Talk:Damage calculation

TRAIT THAT INCREASE DAMAGE

Trait like Slashing Power for the Warrior, increse the Greatsword damage by 10%. But trait like that, make the icon of the skills become Blue. Have someone find difference between Normale damage increse, and Weapon damage increse?

Not quite sure what you're actually asking about... —Dr Ishmael 17:28, 8 October 2014 (UTC)

Probably other damage bonus traits. The table is only concerned with weapon-based damage increases, otherwise it would look similar to this.--Relyk ~ talk < 04:12, 9 October 2014 (UTC)

Blue skill tooltip text indicates that the skill is affected by traits. Generic damage increasing effects should only change skill tooltip numbers but not always. 87.95.29.202 08:48, 9 October 2014 (UTC)

Ah, I see what you mean now. Most "generic" damage bonuses from traits are conditional - i.e. "Deal bonus damage when below the health threshold" or "Deal extra damage against burning foes." These bonuses can't be shown in tooltips because of that condition. —Dr Ishmael 12:25, 9 October 2014 (UTC)

Skill coefficient

Any suggestions how i can calculate proper values for the skill coefficients without the removed steady weapons? And are these coefficients equal independent of game type?--62.224.67.208 18:27, 9 July 2015 (UTC)

Damage multiplier stacking likely wrong in article

In a recent Reddit discussion, it was said that multiplier stacking is multiplicative.

Rebuttal via Wiki article was put into question via this post

It piqued my interest and I went to HotM to try it. Preliminary results are, that it does stack multiplicatively. Since I'm not good enough with statistics to give confidence levels, this warrants further investigation + discussion.

my conclusion

I responded to you on reddit. Need more clarification. —Dr Ishmael 14:14, 8 October 2015 (UTC)

Its the first time I see someone who claim dmg multipliers stack additive. When you search the internet everyone will say its multiplicative. 2 Years ago I calculated it myself with steady pvp weapons and found out it is multiplicative (btw sry for my bad english). Was it changed some time ago or why do you claim the opposite? —Anubarak 14:38, 9 October 2015

I'm not for one side or the other. However, since there appears to be confusion, I feel that wee need some clear, statistically significant data in order to prove one of the hypotheses. —Dr Ishmael 14:13, 9 October 2015 (UTC)

Assuming weapon damage was exotic, I determined that heavy golem had ~2680 armor looking at min and max damage values from large amount of casts of Fireballs, Lava Fonts and Dragon's Claw. Coincidently, tooltip matches average weapon damage on the same amount of armor. However, knowing that golem used to have 2597 armor I went back to Lion's Arch and equipped a level 80 exotic weapon. Tooltips now matched the 2597 armor value. Conclusion: Weapons in PvP lobby are approximately 3% weaker than exotics. Either adjust weapon damage appropriately or use the higher armor value. I choose the latter as it is one number to keep track of instead of many.

The second test was easy. Equip, Scholar, Water "Scholar trait" and Force Sigil. With 2375 power, expected damage with fireball if additive 927-1046, multiplicative 942-1063. Conclusion: Multiplicative is correct. --Wildclaw (talk) 17:25, 9 October 2015 (UTC)

This is probably because I have an analytical scientific background, but the way you and the OP both presented your results is bugging me. You're not presenting enough of your data for me to understand or trust your methodology. For one thing, your conclusion that "Weapons in PvP lobby are approximately 3% weaker than exotics" seems incorrect. Did you know that your PvP Build is completely separate from your PvE equipment? You probably had a lower Power attribute in PvP than in PvE, and I bet that's where this difference came from.

The proper way to test this (or anything, for that matter) is to run 2 trials, one without any damage modifiers (control) and one with the damage modifiers (experiment), and keep all other things identical, then report the results.

1. Control
   • Remove everything that gives you a damage bonus.
   • Obtain a large dataset by using the same skill against the same opponent repeatedly and record the damage of non-critical hits.
   • Average the results to get the baseline, non-modified damage.
2. Experiment
   • Equip multiple damage bonuses.
   • Same as above.
   • Average the results to get the final modified damage.
3. Divide the result from 2 by the result from 1 to find the observed aggregate damage bonus. Compare this to the expected additive bonus and multiplicative bonus to see which one is the closest to the observed bonus.

Since it seems like too much trouble for anyone else to do this, I did it myself. I took my engineer to the Heart of the Mists and equipped the Bomb Kit.

1. Control
   • PvP equipment: Soldier amulet (Power as primary, but no Precision kept my crit rate at 4%), Rune of Fire (same Power bonuses as Scholar), Sigils of Chilling and Benevolence. Trait lines: Firearms, Inventions, Alchemy - selected traits that did not grant damage bonuses or apply any conditions.
   • Used Bomb against the Target Golem - Heavy ~100 times. The golem wasn't dead when I hit 100, so I kept going until he died and ended up with 104 data points.
   • Mean (average) damage was 1051.18.
2. Experiment
   • PvP equipment changes: swapped Rune of Fire for Rune of the Scholar (+10% damage while health > 90%), Sigil of Benevolence for Sigil of Force (+5%). Trait lines: Explosions, Tools, Alchemy. Important traits: Glass Cannon (+5% health > 90%), Explosive Powder (+10% explosions), Excessive Energy (+10% full endurance), Steel-Packed Powder (inflicts vulnerability for +1%), Shaped Charge (+5% against vulnerable).
   • Same method as control, except I had to wait for the vulnerability to wear off (5 s) between each strike so that I wasn't getting an extra 1% damage on some strikes. Since I was recording data in a spreadsheet, I recorded the same number of data points (104) to make a nice table.
   • Mean damage was 1644.46.

You can view all my data in this Google spreadsheet and check my calculations.

• Expected results: The additive total damage bonus would be +46%, while the multiplicative total would be +55.6%.
• Observed results: The damage bonus was ~56.44% based on average damage. When comparing either the minimum or maximum data points, however, the damage bonus was ~55.64%, almost exactly matching the multiplicative expectation.
  • It looks like the control data skewed slightly to the low end of the range, since the overall mean is lower than the midpoint between the max and min (1051 vs. 1054), while the experiment data skewed slightly higher than the midpoint (1644 vs. 1640); this made the bonus based on the means skew slightly higher than expected.
• Conclusion: Damage bonuses combine multiplicatively.

This cost me about 15 minutes in prep time, 30 minutes in data collection, and another 15 minutes writing and formatting this post, so about 1 hour total. Was that so hard to do? No. And since I'm finally satisfied that we have some real data to back up this assertion, I'll update the article. —Dr Ishmael 02:54, 10 October 2015 (UTC)

Well done + thanks for providing the data too. -Chieftain Alex 11:31, 10 October 2015 (UTC)

If Anet ask for serious people, i will give them your name first, Doc. Yseron - 92.157.122.195 11:59, 10 October 2015 (UTC)

I provided all the data that was needed, but perhaps not clearly enough for everyone to understand. (which is my mistake)

• Tooltip damage scaling in PvP is 3% less than in PvE with a level 80 exotic weapon for the same power. (don't know why you think power and setup needs to be the same in both PvE and PvP. Percentage traits aren't included in tooltips and the tooltips scale linearly with power and average weapon damage. The math is trivial).
• The whole PvE part is irrelevant to this discussion anyway. All you need is the MinWD/Toughness and MaxWD/Toughness ratios that I provided a close approximation (0.2% error) with my first test round. 985/2680 and 1111/2680 (0.85 skill coeff, 2200 Power, Min: 647, Max: 728 with no multipliers) for PvP Staff against Heavy Golem.
• Armed with the MinWD/Toughness and MaxWD/Toughness, it is trivial to calculate the expected damage range as long as you know if damage is multiplicative or additive. Since the point in question was which, you just do the calculation both ways and then test to see what reality does. Which is was what I did.

--80.217.230.74 15:44, 10 October 2015 (UTC)

Source Data

I thank you all, especially Dr. Ishmael, for your inputs into this category. My question is about the source data for this article. Is there a website or repository where this inoformaiton is kept? Myates32 (talk) 23:41, 17 October 2015 (UTC)

Apparently contradictory info

The table on this page seems to be contradictory with the damage range on the different weapon pages. For example, axe has a 857-1048 weapon strength range on this page, and 900-1100 damage range on the axe page. I don't quite get the difference. --Ruine Eternelle (talk) 18:40, 18 October 2015 (UTC)

Ranges shown are for exotic rarity. Raljeor (talk) 19:00, 18 October 2015 (UTC)

Ah okay, thanks for the precision. Why not ascended rarity ?--Ruine Eternelle (talk) 19:08, 18 October 2015 (UTC)

It's NOT damage range, it's weapon strength. As this page should make clear, damage calculation is very complicated, and weapon strength is only one component. —Dr Ishmael 21:26, 18 October 2015 (UTC)

Yeah, guess I kinda realized that too. The hardest part is calculating the dps of each weapon skill set. And I'm not even talking about boons, conditions and other effects in my analysis. I just want to understand how things works and not brainlessly follow Metabattle.--Ruine Eternelle (talk) 21:43, 18 October 2015 (UTC)

I've noticed 'another' inconsistency. The power value used in tooltips was never stated, so I tried to find what it was by going backwards from info on the wiki. I used the guardian GS abilities (2-4) and got that the power was never constant, however 916 showed up twice. I ended up googling and finding that in the past, level 80s had 916 power (naked), so this suggested that 916 was the power used. If that was the case, then that means that 2 damage modifiers were incorrect (I got 2.94 for WW and 2.5065 for SoW, BB and LoF were accurate). Would someone mind checking my math and elaborate? Also, is there a standard on significant figures on the modifier? I feel like most mods come pretty clean when rounded to the nearest hundredth, allowing for more accurate calculations. --Quarks0 (talk) 07:16, 29 October 2015 (UTC)

Are you talking about tooltips on skillbar or hero build? On skill bar Eviscerate shows 2924 damage. Ascended axe has average wep str of 1000. My power is 2531. Reference armor is 2597. Eviscerate coefficient is 3.0. 3 * 1000 * 2531/ 2597 = 2923.76. Also some traits affect the tooltip damage which may explain your results. Wethospu (talk) 07:37, 29 October 2015 (UTC)

I'm talking about the wiki only, since I don't have a 80 guardian to fiddle with. Again, some of the modifer values are right. But for Whirling Wrath the mod should be 1085*2600/(916*1047.5), where 1085 is the tooltip damage, 2600 is the armor (close enough), 916 is the power, and 1047.5 is avg wep str, right? That comes out to 2.9400, which is noticeably higher than the 2.8 listed on the wiki page. Oh, I also wanted to bring up that it might be helpful to mention that wiki tooltip damage is done with a power value of 916 for those that would like to work backwards. --Quarks0 (talk) 07:50, 29 October 2015 (UTC)

Since both damage and coefficient are given, inconsistencies are guaranteed. IIRC this has been an issue for a while.Wethospu (talk) 09:02, 29 October 2015 (UTC)

Feedback 2016/09/05

Damage = (Skill damage * Positive multipliers) / (Armor * Negative multipliers) Where does this formula come from? All damage modifiers should be part of the dividend, not the divisor (i.e. stack on top of each other, not calculated separately). This formula shows positive and negative multipliers being calculated separately. Negative multipliers are not meant to be armor modifiers, but modify damage. Damage = (skill damage * all multipliers) / Armor. For increasing damage take the bonus % and add one. For decreasing dmg take the reduction % and subtract one. (i.e. Protection is 0.67) Think about how 100% dmg reduction fits into this article's formula compared to my correction. --76.218.108.123 20:51, 5 September 2016 (UTC)

Can We Make Better Calculation Tooltips?

Is it possible to add functionality to articles that displays the "real" damage / healing that is closer to what we see in-game? If so, what would it take to start and undertake such a project?

An example: Troll Unguent. We see the following text as shown in-game:

Health per second: 1,062 (0.12)?

However, mousing over that question mark reveals a tooltip with the following:

1062 + 0.12 * Healing Power

Why do we not have a default value for Healing Power and display the resulting number on the article?

Example: Health per second: 1,062 (0.12)? ((1062)) - Here, I've used the value 0, which is how much Healing Power most players have. But we could also use 700, which is the approximate value from a full Celestial set ((1146)) or 1400, which is the approximate value from a full Cleric's set ((1230)). Or, it could display all 3, scaling, similar to the Guild Wars 1 Wiki, which would look like ((1062...1146...1230)), or something else entirely different.

Extending this change in how numbers are displayed across regeneration, damage, condition, etc. would, I think, give players a much better idea of how skills work. The concept isn't complicated by factoring in criticals and other modifiers, because they wouldn't be used to begin with. The goal isn't to mirror in-game numbers with wildly complicated calculations, rather just to more clearly represent the numbers that a skill puts out. It'd be a large undertaking, yes, but is such a thing possible to do in the first place?

Clara Fee (talk) 19:56, 29 November 2017 (UTC)

Life Steal Damage Calculation

Life steal damage, e.g. from traits like Focused Siphoning uses a completely different damage calculation, which is:

Damage = mechanic-specific base damage + power * mechanic-specific coefficient

It scales by level (in an unclear way) and is seemingly unaffected by damage multipliers (e.g. Vulnerability)

This is confusing for skill fact damage coefficient tooltips because it shows the normal damage calculation with armor and weapon strength.

-Selkies (talk) 01:22, 24 February 2018 (UTC)

Utility Skills' Weapon Strength

Does anybody know, or is it listed somewhere on this wiki, what values are used for weapon strength when calculating the tool tips for utility skills? All it says here is that it is based on level, so how were the skill-specific coefficients actually found? --Musha 10:38, 30 April 2018 (UTC)

Utility skills use "unequipped" weapon damage, which is 690.5 at level 80. I'm not sure what it uses at lower levels, but if you need a specific level calculated I can try to math one out for you? --Imry ☎ 15:45, 30 April 2018 (UTC)

Thank you for showing me this, Imry! Now, how certain are we that 690.5 is the correct value here? Perhaps I'm being too exacting, but as a Ranger, I'm looking at the tooltip damage for Flame Trap at differing power values, and at higher power, the tooltip in game shows slightly different damage values than when I calculate it myself using 690.5. My numbers match the game's until I hit power value of 2131. The game shows Flame Trap's damage to be 171, but it actually calculates out to 170; and then at power value 2382, game shows 191, but I calculate 190. --Musha 19:36, 30 April 2018 (UTC)

While I don't have your exact gear, at 2136 power (only 5 power higher than your 2131) my tooltip damage skill fact shows a value of 170, which would be fine with the calculation. Maybe you have any other modifiers active?

To answer your second initial question, we can just use the API (Flame Trap example) to get the skill coefficients.

The 690.5 value was determined to be the unequipped/utility/level 77 fine sword weapon strength thanks to testing with known coefficients from the API. —Nefastu 22:06, 30 April 2018 (UTC)

Feedback 2018/09/13

marking this for updates. Listed traits like eagle eye are no longer current. Could do with a table of traits that give flat damage increases. --Turbo404 (talk) 06:47, 14 September 2018 (UTC)

thoughts on moving this back to mainspace

I have no idea why I moved this page to the help namespace, shall I move it back? -Chieftain Alex 12:39, 26 March 2022 (UTC)

Sure. Link it from Damage page too. —Kvothe (talk) 19:40, 27 March 2022 (UTC)

already linked lol. -Chieftain Alex 23:37, 27 March 2022 (UTC)

There is no hidden general damage scaling depending on the armor class

In the section "Armor" there is a statement:

"On top of the base values from armor pieces, the game places inherent damage reduction on the different armor classes. A light armor class takes roughly 25% more damage than a heavy armor class given the same Armor value (if the light armor class adds Toughness to reach the same value)."

According to my test this is not true in this general form as of September 2023.

Tests in the Special Forces Training Area. 
##########################################

The damage of the mildly threatening pulsing arena damage was used for the test.

All used characters had no buff besides a "Guild Gathering Boost (effect)".
At all characters a cleared build template was used with no specialisation chosen.
No Jade Bot Power Core was equipped.

(1) Test with nothing equipped 
==============================

(1a) Warrior
------------
Toughness=1000, Defense=0; Armor=1000
Health: 19212
Health after 5 hits: 10967
Health lost from 5 hits: 19212-10967 = 8245

(1b) Elementalist
-----------------
Toughness=1000, Defense=0; Armor=1000
Health: 11645
Health after 5 hits: 3400
Health lost from 5 hits: 11645-3400 = 8245


(2) Test with 2271 armor
========================
That is the armor value of a Warrior, that has equipped a legendary armor with no stats selected, but no other items.

(2a) Warrior
------------
Toughness=1000, Defense= 127+127+381+191+254+191 =1271; Armor=2271
Health: 19212
Health after 10 hits: 11952
Health lost from 10 hits: 19212-11952 = 7260

(2b) Elementalist
-----------------
Toughness=1000+215+88=1303, Defense= 77+77+330+140+203+140 = 967; Armor=2270

To match the armor value, the following equipment was used:
* a legendary light armor: defense = 77+77+330+140+203+140 = 967
* a legendary staff was equipped with Minstrel's Stats selected -> Toughness = 215
* no stats were selected for the head, the chest and the shoulder armor piece
* for the foot, the leg and the hand armor piece Wanderer's stats were selected: Toughness = 22+44+22=88

Health: 11645 Base value; ascended Minstrel's staff 118 Vitality; Vitality from the 3 Wanderer's armor pieces: 40+81+40= 161
Health: (118+40+81+40)*10+11645 = 14435
Health after 10 hits: 7175
Health lost from 10 hits: 14435-7175 = 7260

Result and conclusion
=====================
In both cases the Elementalist and the Warrior took the same damage with equal armor values.

This shows, that there is no hidden general damage scaling depending on the armor class.

The statement might be true in some special cases, but until the author of the statement has shown those cases in detail I delete the statement from the page, because it is false in it's current unrestricted general form.

Aloha, Ashreen --80.135.247.154 12:41, 20 September 2023 (UTC)