Guild Wars 2

What follows this post is a bunch of back-and-forth where I had foolishly missed that Ogre Runes provide a 4% bonus to damage. I argued that there is a hidden +4% damage, while three people set me straight. Laughable. I deleted the original post, and replaced it with the post intended for this thread.
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Below is the post as it should have been
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The product of two numbers is always largest if the numbers are equal.
Spend 6 points between two variables
3×3=9
4×2=8
5×1=5

The number of hits it takes to kill a GW2 character in PvP is:
Given that the product of all damage is “Offense”,
N = targetHealth / (Offense / targetArmor), or
N = (targetArmor * targetHealth) / Offense

Notice that the numerator is a product of two numbers, so we know it is largest when both numbers are equal. Health and Armor will never be equal, but we can express this in equivalent terms. If A = B, then B = A, and A * B = A * A = B * B. If we assume that Armor Efficiency is 100%, meaning that points in Armor are worth the same Health as points in Vitality, then we will see maximum survivability. We can rewrite the equation as:
N = (targetArmor * (targetVitality * 10)) / (Offense), or
N = (targetArmor * (targetArmor * 10)) / (Offense), or
N = (10 * (targetArmor * targetArmor)) / (Offense), or
N = (10 * targetArmor^2) / (Offense)

To restate, the term (targetArmor^2) is only possible with 100% Armor Efficiency, otherwise the terms cannot combine. We could, instead, stay simple by changing the original kill equation, but assume total Offense equals total survival.
1 = (targetArmor * targetHealth) / (Offense), or
Offense = (targetArmor * targetHealth)

The above equation can be used to figure out how much extra survival will come from changes in Armor or Health. It is represented by the total Offense required to meet the total survival (Armor * Health). We need to work toward 100% Armor Efficiency. This is basic. We can find out how much Armor it takes to be equally as helpful toward survival as Vitality by making a conditional equation.
Armor = Vitality if (Armor_Equivalency * Armor) = (10 * Vitality)

There it is. We have a test for whether Armor Efficiency is 100%. Now we need to set that condition into an equation.
1 = ((10 * Vitality) / (Armor_Equivalency * Armor))

The goal here is to find out how efficient Armor is at any given value, so we need to combine equations.
First, we will rewrite the test.
Armor_Equivalency = ((10 * Vitality) / Armor), or
Armor_Equivalency = (Health / Armor)

If it has not occured to you yet, then recall that Armor = Vitality if Armor_Equivalency = 10. Armor Equivalency will be 10 when Armor is 10% of Health. This was figured out a year ago, but still not everyone knows that Armor as 10% of Health is 100% Efficiency. That means that zero healing is being accounted for. Anything that bypasses Armor cancels out an equal value of healing. Essentially, how much Armor you want above 10% of Health depends upon how much healing you are counting on. Every ten points of healing you expect to receive should be matched by one point of Armor in order to achieve maximum survivability.

There is nothing other than that to know about Armor Efficiency.

Cheers! Be good to one another. Special thanks to Sabull.5670 for the awesome ss and Nilgoow.1037 for figuring out my fault.

—meaningless second post because I had written so dang much, haha—

No one understands what you are doing, sorry!

The damage formulas for calculating damage dealt and the relative contributions of toughness and vitality to EHP are already well known.

You should probably explain, briefly, what part of those calculations are incorrect before you make up a bunch of terms and write 10,000 words about it.

Where is a formula for actual direct damage shown? If you are referring to the wiki, then under what topic is it shown? The topic “damage” only shows an equation for calculating the tooltip value, and that equation uses a skill coefficient that is divided by the 1/4 scalar in my formula up to that point. Actual direct damage is not the same as the tooltip. I have introduced a formula that completes the calculation for actual direct damage, which must account for the Armor value of the target. The equation on the wiki that shows an equation that incorporates the target’s Armor value in the denominator is not correct. Additionally, we do not know how Armor values over 2600 affect actual direct damage.

Actual damage on a 2600 armor target is the same as that of the tooltip.

(Before damage modifiers)

Zelyhn.8069:

Actual damage on a 2600 armor target is the same as that of the tooltip. (Before damage modifiers)

That might be true, if Armor Vulnerability% is removed at the 2600 threshold. All Armor values below 2600 take an additional 4% damage. If that Base Armor Vulnerability% is not removed at 2600 Armor, then you are wrong, and a target with 2600 Armor will also take an additional 4% damage. The real question is whether Armor Vulnerability% (AV%) continues above 2600 uniformly for every class, and whether there is an extra adjustment to the equation for Armor over 2600.

What is armor vulnerability?

The damage calculation has a constant record of vulnerability that the Vulnerability condition adds to. It is an armor value that increases damage based upon the Armor Points. The heavy armor golem has 2597 Armor, so it has close to the Base Armor Vulnerability% (bAV% = 4%). If you were to apply 10 stacks of Vulnerability to the heavy golem it would add 14% extra damage (4% + 10% = 14%).

I have updated the image attachment in the second post, so you should be able to follow the headings to see what is being calculated and compared for accuracy.

So you are telling me there is a base vulnerability of 4% flat?

Yes, but I can only prove that with testing up to the heavy golem, which is 3 points below the mean score of 2600.

So you are telling me that you deal 4% more damage than tooltip on the heavy golem?
Or that damage on the heavy golem is 4% higher than expected with the normal formula (coefficient . power . weapon strength . modifiers) ?

I have provided a lot of information in the first two posts, and my hope is that people will start to use it to get a better understanding of balance, and how to gear for it.

Zelyhn.8069, I know you have worked on a damage calculator to help Ele players reach a peak damage output. Yes, you can simply multiply the Tooltip Damage by 1.04 to figure Direct Damage as reported by the game.

I deleted a bunch to get to the answer for your question, but recognize that damage is not a 1:1 comparison between classes of different Armor types. An Ele can not attain the Toughness that a warrior can because of the lower base Defense of the gear. If the heavy golem fought the light golem with the same skill and weapon, then the light golem will hit for (Tooltip * 1.041) and the heavy golem will hit for (Tooltip * 1.233). The heavy golem would need its Tooltip damage reduced by 15.6% to make their damage equal. That is without considering the Health difference.

kitten man. Your post does not make much sense, atleast when given no context.
You should start off your post by telling your overall goal or argument of the post. And then follow with math and argumentation. Instead I get thrown into tens of random terms that just calculate something.
’ take armor and divide by power, this is oPA. If you now take this and multiply this by 4% conversion constant and divide by 4 you will get normalized armor coefficient’
Nothing wrong saying that, however it doesn’t provide anything.

Are you trying to say that:

k*PROD(1+Attack_Mod) x (1+SUM(Defender_Mod) )x Power x Weapon / (Toughness + Defence)

where Attack_Mod are stuff like 10% bonus while in fire, 5% against burning and 10% while inside 600 range. PROD is product (Pi).
Defender_Mod are stuff like -33% protection, -10% signet of judgement and 5×1% vulnerability (5 stacks). SUM is summation (sigma).
And I put k as the skill dependant coefficient, like 0.85 for fireball.

AKA modifiers on attacker are multiplied and modifiers on target are additive.

For example me fireballing this guardian (using things mentioned above):
0.85 x PROD[ 1.1, 1.05, 1.1]x (1+ SUM[ -0.33, -0.1, 5x 0.01 ] x 2000 × 1100/ 3000
0.85 × 1.2705 × 0.62 x 2000 × 1100 / 3000 = 491 Hit

Are you saying this does not hold true?
If you say it’s correct, then what is this topic about?
If you say it’s incorrect and ingame direct damage against normal npc and player characters does not follow this formula ( don’t get hang up on the modifier part if you didn’t know, that is how they work as far as I have tested).
Then I would REALLY love some show, or proof, or atleast abit of tease, pix. About a case where the damage does not follow the well known formulations.

Seriously present your case first. I’m not going to even go into detail and try to understand the mess you wrote. If you don’t first give a reason (show that something is wrong with current knowledge) and then present yours. I do think the burden of proof is on you here.

Sabull.5670:

.. Your post does not make much sense … You should start off your post by telling your overall goal or argument of the post …

k*PROD(1+Attack_Mod) x (1+SUM(Defender_Mod) )x Power x Weapon / (Toughness + Defence)

… Are you saying this does not hold true?

If you say it’s correct, then what is this topic about?
… the burden of proof is on you here.

I thought it was common knowledge that the equation you showed is incorrect for calculating Actual Direct Damage (what is reported by the game in the combat window). Your equation, which is shown on the wiki, is for calculating Tooltip Damage only. I have broken the steps down to be thorough, and for proofing. All I have done is complete the wiki equation by adding in the Armor Vulnerability, so that the output you see in the combat window equals the formula result. In addition, I have proven that using the Target’s Armor as a value in calculating damage versus any other Armor value is incorrect.

First, I will address the value often referred to as the coefficient. The coefficient has become an estimate because the equation is not being used correctly. The only correct coefficient is the one that calculates Tooltip Damage. People that changed the coefficient so that it equals Actual Direct Damage made a math error.

Second, I will address the misuse of (Toughness + Defense) as a general rule. My formula shows that the Target’s Armor (tA) modifies the Tooltip Damage, and that there exists a base 4% (bAV%) increase to Tooltip Damage. The skill coefficient is correctly calculated based solely on the mean score (2600), and is compounded by the Armor Vulnerability%. Bottom line, you must calculate the Tootltip Damage before entering tA into the calculation. Also, you must account for the automatic 4% damage adjustment.

Third, I have provide proof in the second post attachment. Where is your proof?

It is almost impossible to understand anything from your posts or your calcs because you are using your own weird terms. If you have a point to make, please make it, but be clear.

I tried in game and I hit the heavy golem for tooltip -1 damage (stable, with/without amulet) wich is perfectly consistent with the damage formula.

I have no idea what you are on, but if there is something we have been doing wrong then you need to explain it clearly and with proof (understandable proof).

You have not shown anything sorry. Unfrontunately I cannot attach more than 1 picture per post so I will have to post couple of times for these.
Tbh I can’t understand why I’m even seeing the trouble to do this.

3 pictures that show damage seems to follow the well known formulas for direct damage by +-1 damage point ( rounding). The modifiers behave like I presented before, which might be abit less known as it doesn’t seem to be in wiki.
Varying power, armor, attacker modifiers and target modifiers.

So my request stays the same: If you think damage is calculated differently, you find anomalies. Take a picture of it and take note of all the stats and buffs active in the event. Thats all you need to do.

Picture shows hits without amulets (lower tough and power), one with a modifier, one without. More details in the picture ofc!

continueing previous post for another attachement. Sorry for spam.

Picture shows the fireball damage without some attacker modifiers and with attacker modifiers. This time with amulets on.

And lastly all out with the modifiers. Showing attacker multiplicative mods and targets additive mods.
More details in the picture ofc and sorry for the spam. Just wanted to make this clear as these things are close to my <3.

Hoping no typos in the pics.

I like the screenshots. The math needs to be verifiable, too. I have attached a small spreadsheet that is straight forward. Proof does not get more concise than this. Every number is in there. The equations have been repeated through this thread, so anyone can duplicate the math. One difference is that I divided the Skill Factor in my formula by four, so that it would be equal to the Skill Coefficient in the wiki formula. As well, anyone can get on their Ele in the Mists and verify every number.

Any predicted number more than 1 point off was shaded purple, meaning failure. Notice every number predicted by the wiki formula failed. The AV% was shaded red. The coefficient was shaded blue. If this is not proof, then nothing is.

Ogre runes have a 4% damage modifier.

Nilgoow.1037:

Ogre runes have a 4% damage modifier.

Quoted for the truth. Oh-my-kitten. You forgot to calculate the runes.

Take your air part in your picture.
Power 2004, tooltip 139. Just as expected. Confirmed ingame and calculations.
Damage predicted by wiki equation against heavy golem:
1.04 × 0.7 × 2004 x 258 / 2597 = 144.93, NOT 139.2

Damage shown on the screen 144. Confirmed ingame, fits calculation as I have presented in my pictures aswell. Working as intented.

I understand mistakes happen to all of us and it’s hard to let go of theories you clearly have seen alot of trouble for. So I won’t bash you. Just all this because you forgot to factor in the runes :P.

Good luck have fun!

Lol, so I missed that fact, but there is something very interesting that happened as a result of my big mistake. It proves that bonus damage is not calculated the same. The spreadsheet I posted is correct. Effectively, the wiki formula ((P * WS * SC) / (Armor)) is increased by (0.04 * Tooltip). Therefore, the bonus damage from the Ogre is working off the mean score (2600), not the Armor of the opponent.

Eh. you’re probably right. I will continue checking the math. My intent for this post was not the damage part, but the Armor Efficiency part. I needed to get the damage calculation right, though. Thanks for helping.

ImProVocateur.5189:

Lol, so I missed that fact, but there is something very interesting that happened as a result of my big mistake. It proves that bonus damage is not calculated the same. The spreadsheet I posted is correct. Effectively, the wiki formula ((P * WS * SC) / (Armor)) is increased by (0.04 * Tooltip). Therefore, the bonus damage from the Ogre is working off the mean score (2600), not the Armor of the opponent.

Dude? What?
1.04 × 0.7 × 2004 × 258 / 2597 = 144.93

That is the formula. What are you talking about. What are you saying about mean score tooltip what. What. The 4% bonus is a 1.04 modifier around the formula. Just as I have shown multiple times.

I see your edit… Dude just check my pictures and understand what is happening in them. Can you find a situation where the damage on screen does not seem to follow the formula (DONT SCREW UP WITH THE BUFFS OR MODIFIER CALCULATIONS). Take a picture of it and describe the situation. I highly recommend starting from the point of view of the well known formulas, not trying to skew your wierd formulations (based on a mistake) to try to match the actual numbers with new terms.

Please don’t post without providing a showcase of anomalie, that we can even talk about. Unless you wanna say, “ah darn, yeah looks like I just made silly mistake!”.

Done. The attached spreadsheet now accounts for the 1.04 multiplier with the wiki formula. This allowed me to be more picky about results. Now, only numbers that are not exact are shaded purple. My formula is still more accurate.

—Moved to the original post—

ImProVocateur.5189:

The product of two numbers is always largest if the numbers are equal.
3×3=9
3×2=6
3×1=3

3×4=12 > 9

And I still have no idea what you are talking about because you are not clear and I have no energy to waste on unclear theories when I see they are likely wrong.

Like Sabull said : give us pictures showing that the wiki formula fails, and then we will get interested.

Yeah, my brain is having some hiccups, huh? Corrected it. The principle was about spending the same amount of points. Zelyhn.8069, thank you for your patience with me during a troubled time.

Given that the product of all damage is “Offense”

I think you mean the sum of all damage, not product.

Anyway it looks like you are trying to saying something close to this:
https://forum-en.gw2archive.eu/forum/professions/elementalist/Build-Analysis/first

While it is helpful, this has very little value in PvP because fights can hardly be modeled on a spreadsheet.