PvP Tooltip DPS Calulator - backed up by answers from GGG

2016 03 31 update: I asked GGG about unclear things and I got replies:

ME:
If a hit has multiple components of damage (fire, cold, lightning, physical, chaos), does the game calculate the damage reduction by the formula separately for each component, or does it add them up and calculate them together?

With an example:
First case, assume D = 1000 lightning damage, and an attack time of T = 1 second. The given formula would reduce the hits to 594.
Second case, I convert half of my damage to cold, so my hits have 500 lightning damage and 500 cold damage. If I add them up before the calculation I get the same, 594. If I calculate for each separately I get 398 for each, so 796 total damage.
What damage is applied in this example, 796 or 594?
The latter calculation seems weird for me, because it would give significantly more damage, by just converting the damage. If the first one is used, then adding up all of the components would cause a problem too, because the formula for physical/chaos is different.

GGG:
"For the elemental damage, you use your total average elemental damage in the calculation. So if you had 500 lightning damage and 500 cold damage, you would use 1000 elemental damage in the equation to get the value of 594. If you land a hit that has elemental damage and chaos/phys damage, you use both calculations separately, and then use the average of both values. So if you have a final elemental damage of 594 and a final phys/chaos damage of 300, you would have a final total damage of (594+300)/2 = 447"

ME:
As the formula is not linear, It yields different results if I apply certain modifiers before or after running the numbers through the formula.

My main question is: should I modify the damage values by the following multipliers / modifiers before or after applying the pvp formula on it: resistances, critical strike multiplier, armour, more / less damage taken (for ex. opponent using Arctic Armour or Abyssus helmet), more / less multipliers on the attacker that are not displayed on tooltip (for ex. Flameblast at 10 stack having 1100% more damage, pvp penalty mentioned separately such as Freezing Pulse: 25% less damage in PvP)? If all of these I mentioned are in the same case, is there any exception?

Currently I take the initial damage values, if there is physical damage reduce it by the Armour formula, then run them through the PvP reduction formulas separately, then I apply resistances and other multiplicative modifiers if the user entered any in the appropriate fields. Then I add all 5 components, divide them by skill use time, then I calculate modifiers with accuracy, crit chance and crit multi, and that is the final pvp dps I display. The source code is in Javascript right in the source of the html document, so you can easily view it if you want.

Excuse me, but I find the last calculation example you wrote very weird, where both elemental and phys/chaos damage are present, why do I have to take the average of the elemental and the chaos+phys values? With the previous example, If in the first case I have 1000 initial average elemental damage that becomes 594 final elemental damage after pvp reduction. In the second case if I add a very small amount of chaos damage (which should barely affect the damage) for example an amount that yields final 2 chaos damage, that would mean (594 + 2) / 2 = 298 final total damage, so almost halved the damage, but all I did was adding a very small amount of chaos damage.

GGG:
"The PvP scaling occurs after all other modifers, except for modifiers which directly affect PvP damage of specific skills. So you have resistances/crit/armour/more/less/increased/reduced/etc -> PvP scaling -> PvP damage scaling of skill (25% less freezing pulse damage as an example). So you basically want to calculate the total damage you would be dealing as if you are attacking a monster, and then after you have the final value you run that value through the PvP formula.

For the damage dealt by phys/chaos + elemental damage, the method I was using was based on some out of date info. The correct way to do it with both sources uses the total damage you are dealing (phys/chaos+ele) and then uses a ratio based on how much phys/chaos and elemental damage is dealt to get the final values, which are then added together. As an example;

You have an attack that deals 100 lightning damage and 10 chaos damage for a total of 110 damage, with an attack time of 0.53s
Putting those values into the PvP formulas gives these results:
Physical/Chaos formula: (((110/0.53)/125)^0.61)*125*0.53 = 90.26347147
Elemental formula: (((110/0.53)/290)^0.58)*290*0.53 = 126.5933177

You then need to find the ratio of chaos/phys to ele damage you are dealing, which is;
portion of total damage dealt as chaos/phys = 10/(10+100) = 0.09090909091
portion of total damage dealt as elemental = 100/(10+100) = 0.9090909091

Then multiply the phys/chaos value with the portion of damage which is phys/chaos, and do the same with the elemental damage
90.26347147*0.09090909091 = 8.205770134 total phys/chaos damage
126.5933177*0.9090909091 = 115.0848343 total elemental damage

Then just add them together to get the final total damage
8.205770134+115.0848343 = 123.2906044 damage dealt"


Based on the above answers I changed the calculations. I had to change the order of calculations, I do all multipliers before PvP reduction formula (except PvP multipliers specific for certain skills), and if multiple damage hits are present in one hit then I don't do them separately.

This means that ALL modifiers, including Resistances, Critmulti, and Less damage taken on the opponent (such as Arctic Armour) has different magnitudes in PvP, in most cases they are LESS effective as in PvE.

Overall the PvP damage displayed in the calculator got lower in most cases.

2016 03 20:
You can save your input and load it from the side
Armour now mitigates physical damage before pvp reduction and not after (this is only based on my experience, so I would need some feedback on this)
Separate min and max damage calculated for pvp
Corrected average damage
Drawing graph of the results
2016 03 31:
Changed calculation order, modifiers are now calculated before PvP reduction
Drawing graph of crits and non-crits

2018 05 19:
Fixed some bugs
Added more explanations
Added an input for "Hits per use" for multi-hitting skills

2018 08 29:
Added new damage formula, you can switch between old and new formula modes to compare results

definitely doesn't hit for 12k +. Math is hard. / Brain hurts.