ESO Calculations For Advanced Players - UPDATED FOR 2.0.3

evedgebah · November 2014

Hello everyone.

I've seen questions posted about maximizing DPS output and whether or not Spell Power/ Weapon Damage, Critical %, and/or Magicka/Stamina is best for focusing on in gear selections. As such, I did a search on the official forums for formulas and was surprised that I did not find a post with the exact formulas here. Thus, here they are:

Tooltip = (max_ABILITY + wpn/spelldmg × 10.46) × skill_coef × rank_coef

For the rest of the thread, I will abbreviate these values as such:
max_stamina/magicka: A (for ability, the game's labeling of magicka/stamina)
wpn/spell_dmg: P (for power, which the game uses for these collectively)
skill_coef: S
rank_coef: R
critical hit %: C (will be used later, stay tuned or skip ahead)

Thus, the formulas become:
Tooltip = (A+P×10.46)×S×R

What is my rank_coef?
Base is 1.00, add 0.01 for each rank (morph rank 1 counts as rank 5, or 0.04)

What is my skill_coef?
It varies for each skill, and you can calculate it if you really want to by fiddling with your stats in-game and a spreadsheet. I used to have a list, but it's long, inaccurate in the current version, and I'll leave that as an exercise to the reader. You don't need it really for stat comparison, but I'll explain that below.

How do critical hits and critical hit percent chance factor in?
Critical hits multiply your damage by 1.5 (~1.55 for shadow stone, more with divine trait gear). Thus, a critical hit ADDS 0.5 times your tooltip value. This event occurs only has a critical_hit% chance of happening. Thus, you can take your skill, multiply it by 0.5, and then multiply that by your chance of having a critical hit, and you get your added average benefit from your critical hit percent. Let's add it into our formulas.

Average Skill Damage = ((A+P×10.46)×S×R) + ((A+P×10.46)×S×R)×C×0.5
- NOTE: C is a percent value, so make sure to use 0.40 for 40% and so on.

This all seems awfully complicated, and my numbers don't match up right!
That's right, it is complicated, and the numbers don't work quite right. That's because these formulas were reverse engineered, and they involve something called truncation and/or various forms of rounding. For really advanced players, or those already comfortable with math, you'll figure out, in fiddling with the math above, that the values in those formulas are truncated at various stages. For the most part, the changes are so small that you can accept your values being off some and just ignore truncation in calculating your best setup of power, ability, and critical percent.

Lovely thread, complicated math, I have no idea what to do with this.
Find out what you want (max burst damage, highest ultimate generation, best overall DPS, etc) and use the math to help you. For simplicity's sake, you can frequently remove S and R from your math for ability/crit/power comparisons, as they'll remain constant (by comparison) no matter what skill you use. In doing calculations.

Resist
Damage Multiplier = 1- (TRUNC((RESISTANCE - PENETRATION) ÷ 63000),2)

TL:DR See above for variable definitions.
Average Damage = ((A+P×10.46)×S×R) + ((A+P×10.46)×S×R)×C×0.5

To the best of my knowledge, these values are accurate for ESO 2.0.3

static_recharge · November 2014

Thank you for all of this amazing information!

I have heard some people say that a "melee" range spell will use weapon crit or some craziness like that. An example would be the NBs Killers Blade ability. Have you experienced / calculated anything along these lines?

Cuyler · November 2014

evedgebah wrote: »

Average Weapon Damage = ((A/20+P/1.9)*S*R) + ((A/20+P/1.9)*S*R)*C*0.5
Average Spell Damage = ((A/20+P)*S*R) + ((A/20+P)*S*R)*C*0.5
CREDIT WHERE CREDIT IS DUE:
Thanks to Mystborn, Andy44, Septemvri, and more for their contribution to this work.

I may have missed it there but what do the constant signify (i.e. 20, 1.9)?

Were they interpolated using a program like "finder" in excel or "reverse engineered" as you put it?

Pmarsico9 · November 2014

Outstanding. Kudos to you!

evedgebah · November 2014

I reverse engineered everything, no other programs.

Constants are constants, they were calculated manually. No other significance.

If the spell is melee range (8 meters) it generally uses weapon crit.

Shunravi · November 2014

evedgebah wrote: »

I reverse engineered everything, no other programs.

Constants are constants, they were calculated manually. No other significance.

If the spell is melee range (8 meters) it generally uses weapon crit.

As it should.

Pmarsico9 · November 2014

evedgebah wrote: »

I reverse engineered everything, no other programs.

Constants are constants, they were calculated manually. No other significance.

If the spell is melee range (8 meters) it generally uses weapon crit.

I can claim with certainty that Puncturing Strikes (and its morphs) Scale off Spell Damage, Magicka, and Weapon Critical Strike.

All other Templar Class Abilities work off Spell Critical Strike.

cschwingeb14_ESO · November 2014

evedgebah wrote: »

Armor
Mitigation % = (Armor - 100) / Enemy Level
- Use 50+VR for VR ranks, thus 64 for VR 14
- Cap is 50% reduction, though your armor can push past this value for VR14
- 3300 Armor is 50% cap for V14 Mobs (current highest end content).
- Spell Resistance uses the same formula, but you can add and EXTRA 50% to the 50% (for 75% reduction) by adding specific resist.

This leaves me wondering about DK melee fire attacks. Do they go against armor or spell resist? If it's armor, does fire resist help? Inquiring Dunmer minds want to know!

I guess ditto for lethal arrow and poison resist...although we already know that goes against armor

evedgebah · November 2014

I have not tested those things. Would have to happen in pvp though.

glavius · November 2014

Mitigation does not go over 50% total if you stack armor plus fire resist vs for example flame whip. However It does make it alot easier to hit the 50% cap.

itsBishop · November 2014

Great stuff. I didn't read it too comprehensively at this point in time, but it seems as if this is more of a general tool for calculating the various contributions of wep/spell/resources/crit on overall output potential in abstract, rather than a specific tool to calculate the effects that those variables would have on a particular ability. In order to do that, we would need some modifier that takes into consideration the base damage of the spell/ability in question.

For instance, the result remains identical across skills given that their ranks are identical and all other variables are held constant. Thus, it's not a tool to calculate how much extra damage crushing shock will do if you bump your weapon damage from 170 to 175, but rather it's a tool to provide you with an overall estimate of the expected return on investing in more weapon damage over investing in more crit for your build as a whole. Is this a correct interpretation?

evedgebah · November 2014

That is where S and R come into play.

skill_coef: S
rank_coef: R

In practice, you can really combine these variables (or consider their separation a moot point) since at end-game your skills are all rank 4 (I should hope), and they are effectively one number for our purposes. Then, all you do to reverse calculate the number is to play around with the variables and figure out the coefficient for the skill you're interested it. Crushing shock is around 0.8, for instance, for the main number listed (but remember that it's multiplied by 3, and there's the DOT too.)

schroed360 · November 2014

Just "awesome"I ve been looking for a post like that since april 1st^^.
Thanks a lot for your work.

Vizier · November 2014

Very insightful.

Izzban · November 2014

Thank you for your work.

IcyDeadPeople · March 2015

This is very helpful info - have you updated these for 1.6/2.0?

Gandia · March 2015

This is a great post, something that I usually have to spend weeks to find. Thank you!

evedgebah · March 2015

The original numbers are no longer correct as of 1.6. I will be editing the first post with the correct numbers and state when I am finished.

evedgebah · April 2015

Updated as of 2.0.3

Dositheus · April 2015

So, it's been a number of decades since I've done more than the most basic of math... allow me to ask a question for further clarification just to ensure I am on the same page. By your forumula of "(A/20+P×10.46)*S*R", would one therefore extrapolate that it takes 209.2 points of Stamina to equate to 1 point of weapon damage for equal effect on end damage?

Jules · April 2015

Brilliant. Wish I could fully understand how to use this information to help optimize but I'm just crappy at math. Thanks for your contribution all the same.

evedgebah · April 2015

Notced a typo. I forgot tonremove a /20 from one instance of the formula. 10.46 magicka/stamina is equal to 1 spell/weapon power.

curlyqloub14_ESO · April 2015

evedgebah wrote: »

I reverse engineered everything, no other programs.

Constants are constants, they were calculated manually. No other significance.

If the spell is melee range (8 meters) it generally uses weapon crit.

Wait... what??? I thought the whole big change in 1.6 was all magicka skills scale off mag, and stam skills off stam. Yet you're saying magicka skills can use stamina/wep crit if they are in melee range? WTF? So my Sap Essence uses my wep crit rate? Is this new?

What other inconsistencies like this are there? Where do you guys get this kind of information?

evedgebah · April 2015

Oops my bad. I edited my original post and missed that line too. Should have dilone it today instead of on too little sleep.

Ignore the melee crit part. Resource and associated crit for all skills. Magic is spell power spell crit and stam/weapon/crit

dsikkema_ESO · July 2015

Egad... That average skill damage formula gave me a headache: Let's make it easier to follow:

Average Skill Damage = ((A+P×10.46)×S×R) + ((A+P×10.46)xS×R)×C×0.5

(eliminate those lowercase x's)

Average Skill Damage = ((A + 10.46P)SR) + ((A + 10.46P)SR) 0.5C

--- Substitute ((A + 10.46P)SR) as X

Average Skill Damage = X + X 0.5C
Average Skill Damage = X + 0.5CX
Average Skill Damage = X(1 + 0.5C)

--- Replace X with ((A + 10.46P)SR)

Average Skill Damage = ((A + 10.46P)SR)(1 + 0.5C)

Summary:

Average Skill Damage = ((A + 10.46P)SR)(1 + 0.5C)

A = max_stamina OR max_magicka
P = Weapon OR Spell Damage
S = Skill coefficent
R = Rank coefficient (0.4 at max?)
C = Critical Hit % (60% = 0.6)

Hope that makes this simpler to follow!!!

SkylarkAU · July 2015

This is timely.. I noticed when playing around with my CP recently that shifting points around on my tree had no effect on tool tip damage values (in particular thermatuage and elemental expert), though when I did some testing the real damage output was different.. Since I don't see CP mentioned above, is it fair to assume they are applied separately on-hit?

dsikkema_ESO · July 2015

Hrmmm... can't delete a reply before you click Save/Post?

dsikkema_ESO · July 2015

Ignore this

Colosso-monstro · July 2015

evedgebah wrote: »

Hello everyone.

I've seen questions posted about maximizing DPS output and whether or not Spell Power/ Weapon Damage, Critical %, and/or Magicka/Stamina is best for focusing on in gear selections. As such, I did a search on the official forums for formulas and was surprised that I did not find a post with the exact formulas here. Thus, here they are:

Tooltip = (max_ABILITY + wpn/spelldmg × 10.46) × skill_coef × rank_coef

For the rest of the thread, I will abbreviate these values as such:
max_stamina/magicka: A (for ability, the game's labeling of magicka/stamina)
wpn/spell_dmg: P (for power, which the game uses for these collectively)
skill_coef: S
rank_coef: R
critical hit %: C (will be used later, stay tuned or skip ahead)

Thus, the formulas become:
Tooltip = (A+P×10.46)×S×R

What is my rank_coef?
Base is 1.00, add 0.01 for each rank (morph rank 1 counts as rank 5, or 0.04)

What is my skill_coef?
It varies for each skill, and you can calculate it if you really want to by fiddling with your stats in-game and a spreadsheet. I used to have a list, but it's long, inaccurate in the current version, and I'll leave that as an exercise to the reader. You don't need it really for stat comparison, but I'll explain that below.

How do critical hits and critical hit percent chance factor in?
Critical hits multiply your damage by 1.5 (~1.55 for shadow stone, more with divine trait gear). Thus, a critical hit ADDS 0.5 times your tooltip value. This event occurs only has a critical_hit% chance of happening. Thus, you can take your skill, multiply it by 0.5, and then multiply that by your chance of having a critical hit, and you get your added average benefit from your critical hit percent. Let's add it into our formulas.

Average Skill Damage = ((A+P×10.46)×S×R) + ((A+P×10.46)×S×R)×C×0.5
- NOTE: C is a percent value, so make sure to use 0.40 for 40% and so on.

This all seems awfully complicated, and my numbers don't match up right!
That's right, it is complicated, and the numbers don't work quite right. That's because these formulas were reverse engineered, and they involve something called truncation and/or various forms of rounding. For really advanced players, or those already comfortable with math, you'll figure out, in fiddling with the math above, that the values in those formulas are truncated at various stages. For the most part, the changes are so small that you can accept your values being off some and just ignore truncation in calculating your best setup of power, ability, and critical percent.

Lovely thread, complicated math, I have no idea what to do with this.
Find out what you want (max burst damage, highest ultimate generation, best overall DPS, etc) and use the math to help you. For simplicity's sake, you can frequently remove S and R from your math for ability/crit/power comparisons, as they'll remain constant (by comparison) no matter what skill you use. In doing calculations.

Resist
Damage Multiplier = 1- (TRUNC((RESISTANCE - PENETRATION) ÷ 63000),2)

TL:DR See above for variable definitions.
Average Damage = ((A+P×10.46)×S×R) + ((A+P×10.46)×S×R)×C×0.5

To the best of my knowledge, these values are accurate for ESO 2.0.3

Someone quoted you about armor and I have a question about that. 57 being vr7 which I am.

At 21000 (phyarmor) -100/ 57 = 366.66

When people say 3300 as soft cap then are they removing that decimal point or am I actually 3000 off?

Sorry if it's a stupid question

evedgebah · July 2015

Not stupid. 33,000 is (nearly) armor cap for VR 14 mobs. It appears to scale off of your enemy's level to my testing, not your level. 1% Damage reduction = level x 10 armor.

pWn3d_1337 · July 2015

SkylarkAU wrote: »

This is timely.. I noticed when playing around with my CP recently that shifting points around on my tree had no effect on tool tip damage values (in particular thermatuage and elemental expert), though when I did some testing the real damage output was different.. Since I don't see CP mentioned above, is it fair to assume they are applied separately on-hit?

It seems like CP are indeed applied afterwards and are not included in the tooltip.

Also, does anybody know how exactly crit dmg does work?
Lets say you have 10% increased critical damage- (Through CP)
is it (dmg *1,5)*1,1? Or maybe (dmg * 1.6)? Or maybe (Dmg+(Dmg*0.5)*1,1) ?