HeavyLifting
5) Now use a skill like EmberHammer, based on WeaponDPS
6) Because both weapons have the same Weapon_DPS on the WeaponTooltip, if that is the value used, there should not be differences between the 2H-Axe and the 1H-Axe if it's true
7) Because both weapons have different Weapon_DPS on the ArcaneStatistics, the 2H-Axe should show a higher Weapon_DPS there, thanks to the ASPD bonus from HeavyLifting, then Ember Hammer should hit harder with the 2H-Axe instead the 1H-Axe for about... 30% if it's true


I TESTED IT

Cheated Engi, lvl 72

    Status

    STR = 415
    DEX = 5
    INT = 5
    VIT = 15

    Weapons used

    A) Hammer (Lvl 25 Mace)
    139 DPS (Weapon Tooltip)
    ASPD 0.88
    Physical Damage 81-163
    Convey 90% Chance Interrupt

    B) Hasty Great Maul (Lvl 19 Great Hammer)
    148 DPS (Weapon Tooltip)
    ASPD 1.44
    Physical Damage 142-284
    +4% ASPD
    Convey 90% Chance Interrupt

Now, because the explained before about ASPD, Weapon_Base_Damage and Weapon_DPS, when Auto-Attack obviously the damage of every hit on the TwoHanded was HUGE but it was so damn slow without HeavyLifting, and the damage of the OneHanded was POOR but very quick

The Weapon_DPS on the Weapon_Tooltip for both of them was almost the same, regardless HeavyLifting enabled or not, and also it was similar on the Arcane Statistics

Spoiler: show
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Using Ember Hammer Lvl 1 now... with AlwaysCrit activated and without Heavy Lifting Enabled

Code: Select all
Weapon A = 1484 Damage
Weapon B = 1660 Damage


Ok, the Weapon B had a slightly better Weapon_DPS on the Tooltip... so let's spend points on Heavy Lifting (13), that should only rise the ASPD for the Weapon B, and its damage should be reflected on the Arcane Statistics, but the Weapon Tooltips should remain exactly the same, and because if it, the damage for EmberHammer would change or not at all...

Heavy Lifting Lvl 13 added only ASPD, exactly +26% ASPD, which is shown on the Arcane Statistics, it doesn't add more Power, just Speed to the Attacks, explained before on page 1 of this thread

Code: Select all
Weapon A = 1484 Damage (no changes, but the Arcane didn't change anyway for it)
Weapon B = 2070 Damage (ok, it is waayyy better, but only the Arcane changed)


Conclusion? The "% of Weapon DPS" is based on the Weapon_DPS from ARCANE STATISTICS instead the WEAPON TOOLTIP for skills, unless I am missing something


PD: As you can see, I found that stupid info about the Arc of the Weapon and the Natural Splash Damage, but still I don't know how it decides the Main Target when you use Shift + Click without targeting anything specifically


EDIT 2:

I use Speed Gems on my Lance with high Base_Raw_Damage

Here is something some people forget, there are "HIGH" DPS Weapons which sux for Auto-Attacks more than others with lower DPS

More ASPD on the Weapon = Faster Attacks = More Weapon DPS

But that is not true at all on Auto-Attacks, because the way damage reduction works on this game, every single hit you perform is reduced by Enemies' Armor, then if you have a "Low Base Damage" Weapon but super fast ASPD, that Weapon supposedly deals "A lot of damage", but only on paper (or while used for Skills based on Weapon_DPS)

Let's say your weapon has a 40 Base Damage but hits 10 times in a Second, that is like 400 Weapon DPS, but every single hit you do is only for 40 Damage, if some mob has 30 Armor, your damage is 10 per hit, then it reduces every single hit you are doing by 10, and your "Supposedly good Weapon DPS" ends sucking so much

Then you use some stupid low ASDP Weapon with 400 Damage but hits 1 time per second, then you perform 1 single hit and the mob obtain 400-30 = 370 Damage. Quite good, right? You hit slow, but you deal a lot more of damage

Then, if you are not going for Leeching, applying effect "On-Hit", or something like that, you better try to use a Weapon with not super fast ASPD, but mainly with high Raw_Damage

The same thing happens with Multi-Element Weapons, they have like 400 Weapon Damage but they do 100 Damage of each element, which means, the mob will reduce every part of the hits based on different Armors, for example

Some mob with 30 Physical Armor and 50 Fire Armor, you hit it with a 200 Physical Armor damage, it reduce it to 200-30 = 170, nice
Then you hit it with a 100 Physical Damage and 100 Fire Damage (200 Weapon Damage Total), the mob reduces it by 100 -30 = 70, and 100-50 = 50 (50 + 70 = 120)

Finally there are weapons with huge Arc, and splash damage, which increase your final damage drastically on Auto-Attacks

PD: Outlanders uses mostly Shotguns, while Engineers uses mainly Cannons
Last edited by Sogetsu on Sun Nov 11, 2012 3:26 am, edited 4 times in total.
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Re: [How Stuff Works] Damage

Postby armis » Thu Oct 25, 2012 7:35 am

beastmodeengaged wrote:Edit: I'm extending it now to account for the max crit thing. I didn't know that, I'm just going to take your word for it.

Happy to provide a combat log dump if you want to take a look: voilà

I edited the top post for a little mistake: skill DPS is also dependent on the time between two consecutive castings (otherwise the equation just gives damage per casting, not damage per second). That variable isn't listed anywhere so you have to figure it out yourself with the combat log. If you're just comparing different setups for the same skill though, you don't really need it.
edit: also clarified that fixed damage weapon enchantments work like weapon socketables for the purposes of DPS calculation.
edit2:
beastmodeengaged wrote:I've used some data from this post as well as other sources to create a gdocs spreadsheet. Right now it's a bit customized on Engineer/Emberquake, but could easily be extended for more classes and skills.

Link: https://docs.google.com/spreadsheet/ccc ... U5sb3U3dEE

Tell me your gdoc name if you want to collaborate on making the ultimate spreadsheet.

Gdocs is blocked at work so most of the time I won't be able to view it, let alone modify it. Be sure to check in here over the next few days as I iron out the last uncertainties and inaccuracies. :)
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Re: [How Stuff Works] Damage

Postby Sogetsu » Thu Oct 25, 2012 7:53 am

Well, I edited the previous post (check it) about the ASPD and Weapon_DPS

Also, I am trying to find a good explanation of few things, maybe you can add it to the first post if you know them, they are these

1) What is the standard Arc of Weapons? Obviously in some Angle value
2) How does the game apply damage to Secondary Targets? I mean, what is the standard Damage_% you deal to them?
3) How does the game decide which are Secondary Targets when you don't target any main mob? Like when you Shift+Click to anything in front of you

I ask because I tried with the Dummy specifically the point 3, and I don't see ANY difference, every hit targeting the Dummy deals the same damage as the ones that just hit it when spaming Shift+Click at its side
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Re: [How Stuff Works] Damage

Postby jwallstone » Thu Oct 25, 2012 8:08 am

Hey, this is absolutely amazing. Nice work. I've been looking for precisely a detailed explanation like this.

A couple more questions:
1. So flat damage bonuses on armor get added to the end of the calculation? Does it work for skills or just normal attacks? That could actually very good for skills, in the case of a fast casting skill with a low % of DPS number (like Magma Spear). I've tried it before on a flat damage skill, and it doesn't seem to get added there.

2. I've read somewhere on the forum that Focus was being double counted in some cases. A weapon with elemental damage would have its DPS boosted by Focus, then a skill that did "% of weapon DPS as elemental damage" would be boosted again by Focus. Is this accurate?
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Re: [How Stuff Works] Damage

Postby Arlian » Thu Oct 25, 2012 8:08 am

Still need to know how adding a +dmg socket to a weapon changes the DPS.

This part has evaded me forever, essentially, adding in a +7 damage gem has added like +10 to DPS which would make sense if the attack speed didn't automatically illustrate a 0.5 AS.

I need verification on this, or maybe I'm just reading it wrong.
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Re: [How Stuff Works] Damage

Postby omnipotus » Thu Oct 25, 2012 8:19 am

OMG, can I like... call you when I'm working on DEEPS?:)
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Re: [How Stuff Works] Damage

Postby jamajohn » Thu Oct 25, 2012 9:08 am

Arlian wrote:Still need to know how adding a +dmg socket to a weapon changes the DPS.

This part has evaded me forever, essentially, adding in a +7 damage gem has added like +10 to DPS which would make sense if the attack speed didn't automatically illustrate a 0.5 AS.

I need verification on this, or maybe I'm just reading it wrong.


Pretty sure what shows on the weapon is wrong because the arcane statistics page for weapon is:
Weapon_Damage = (Base_Physical_Damage + Physical_Bonus)*(1+ a_1 + a_2 + ...) + (Base_Ice_Damage + Ice_Bonus)*(1+ b_1 + b_2 + ...) + (E2 + ...) + ...

where a_n and b_n are bonuses that apply to each stat
strength bonus applies to each one, % melee applies to each one, % all damage applies to each one, focus bonus only applies to magic damage of the weapon, etc

Then DPS is:
Weapon_Damage*IAS_Bonus/Weapon_Speed

This is the reason why % All Damage Gems suck, and why IAS is super good to increase dps because it's a flat (1+IAS) multiplier on damage. It's also the reason that the 4 socket kidney dagger is by far the strongest physical in game weapon.
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Re: [How Stuff Works] Damage

Postby Sickness » Thu Oct 25, 2012 9:19 am

So the variation of crit damage comes from the targets armor?
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Re: [How Stuff Works] Damage

Postby Arlian » Thu Oct 25, 2012 9:22 am

yes.

That's why when you pelt the target dummy with a -armor weapon/skill, your crit damage levels out.

ALL armor is measured between 50% to 100% effective. On average, this represents a 75% effectiveness of armor.

Essentially, 50 armor is actually more 37 damage reduction on average.

Imagine you crit on a weapon dealing 50~100 damage on a monster with 50 armor. If your bonuses are +50%, this is 75~150 damage. On a natural +50% damage crit (it'll never be this low), you're taking the 150 * 1.5 or 225 damage. The enemy armor cuts 25~50 damage out. This means the crit will hit anywhere from 175~200 damage. With armorpierce/armorsteal of 10, the monster's armor goes as so:
50 - 25~50 armor or 175~200 dmg
40 - 20~40 armor or 185~205 dmg
30 - 15~30 armor or 195~210 dmg
20 - 10~20 armor or 205~215 dmg
10 - 5~10 armor or 215~220 dmg
0 - 0 armor or 225 dmg
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Re: [How Stuff Works] Damage

Postby armis » Thu Oct 25, 2012 9:29 am

Update!
Managed to squeeze in some time. Character screen and stats pages never take fumbles into account in their numbers, +attack speed does increase the DPS of weapon DPS skills, and preliminary tests indicate that the formula for dual-weapon DPS is wrong (the (A+B)/(a+b) * (1+execute%) doesn't match the combat log). More tests needed.

@Sogetsu: I did a few tests on how different damage types are applied and you're correct on all points, so I've updated the post to reflect that, thanks. I haven't got around to splash damage weapons yet though.

@jwallstone: Focus is never double-applied. Flat damage bonuses are applied to skills too, definitely towards the end, but I need to find the exact way (edit: at the very end. Neither Str, Focus or elemental bonuses apply. Basically, even with 1000 Str and 1000 Foc, a +173 ice amulet adds 146 damage to a level 15 rapid shot with a .64 speed weapon: 173/.64*0.53= 143.26, bit off but close enough)
Last edited by armis on Thu Oct 25, 2012 9:38 am, edited 1 time in total.
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Re: [How Stuff Works] Damage

Postby Arlian » Thu Oct 25, 2012 9:37 am

I believe it's because I read that focus was double applied and followed some really fuzzy logic about how the system works.

No, focus is only applied once.

A DPS based skill only calculates from the DPS as seen on the weapon itself. If a weapon tooltip says 350 DPS, the system will use THAT DPS to calculate from.

The bonuses are only applied ON HIT.
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Re: [How Stuff Works] Damage

Postby Sickness » Thu Oct 25, 2012 10:01 am

When dualwielding weapons with different attackspeeds, does the faster weapon wait for the slower? If not, what happens if you proc execute with your fast weapon and your slow weapon is in the middle of an attack?
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Re: [How Stuff Works] Damage

Postby mattmisk » Thu Oct 25, 2012 10:10 am

Wow, great post! You should post this to the TL2 wiki

Quick question, should be easy: does execute increase your listed dps or % weapon dps skills?
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Re: [How Stuff Works] Damage

Postby Sickness » Thu Oct 25, 2012 10:35 am

mattmisk wrote:Quick question, should be easy: does execute increase your listed dps or % weapon dps skills?


No, it doesn't. The listed DPS is specificly for each hand and skills only use the "main" hand.
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Re: [How Stuff Works] Damage

Postby mattmisk » Thu Oct 25, 2012 11:03 am

No, it doesn't. The listed DPS is specificly for each hand and skills only use the "main" hand.

Thanks. So execute only benefits basic attack; somewhat of a bummer, but that's how I thought it worked anyway.

Arlian wrote:A DPS based skill only calculates from the DPS as seen on the weapon itself. If a weapon tooltip says 350 DPS, the system will use THAT DPS to calculate from.

The bonuses are only applied ON HIT.

Are you totally certain? Can someone confirm this? I just ask because I've read many different opinions from people doing tests, and I've always heard it was the arcane statistics panel that mattered. Another thing slightly related, is that I have read many times that STR and FOC are equally good for weaponDPS as elemental skills, which would seem to suggests bonuses are applied before and after the skillDPS calculation...

I guess what I'm saying is, I'd love to see the calculation for weaponDPS skills. We'll figure it out before long :D

Another interesting observation I made is that DOT effects don't increase either the listed arcane or tooltip DPS, but are just applied ON HIT for basic attack/skills. This makes it a nightmare trying to figure out the true power of weapons...for example, I have an act 1 NG berserker with a claw that gives +70 fire DOT. It doesn't affect any listed DPS, but man does it make a difference!
Last edited by mattmisk on Thu Oct 25, 2012 11:32 am, edited 3 times in total.
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