Talk:Damage calculation

I archived User:Cloak of Letters's big list of questions and their responses. Most have been answered (and the articles explain them now). The only question that seems to be unresolved is whether Necrotic/Tormenter take extra damage from light damage.

Archive2 has more concluded discussions whose conclusion has been incorporated into the main article.

Things to check: X% more/less damage (and double/half) vs Y additional damage, order of operations
The X:
 * Frenzy - double damage received
 * Flurry - deals 25% less damage
 * Life Attunement - deals 30% less damage
 * Aura of the Lich - halves damage
 * Dual Shot - 25% less damage

...and probably more

The Y:
 * Executioner's Strike
 * Point Blank Shot

etc etc

The Question:

I assume X gets applied first, but is that always the case? I see something like Aura of the Lich as possibly halving the additional damage even from Executioner's Strike, but I'm not sure. -PanSola 03:54, 22 November 2005 (UTC)
 * Now that I think about it, if X is applied first, then that's no different than -40 AL. As that's proved not the case for Frenzy, is X always applied scond then?  Or are the X% a different type of damage modifier than Double/Half? -PanSola 04:05, 22 November 2005 (UTC)
 * x% is applied just before armor. Base * x% * armor% + static bonus. --Dragos 07:50, 22 November 2005 (UTC)
 * Easy to test. Find something that you hit for 0 and use a +dmg skill. You will get the listed bonus to hit. --Dragos 07:56, 22 November 2005 (UTC)


 * Well, that proves the listed bonus is after armor. I don't see how you tested x% is applied before armor.  Though Frenzy is proved to be after armor (but Double could work differently from x%). -PanSola 08:08, 22 November 2005 (UTC)

Ok in my own experimental article, I've made X% (which I called DMod and the current article calls DScale) concurrent with AE, while Double/Half (labeled DMult) after the rounding as proved by Fryen. Take a look at User:PanSola/Damage. I simply assumed the +Y will happen AFTER double/half, which I'd appreciate if someone test it out. Also the x% not being after the rounding is also an assumption based on what makes intuitive sense from their description (especially weapon mods), so that needs testing too.

How I think the damage actually look like is really (in order of likelihood):


 * [[[BD &times; DScale] &times; AE] &times; DMult] + DShift

or
 * [([[BD &times; DScale] &times; AE] + DShift) &times; DMult] 

or
 * [([[BD &times; AE] &times; DScale] + DShift) &times; DMult] 

or
 * [[BD &times; AE] &times; DScale] + DShift  (in this case DMult and DShift happens at the same place, so I just combined them into one factor)

Each square bracket indicates rounding to the nearest integer. Though my own experimental article does not currently have the innermost square bracket. I'm lazy -PanSola 08:31, 22 November 2005 (UTC)


 * I mentioned earlier today that DMult happens after DShift, so 1 and 4 are definitely wrong. My guess would be ([BD * AE * DScale] + DShift) * DMult.  I don't think you can have a non-integer DShift, so that could be inside or outside the round.  I haven't actually tested anything with a "DScale" yet.  --Fyren 17:22, 22 November 2005 (UTC)


 * Hmm, so that's a much bigger problem where the SonOfRah article on GWOnline is wrong (but then for all we know, like the case with the article hosted on RPGStar, this one can be totally updated and SonOfRah might have a newer article that already corrects all these mistakes...). You voted 3, though I'm more inclined towards 2.  It is also possible that there is ONE MORE multiplier, so that the multiplier from weapons and the multiplier from skills are separated...  I really think the +20% damage on customized weapons (as well as those +15% stanced/enchanted/HP>50 mods) are applied (and rounded) before armor). -PanSola 18:23, 22 November 2005 (UTC)


 * The difference between your 2 and 3 is just rounding. Mine rounds differently from them both.  --Fyren 18:38, 22 November 2005 (UTC)
 * I know. Ideally only the rounding issue should remain, cuz it's the trickiest to check...  Blah, 2 and 3 are both wrong?  How about this:
 * [([BD &times; AE &times; DScale] + DShift) &times; DMult] 
 * (one less rounding stage)? What was your test and numbers? -PanSola 19:08, 22 November 2005 (UTC)


 * There's definitely rounding before DMult, like I mentioned before with the frenzy/healing signet test. It doesn't really make sense to me for there to be more than one round involving BD, AE, and DScale.  All it would do is sacrifice precision (I can't think of a reason for it to be calculated/programmed that way).  I suppose there is necessarily rounding or truncation after DMult, since aura of the lich might require it, but I don't have a PvE character anymore with aura to make testing easy.  I haven't tested anything yet regarding DScale rounding, so it's possible I'm incorrect.  Are frenzy and aura of the lich the only things that we think involve our DMult?  --Fyren 19:47, 22 November 2005 (UTC)
 * Undead and minons could either be a -40AL thing or a DMult, depends on the whim of Anet (-: Also I have no hard proof that Aura is DMult as opposed to DScale.  I just assumed it's DMult because it doesn't involve percentage.

wrong usage of "Melee".
Melee is the opposite of ranged. Bow attacks are not melee, and thus it's incorrect to consider Marksmanship as a melee attribute. -PanSola 03:00, 22 November 2005 (UTC)


 * Well spotted. Changing "melee" to "weapon". &mdash; Deldda Kcarc 03:02, 22 November 2005 (UTC)


 * Cane, Staff, and Wands are weapons too. How do your formulas account for them? -PanSola 03:26, 22 November 2005 (UTC)


 * Hmm, too sleepy to think up something atm -- do you perhaps have a suggestion for how to reword it to be unambiguous? I'm sure you know what I meant. &mdash; Deldda Kcarc 03:51, 22 November 2005 (UTC)

"Physical Damage" is still not right
Fiery Dragon Sword... damage still depends on Swordmanship rank, but does NOT deal physical damage. As a simple example. I vote to stick with "Melee Weapons and Bows". -PanSola 06:40, 22 November 2005 (UTC)
 * or "Weapons with their own attributes", to cover whatever Chapter 2 throws at us. BTW, pet damage depends on rank in Beast Mastery... -PanSola 06:43, 22 November 2005 (UTC)

Holy on undead: Double or -40?
I'll leave other ppl to figure out how to test it, I'm just asking the questions to make our knowledge more complete d-:

One interesting thing I noticed about holy damage on undead is that it can't crit. It will always do double the normal value, never critting.--Dragos 13:21, 22 November 2005 (UTC)

Lost in Translation: Lost in the plethora of rewrites over the past three days was a section on holy damage. Was it wrong? Was it inaccurate? Whatever became of it?

I strongly call upon the editors of this page to stop their "rewrites" and fix what is already there. This is insane. The article has been rewritten like 3 times in 3 days and each one offered different theories. --Karlos 07:07, 23 November 2005 (UTC)
 * I don't think Holy ever had a section here. It's in my experimental article User:PanSola/Damage, and I don't think it ever got incorporated here.  Sorry to getyou confused.  But yeah, I did my own stuff in my experimental article precisely to avoid what you think is happening d-: -PanSola 07:12, 23 November 2005 (UTC)

The skill "Smite" when weilding a sword
While Smiting Prayers affects the base damage, I wonder whether Swordmanship or Smiting Prayers affect the AE. The current formula would indicate Swordmanship, and I'd vote for that, but really worth testing out.-PanSola 10:01, 22 November 2005 (UTC)
 * An implication of this is, whether Smite do Light damage like Judge's Insight (if AE is affected at all), or does it ignore armor so you always get base damage out of it (on mobs w/o weakness against Holy)
 * Smite does Holy Damage. I've not been following the discussion, but I can tell you it does the same damage to all PvP characters (who all happened to be level 20 when I used it on them, if that matters). Except possibly Tormentor's necros. Shandy 10:08, 22 November 2005 (UTC)


 * Smiting. Your weapon doesn't deal any damage.  Smite doesn't do +X damage on top of your attack, it is the attack.  --Fyren 12:17, 22 November 2005 (UTC)


 * Yep. "Smite" will ignore armor and uses Smiting Prayers for the attack level. Was easy to test on my monk :) --Dragos 13:24, 22 November 2005 (UTC)

Related issue: when using strength or tactics attack skills, the game uses the skill's linked attribute INSTEAD of your weapon attribute. The article on GWonline perhaps eludes to this when Rah mentions power attack. I have verified this. (12 sword, 0 strength, a sword that deals 4-5 damage. Against the doppelganger, who has 60 AL, I always did 4-5 damage besides critical hits.  With griffon's sweep, which says it'll do +1 damage, I would do 2-3 damage.)  --Fyren 17:22, 22 November 2005 (UTC)
 * Oh my, less damage when using a skill d-: This can be used as a "Sparing opponent's live" move (-:  -PanSola 19:11, 22 November 2005 (UTC)
 * Can you test it for Expertise too? 12 marksmanship on a crappy bow etc.  I suspect it'll also do less damage to be consistent with your results on melee weapons. -PanSola 19:13, 22 November 2005 (UTC)

Real-world Tests
I'm quite confused. I took my axe out, and started hacking away at mobs to test the equation. I'm using a Fiery Axe (6-26 fire) with 12 attribute and 0 strength. It's customized, so it get's +20%.

From what I gather, it should follow Actual Damage = ([BD x DScale x AE] + DShift) x DMult. First, I used my fire damage testing with my elementalist to find that Whiptail Devourer has 20 fire AL.

AE = 2 (5x AR - EAL)/40 or AE = 2(5 x 12 - 20)/40. Which is 21. So AE = 2

([6 x 1.2 x 2] + 0) x 1 = 14

([26 x 1.2 x 2] + 0) x1 = 62

Crits should be 124. My actual damage was 22-67. Crits for 76.


 * Based off User:PanSola/Damage, my crits would be for 88. Just ran into that. --Dragos 19:25, 22 November 2005 (UTC)


 * Well I got my critical from SonOfRah, and you aren't doing anything fancy here (not using Mult nor Shift), so what you get using his formula and mine should end up the same... Check his formula, does it also give a theoretical 88 crit? If his formula give 76 instead of 88, then I need to slap myself and figure out what I incorporated wrong. -PanSola 19:35, 22 November 2005 (UTC)


 * I think Rah's critical hit analysis is correct (-20 AL or sqrt(2) scaling). Did you take your crit from just whacking it or from wild blow?  If the former, try wild blow just to be... extra sure.  And I guess doublecheck that it's the right type of devourer.  --Fyren 19:47, 22 November 2005 (UTC)


 * This was with both. I would hit for 76 most of the time (It's a big level difference :)) and Wild Blow always hit for 76. I'll run it through GWOnline's formula now to see what it says. --Dragos 20:10, 22 November 2005 (UTC)


 * Confirmed with GWOnline. Crits should be 88. Considering I used GWOnline's magic to figure out the fire AL, it should mesh up... --Dragos 20:16, 22 November 2005 (UTC)
 * Try something that's not elemental, see if the formulas are still wrong or if they work out. Perhaps elemental axe actually work differently.  AND if they are actually different, change your secondary to Ele, pump some points in fire, and see if anything happens (though I don't really expect it to, consider regular fire ele weapons don't depend on it). -PanSola 21:45, 22 November 2005 (UTC)

I had a guildmate go whack a whiptail. He had a fiery sword with a max of 22. It was customized and he was also getting a +10% for a >50% mod on it. Twelve sword and no strength. Wild blow hit for 83. 22 * 1.2 * 1.1 * 2^((60 - 20 + 20)/40) = 82.138. The difference might be rounding, but it's a lot closer than 76 versus 88. Not to sound too much like tech support, but are you sure you hit a whiptail and not a carrion or plague? Were you able to reproduce the 76 on a different attempt? --Fyren 13:09, 23 November 2005 (UTC)


 * Yeah. I used called targets to make sure I was hitting what I thought I was. I consistently hit for 76 on each whiptail. Hence why I'm just as confused :) --Dragos 13:15, 23 November 2005 (UTC)

The only thing that I can think of is if character level affects melee somehow too. I'm only level 14. I have the same stats as when fighting the whiptails. I tried on Plague now too. I should crit [26 * 1.2 * 2^(60 - 1 + 20)/40] = 123. Actual crits for 105. --Dragos 13:30, 23 November 2005 (UTC)


 * Another theory, though unlikely, is that your axe require more than 12 axe mastery, and because you don't meet the reqs, it deals less damage... o_O""" -PanSola 17:46, 23 November 2005 (UTC)


 * Well, it's listed as req 7. I *should* be doing listed damage. I'm glad to see that Fyren's level 20 guildie was able to get the formula to work. Atleast that shows that fire swords use fire AL... --Dragos 19:13, 23 November 2005 (UTC)


 * Unless they also have 20 slashing/physical AL, heh. --Fyren 19:15, 23 November 2005 (UTC)
 * Well sword and axe do the same damage type, so that wouldn't have mattered d-: This is really mysterious, since Dragos isn't getting hit by weakness either (damage way too high for that).  Do the whiptails have any damage reduction stance?  I thought they just use stormchaser or somethign that adds evasion. -PanSola 19:19, 23 November 2005 (UTC)
 * I was referring to the "at least that shows that fire swords use fire AL." --Fyren 20:18, 23 November 2005 (UTC)


 * Here's some more info. I had a Gladiator's Helm (+1 Axe) and a minor axe rune (+1). My base is 10 axe, but 12 listed. I decided it might be those +'s messing something up and I found another interesting tidbit. At 10 (base, no +'s) I do 70 damage vs. 74 per formula. At 11 I do 73 vs. 80. At 12 I do 76 vs. 88. My real damage only goes up by 3 points per axe mastery, while the formula says I should raise by more. I do 5% lower than the formula for each point. (At 10 I do 95% of what I should, 11 is 90% and 12 is 85%). --Dragos 19:31, 23 November 2005 (UTC)


 * Ok, at 9 I mesh up. 68 vs 68. Somehow I'm being penalized for having 10 or more axe mastery ><. Which is interesting since 9 is 70% of 12 (the general "max"). And at 14 I'm at 70% of max level. Perhaps the game doesn't want you to overpower your attack skills pre-20? --Dragos 19:36, 23 November 2005 (UTC)


 * That's a very interesting hypothesis. SonOfRah's article has it that after 12, you only get 2 more DL per rank than 5.  Maybe that is true for Lv20 only?  Another thing to check is for Axe Mastery (base) 7 and 8 (since the min req on that axe is 7).  Do you do more damage than theoretical, or exactly the same.  Just want to see if there's another different issue lurking around. -PanSola 19:56, 23 November 2005 (UTC)


 * 7 and 8 mesh up still. 57 and 62 respectively. It seems that I'm getting a simple DMult of -.05 per level above 9. What needs to be figured out now is what the breakpoints are >< --Dragos 20:03, 23 November 2005 (UTC)


 * Well you aren't using any skills that deal x additional damage, so we can't tell where the penalty is from. I'm inclined to believe it is a DL (Damage Level, see my experimental article) penalty rather than DMult.  At least that makes explanations more consistent.


 * As a DL, it would be -3 per level above the "cap". At 10 I had -3DL, 11 is -6DL and 12 is -9DL. All those worked perfectly with your formula. --Dragos 20:21, 23 November 2005 (UTC)

I'm going to run a "quick" test. At level 20, you hit diminishing returns past 12 attribute. At level 14, you hit the same diminishing returns past 9 attribute. To make this a simpler equation, it would seem that you hit diminishing returns if your attribute is >65% of your level. I hope it's just that easy (-: --Dragos 20:29, 23 November 2005 (UTC)


 * My best guess: given that Rah's attribute to AR is correct for level 20 and Dragos' drop off starts after 9, I'd say that your attribute is effective up to your level / 2 + 2. This maps 20 -> 12 and 14 -> 9.  Above that, instead of 5 AR per attribute, 2 AR per.  Assuming this, Dragos' crit damage would be: 26 * 1.2 * 2^((9 * 5 + 2 * 3) / 40) = 75.50 (tada?).  It doesn't mean this is correct, but it's a starting point.  --Fyren 20:42, 23 November 2005 (UTC)


 * At level 11 damage diminishes past attribute 7. If it is level/2 +2, it would be rounded down. (11/2 +2 = 7.5). --Dragos 21:08, 23 November 2005 (UTC)


 * I would propose that Level/2 +2 Rounded down is VERY close to correct. Level 8 character diminishes past 6. All characters diminish at the same rate (only 2DL per point past the cap). --Dragos


 * Lovely progress here. May I suggest a different way?  Level/20*12 being the cutoff, round to nearest INT.  It just seems odd that some part of the eq round down while others round up.  Lv11 gives you 6.6, round to 7....  wait is that level 8 diminish at 6 actual or theoretical?  My formula would give 4.8=5 )-: -PanSola 03:43, 24 November 2005 (UTC)

One more theory: DScale might be 2 different terms
Just randomly throwing in some possibiliies. Effects that let you do x% more or less damage might come in 2 flavors.

The PLUS flavor stack by adding the percentages. Say a +20% from customization and a +15% HP>50 would give you +35% damage when you are healthy.

The MULT flavor stack by multiplying on top of each other. Say a +33% from this skill and a -25% from that skill means your damage output is changed by 1.33 * 0.75 = 0.9975%.

This is absolutely pure spectulation based on zero observation of how things work. But just throwing it out there if you can't get the damage numbers to work simply by adding up all the scaling bonuses.

If actual numbers actually back the existence of the two flavors (wouldn't surprise me if it didn't, and wouldn't surprise me if it did), I propose to call the PLUS favor DMod and keep the MULT flavor as DScale. The formula would look something like


 * ED = (BS &times; DMod &times; AE &times; DScale + DShift) &times; DMult + DNeg

I skipped the square brackets to enhance readability. Anyways, just randomly toss it out there. -PanSola 07:27, 23 November 2005 (UTC)


 * Blah, reread the GWOnline SonOfRah article. It actually has some self-contradicting stuff in it, but according to that article, weapon mod enhancements stack by adding, not multipling.  So weapon mods would be the MULT flavor, not PLUS.  Which leaves room for enhancement from skills to be the PLUS flavor.  Anyways, I'll call DMod whatever is associated with weapon modifications and DScale the one from skills, if they turn out to be different terms. -PanSola 08:03, 23 November 2005 (UTC)


 * Ok, you are all driving me nuts!! I graduated college only eight years ago, but I feel like I have never been to school!!
 * Last I checked.. If a modifier makes a weapon do 25% more damage then the math goes:
 * Dmg = D + 0.25 x D = D (1 + 0.25) = D x 1.25
 * i.e. It doesn't matter if you multiply it or add it!! Same thing for reduction:
 * Weakness Dmg = D - 0.66 x D = D (1 - 0.66) = D x 0.33
 * Why are you guys talking as if it makes a difference?? I know that internally in the machine it does make a difference in SPEED if you multiply or add, but that's not what this is about. In the end the result is the same. Right? --Karlos 11:15, 23 November 2005 (UTC)


 * Pan's saying D * 1.25 * .66 versus D * (1.25 - .33). --Fyren 12:24, 23 November 2005 (UTC)


 * The two equations you post are not the same and the difference should be "testable" with Wild Blow + damage prohibiting and damage enhancing upgrades. One implies that the bonuses are applied in succession to the damage and the other implies that the bonuses are first worked out together then applied as a final number. --Karlos 13:23, 23 November 2005 (UTC)


 * Yeah, I'm just lazy. --Fyren 14:14, 23 November 2005 (UTC)
 * Well, you can still "first worked out together" by either multiplying or adding... but anyways now you know what I'm talking about (-:  The point of this section is that BOTH might be in use, perhaps one for weapon mods and the other for skill mods.  And yes, it's definitely testable, just need to find someone to do the test. q-:-PanSola 17:43, 23 November 2005 (UTC)


 * Anyways, here's a simple test to see if the modifiers from skill is PLUS or MULT -- use Life Attunement and Flurry, and see if damage is at 52.5% (MULT) or 45% (PLUS) of normal (one's less than half, the other over half). Seems no skill boost damage as a percentage. -PanSola 05:45, 24 November 2005 (UTC)

Ok just I spent 1 plat to learn Flurry so I can test it myself.


 * Test 1: Life Attunement + Flurry, vs dopple
 * Axe max damage 25, req 11.
 * Theoretical Normal (100%) Crit Hit = 35.36 (round to 35)
 * Theoretical MULT (52.5%) Crit Hit = 18.56 (round to 19)
 * Theoretical PLUS (45%) Crit Hit = 15.91 (round to 16)
 * Actual Normal Crit Hit = 35
 * Actual Life Attune + Flurry Crit Hit = 16

Thus, skills that reduce damage output by a percentage stack by the PLUS.


 * Test 2: 20% customization + 16% when HP<50%, vs dopple
 * Hammer max damage 31, req 11.
 * Theoretical HP>50% (120%) Crit Hit = 52.61 (round to 53)
 * Theoretical MULT (139%) Crit Hit = 60.94 (round to 61)
 * Theoretical PLUS (136%) Crit Hit = 59.62 (round to 60)
 * Actual HP>50% Crit Hit = 53
 * Actual HP<50% Crit Hit = 61

Thus, weapon mod bonus stack by MULT

To stay close to SonOfRah's terminology, I'm going to call the weapon modifications DEnh (for Damage Enhancers), and the skill modifications DScale. QED. -PanSola 07:26, 24 November 2005 (UTC)

"Third Attempt" not completely accurate
It ignores the effect of DShift and DMult. 40 AL only double (or half) the effect of armor. I'm not sure how to reword it to make it both clean and correct though... And leaving something inaccurate in a section that already feels quite long and starting to get hard to read, is doubly annoying )-: -PanSola 18:39, 23 November 2005 (UTC)


 * This is a fascinating article. However, when you introduce so many terms it would help if you didn't abbreviate or form so many acronyms. I find that it improves the readability if they're are kept as words in the text and as acronyms/abbreviations in the equations. I'd change it now, but I don't know if everyone agrees with me ;) Shandy 07:24, 24 November 2005 (UTC)

Rounding
The game appears to use "round to even" as the rounding method, as 2.5 -> 2 and 3.5 -> 4. (Tested using 0 swordsmanship, wild blow, a sword with a max of 5, a sword with a max of 7, and the doppelganger.) --Fyren 21:48, 23 November 2005 (UTC)
 * Um, just want to check if the word had attribute requirements... -PanSola 03:45, 24 November 2005 (UTC)
 * Also which profession is the dopple? I assume warrior dopple has 80 AL and +20 vs phy? -PanSola 04:01, 24 November 2005 (UTC)
 * No requirement, he has 60 AL all the time. --Fyren 04:03, 24 November 2005 (UTC)


 * Can you pump some points into strength (for penetration), use the 5 sword, and see if you still get 2? Basically want to see if "round to even" is only used for exactly 2.5, or is applied even at 2.6 or 2.9 whatever -PanSola 04:48, 24 November 2005 (UTC)


 * That's not what round to even means. Round to even is rounding as everyone would understand, except for cases where the digit to be rounded is a 5 with only zeroes afterwards.  In that case, you round up if the digit before the 5 is odd and down otherwise.  So, you end up rounding to an even number.  The "normal" method of rounding that always rounds 5s up is biased.  --Fyren 05:18, 24 November 2005 (UTC)
 * ah thanks (-: -PanSola 05:29, 24 November 2005 (UTC)