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Introduction to PvE damage calculation (Homestead)

Asayre
Asayre
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ACKNOWLEDGEMENT
A special thank you to all addon developers that have both significantly improved the quality of my gaming life as well as allowing me the opportunity to reverse engineer game mechanics. In particular, Combat Log Statistics by @zeakfury and Combat Metrics by @decay have been instrumental for the majority of my testing. I would also like to extend my deepest gratitude to the community for the kind words, encouragement and valuable discussions.

CONTENTS
  • Introduction
  • Damage Equations
    • Resource Pool
    • Spell Damage
    • Recovery
    • Spell Cost
    • Spell Critical
    • Critical Modifier
    • Damage Calculation
      • Base Ability Tooltip
      • Base Damage
      • Average Damage
      • Ability Metric
  • Analytical Results
    • Champion Point System
      • Thief
      • Mage
    • Mundus: Apprentice, Mage, Thief and Shadow
    • Armour Traits: Divines and Infused
    • Weapon Traits:Nirnhoned, Precise and Sharpened
  • Numerical Results
    • Introduction
    • Details of Simulation Algorithm
    • Simulation Interface
    • Simulation Accuracy
    • Simulation Results for Magicka Sorcerer

INTRODUCTION
This post is divided into three main sections: Damage Equations, Analytical Results and Numerical Results.

Damage Equations covers the majority of equations needed to accurate calculate damage. It is my impression that the majority of these are readily recognisable by the community so my exposition of it will be brief. In addition, the Unofficial Elder Scroll pages boast a comprehensive build editor that not only calculates statistics for virtually all gear combinations it also clearly and tidily demonstrates the underlying equations used.

Optimisation decisions based of the Damage Equations are covered in Analytical Results. These include champion point optimisation, mundus optimisation, armour trait optimisation and weapon trait optimisation.

While the Analytical Results provide some insight into damage optimisation, some optimisation questions are rather arduous to answer, in particular the impact of proc sets on damage. One approach is with a geometric distribution but this only models the average behaviour and leaves much to be desired. Numerical Results summarises some of my combat simulation findings.

While I will rely on magicka sorcerers for the bulk of my examples, most of the concepts apply equally to other classes.
Edited by Asayre on February 4, 2017 1:00PM
Reference for any calculation I make Introduction to PvE Damage Calculation
  • OrphanHelgen
    OrphanHelgen
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    <3
    PC, EU server, Ebonheart Pact


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  • Izaki
    Izaki
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    :heart:
    :heart:
    Thank you so much for all this!
    What is your take on the Lightning vs Inferno staff on the main bar? As well as the Exploiter passive, is it worth spending 75 CP into Thaumaturge and rely on setting enemies off balance for the 10% damage increase?
    I noticed that your setup (6) was using Aether and a random staff, yet there is no considerable DPS loss in comparison to setup (4). Also your minor vulnerability uptime is significantly higher, this leads me to guess that you were using Boundless Storm over Curse? So after all, how does Aether compare to Moondancer and is there a significant DPS increase or decrease with one or the other while using the same skills and rotation? Same question about using an offset staff (for those who haven't had the luck of a sharpened Moondancer or Aether staff) how much of a decrease can we expect?


    Just a side question, what is your rotation with Haunting Curse? Do you just refresh it after the 2nd explosion or do you have a specific rotation?
    Sorry for the pile of questions :blush:
    Edited by Izaki on February 4, 2017 2:15PM
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  • Grabmoore
    Grabmoore
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    Thanks again! <3
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  • kylewwefan
    kylewwefan
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    Saving, in hopes of one day being able to comprehend this!

    PlayStation NA
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  • Waffennacht
    Waffennacht
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    @Asayre wtf do you do for a living?

    Anyway, thanks once again for the insane amount of information!
    Gamer tag: ShenronNacht NA Xbox One
    1100+ CP
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  • GilGalad
    GilGalad
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    Thank you very much for all the efforts. I can imagine how many hours of work went in there!

    The findings in terms of gear are pretty similar to the findings I derived from my spreadsheet, at least for the Sorcerer class. I also found that the theoretically perfect weaving dmg is a lot higher than the observed values and that perfect weavig can make a bigger difference than the gear.

    The only class that is a bit more complicated to approach in terms of gear and weapon choice is the templar class. In my spreadsheets there are 2 setups that are rather close to each other:
    Setup 1:
    2 Grothdarr, 5 BSW, 5 Moondancer (dual wield swords) and MSA inferno
    Bars:
    Dual wield: Radiant Destruction, Puncturing Sweeps, Reflective Light, [filler], Inner Light, Meteor
    MSA Inferno: Wall of Elements, Blazing Spear, Purifiying light, Rearming Trap, Inner Light, Meteor
    Setup 2
    2 Grothdarr, 5 BSW, 4 aether (lightning), MSA inferno
    Lightning: Puncturing Sweeps, Reflective Light, Rearming Trap, [filler], Inner Light, Meteor
    MSA Inferno: Wall of Elements, Blazing Spear, Purifiying light, Radiant Destruction, Inner Light, Meteor

    Skill prio: Rearming Trap >> Wall of Elements >> Purifiying Light >> Blazing Spear >> Reflective Light >> Radiant Destruction (30% ?) >> Puncturing Sweeps
    It might be useful to make a limit for the dots of 25% health, so below that only radiant and maybe trap will be casted.

    One could debate about using unstable wall instead of wall of elements but thats a small detail and not templar specific. The result will highly depend on the weaving error. The basic question when comparing these 2 is: Can good weaving with 2 staffs outperform the lower weaving dmg from dual wield and the additional set bonus you get?

    Would be interesting to see if the new staff passives can break the templar dual wield meta (and the endless grind to get these swords).

    If you don't have the time to run the simulations, send me a message. :wink:
    Animals Unchained | PC EU
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  • Masel
    Masel
    Class Representative
    Great guide again. I've been working on a spreadsheet for my heavy attack build for a while, and a lot of things were taken from your sorcerer arithmagic thread, so huge thanks for the dedication you put into this!
    Econometrics are a part of my profession, so I actually understand everything you wrote :D
    PC EU - CP 1200+ All trials + HM

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  • Masel
    Masel
    Class Representative
    :heart:
    :heart:
    Thank you so much for all this!
    What is your take on the Lightning vs Inferno staff on the main bar? As well as the Exploiter passive, is it worth spending 75 CP into Thaumaturge and rely on setting enemies off balance for the 10% damage increase?
    I noticed that your setup (6) was using Aether and a random staff, yet there is no considerable DPS loss in comparison to setup (4). Also your minor vulnerability uptime is significantly higher, this leads me to guess that you were using Boundless Storm over Curse? So after all, how does Aether compare to Moondancer and is there a significant DPS increase or decrease with one or the other while using the same skills and rotation? Same question about using an offset staff (for those who haven't had the luck of a sharpened Moondancer or Aether staff) how much of a decrease can we expect?


    Just a side question, what is your rotation with Haunting Curse? Do you just refresh it after the 2nd explosion or do you have a specific rotation?
    Sorry for the pile of questions :blush:

    I main bar a lightning staff and have 75 points in Thaumaturge (on both sorc and DK, and last week on the PTS I forced the rest of the DDs in a test raid to redistribute their cps to use it. We had two dds with lightning blockades and it was awesome. Our group dps with 8 dds in the first run without exploiter was between 260-270k on live, and this way we reached 285k. So having two people with a lightning blockade can definetely be worth it.

    With my DK, I get a great uptime on concussion myself:

    parse2.png

    16 procs in 99 seconds means an average time to proc of ~6.2 seconds, and the minor vulnerability lasts 6 seconds. So in my opinion it's definetely worth having one of those builds in the group that main a vMA lightning staff.
    Edited by Masel on February 4, 2017 5:13PM
    PC EU - CP 1200+ All trials + HM

    Intis Ravelen - Stamina Nightblade - Redguard - DD - Flawless Conqueror
    Annisca Micus - Magicka Sorcerer - High Elf - DD - Flawless Conqueror & Voice of Reason
    Shéogórath - Stamina Dragonknight - Imperial - DD - Flawless Conqueror
    Pilar Joranil - Magicka Dragonknight - High Elf - DD - Flawless Conqueror -
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  • RazorCaltrops
    RazorCaltrops
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    Bookmarked :smile:
    PS4 EU
  • code65536
    code65536
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    Oh my. @Asayre, this is beyond awesome.
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  • Stamden
    Stamden
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    Holy hell man, this is amazing. What is your background?
    PC NA

    ~Currently taking a break from the game until my DK can become something more than just a crafter~
  • zerosingularity
    zerosingularity
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    Amazing job! You are the hero we need in these dark times.
    NA-PC

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  • LorDrek
    LorDrek
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    Awesome!!!!!
    Imperial DK stamDPS, Nord DK magTANK
    YDoA CZ/SK Guild
    @LorDrek
  • GCVDJ11T
    GCVDJ11T
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    @asayre You are absolutely amazing for doing all of this work and posting it for us to use! <3 <virtual hug>
  • runagate
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    Would it be difficult to infer the contribution of Staff Expert given that light weaves can contribute a great deal to the overall percentage - but obviously offset by the loss of other CP passives. I ask primarily because I've been testing a number of builds and sets that utilize Staff Expert for PvP and it's too chaotic for me to say much beyond that, for some classes/builds, it's superior. In PvE it's noticeably worse and needn't be pondered beyond that. I'd be interested to see the numbers behind what I experience in PvP, though. Those damned players are always dodging and such so there's no "rotation" per se most of the time but I can say that, anecdotally, basically no one ever tries to dodge or even block light attacks.
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  • YoshinJaa
    YoshinJaa
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    Very nice work, Asayre!
    Any chance we can use the Simulator program at some point?
    Edited by YoshinJaa on February 5, 2017 12:45AM
  • fr33r4ng3r
    fr33r4ng3r
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    AWESOME! Thank you!
  • Asayre
    Asayre
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    What is your take on the Lightning vs Inferno staff on the main bar?
    For single target, I think Inferno staff is better for a main bar. If you are using Burning Spellweave then the light attacks are helping in maintaining a good uptime. But even if you are not using Burning Spellweave, an Inferno staff is preferable on your main bar because the majority of your damage is single target. In terms of simulation comparison, DPS for 2 Ilambris, 5 Julianos, 3 Moondancer with two Inferno staves is 42167 but 41903 if using a lightning staff on the main bar.
    As well as the Exploiter passive, is it worth spending 75 CP into Thaumaturge and rely on setting enemies off balance for the 10% damage increase?
    It depends a bit on how far away you are from putting 75 CP into Thaumathurge. If I assume 40% of my damage is from DoT and I'm just getting Major Breach, then my CP optimiser says to put 100 in Elemental Expert, 46 in Spell Erosion, 42 in Elfborn and 12 in Thaumathurge. The optimisation function output is 1.793. If you open the developer console on my CP optimisation webpage you can see the optimisation function output. If I force it to put 75 points into Thaumathurge it then suggest 100 in Elemental Expert, 5 in Spell Erosion, 22 in Elfborn with an optimisation function output of 1.745. So you'll be losing about 3% damage. This suggest that you need your target to be off-balance for at least a third of the time, possibly higher since Exploiter is presumably additive with other forms of damage done.

    I think @Masel92 provides interesting comments. Putting 75 points to get Exploiter is probably best done in raids where you have heavy attack builds going on. @Masel92 do you happen to use Combat Metrics? And if so, does it show the debuff uptime of Off-balance?
    I noticed that your setup (6) was using Aether and a random staff, yet there is no considerable DPS loss in comparison to setup (4). Also your minor vulnerability uptime is significantly higher, this leads me to guess that you were using Boundless Storm over Curse?.
    Woops I made a mistake there. (6) should have been with an Aether staff. When compared to (4) it is just comparing the difference between using 3/4 pieces of Infallible instead of Moondancer and I find that the difference is too small to be detected by my simulation which agrees well with the weighted ability metric calculations. A straight ability metric calculation for 2 Ilambris, 5 Burning Spellweave, 3 Moondancer is 86580 and for 2 Ilambris, 5 Burning Spellweave, 3 Infallible it is 85870. That means that 3 Moondancer should do about 0.8% more damage than 3 Infallible but neglects to take into account that the damage difference is in favour of Infallible for light and heavy attacks thus the damage difference is smaller than 0.8%. I also made a mistake of putting my notes on Minor Vulnerability for (5) into that of (6). (5) has higher Minor Vulnerability because Blockade of Storms is being used. I've updated my figure. Sorry for the confusion and thanks for spotting it. That simulation was more personal because I have a Sharpened Maelstrom Lightning staff and was interested in what I could expect.
    Same question about using an offset staff (for those who haven't had the luck of a sharpened Moondancer or Aether staff) how much of a decrease can we expect?
    So I took (2) and ran it with non-set sharpened staves and got a mean DPS of 40651 compared to 42167 with a maelstrom staff so it's loss of like 4%
    Just a side question, what is your rotation with Haunting Curse? Do you just refresh it after the 2nd explosion or do you have a specific rotation?
    I tried refreshing Haunting Curse after the 2nd explosion but still haven't gotten totally used to it. But ideally I want to refresh it after the 2nd explosion. And thanks for all the questions!
    GilGalad wrote: »
    The findings in terms of gear are pretty similar to the findings I derived from my spreadsheet, at least for the Sorcerer class. I also found that the theoretically perfect weaving dmg is a lot higher than the observed values and that perfect weavig can make a bigger difference than the gear.
    I do agree that perfect weaving provides a huge amount of DPS but it is hard to replicate in game and that is what I tried to model by allowing only 50% or 75% of my light attacks to hit and it does result in a decent DPS loss. Another thing to note is that my simulations assume that your light attacks are always benefiting from the Maelstrom enchant but this is not always the case. In game if your target is near the edges of Elemental Blockade, light attacks do not benefit from the Maelstrom enchant.
    GilGalad wrote: »
    The only class that is a bit more complicated to approach in terms of gear and weapon choice is the templar class. In my spreadsheets there are 2 setups that are rather close to each other:
    I've tried a few simulation for other magicka classes to make sure things roughly worked. My main problem with templars were that the current magicka is sort of important as Radiant Oppression's damage scales of it. In my sorcerer simulations, I just let the current magicka go negative as there is no real impact in terms of damage calculation. My plan at the moment is probably to just put on Minor Magickasteal all the time or maybe just set the minimum Radiant Oppression magicka multiplier to 1. I'll get back to you once I get around to those simulations. I'll also be sure to try out different levels of light attack probabilities most likely 50% and 75% for both sets and see what happens.

    My gut feeling is that Unstable Wall is a DPS increase however I find it a bit difficult to use in game as I am used to casting my Blockade maybe half a second to a second before it expires and with Unstable you really only want to cast after the explosion.
    runagate wrote: »
    Would it be difficult to infer the contribution of Staff Expert given that light weaves can contribute a great deal to the overall percentage - but obviously offset by the loss of other CP passives. I ask primarily because I've been testing a number of builds and sets that utilize Staff Expert for PvP and it's too chaotic for me to say much beyond that, for some classes/builds, it's superior. In PvE it's noticeably worse and needn't be pondered beyond that. I'd be interested to see the numbers behind what I experience in PvP, though. Those damned players are always dodging and such so there's no "rotation" per se most of the time but I can say that, anecdotally, basically no one ever tries to dodge or even block light attacks.
    Are you planning to put a lot of points into Staff Expert? If you are only planning to put a few you shouldn't be losing important CP passives. If you go to the CP optimisation webpage you can open the developer console and force it to calculate certain CP distributions, the CP optimisation function is basically a multiplier on your base damage so you can see how it varies as you spend more points into Staff Expert. It doesn't tell you how much you will lose from losing CP passives though.
    YoshinJaa wrote: »
    Very nice work, Asayre!
    Any chance we can use the Simulator program at some point?
    You can use it if you want. It's maybe not super easy to use at the moment though. Send me a PM and let me know if you want a Windows executable or the Matlab source code.
    Edited by Asayre on February 8, 2017 1:00PM
    Reference for any calculation I make Introduction to PvE Damage Calculation
  • QahnaarinDynar
    QahnaarinDynar
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    You put the "L" in LEGEND. Thank you very much.
    Guildmaster of Amaraldane Arpen Nenalata

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  • Gilliamtherogue
    Gilliamtherogue
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    Truly impressive @Asayre . Your skill and dedication to providing meaningful mathematics to in game occurrences speak words that cannot be paralleled.

    A few things you may want to look into for testing if you have free time;
    The Unstable Imp is currently doing obscene damage, and a lot of it's interactions with calculations are jumbled (they do not inherit CHD, do not scale with Spell damage, and their basic attacks do not scale with CP, while their special abilities can). It'd be nice to see if you could find it's minimum and maximum damage performances in end game scenarios, with and without Daedric Prey.

    Look into Unstable Wall instead of Blockade, this will move around the desired CP allocation and also adds in some additional calcs if you're using Lightning (proccing Exploiter passive, etc).

    Expansion of your ability dump spreadsheet to incorporate less "meta"-esque abilities, to give mathematical terms to prove disparity between skills. If there's hard math that proves some abilities just flat out suck, Zenimax is far more likely to adjust them.

    Thanks again for all of this. I think I'll stick to using rough estimates when explaining math to most players, but this really gives a lot of insight in the deep end. You'll definitely be the go to referral for the extreme math, prepare your inbox :)
    Old member of The Order of Mundus, Mostly Harmless, Hostile, and Genesis Elite. Avid theorycrafter. Herald to competitive stamina DPS pre 1.5. How far we've come!

    Have questions? Send me a message on the forums or my other social media. Seeing people learn is my dream and passion.

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  • aetherial_heavenn
    aetherial_heavenn
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    Thank you. Linked to my guild for the theory crafters. The info on mundus and weapon types (sharpened etc.) is particularly appreciated.....there has been a lot of discussion on that.

  • Arciris
    Arciris
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    Thank you @Asayre <3
    You are o:) B)
  • swaggasm
    swaggasm
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    Really awesome Asayre a lot of time and effort put into this.
    Mechanically Challenged

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  • Asayre
    Asayre
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    @Gilliamtherogue

    Thanks for the comments!

    Ya, I definitely want to look into the imp but I also want to see how it works in game. It's been a while since I used pets and I just remember my frustration at controlling and keeping it alive. I started with abilities meta'ish abilities to ensure that my calculations matches my experience and I'll slowly expand it to include other skills as well.

    I do agree that rough approximations are always useful, this kind of simulation is for more intense purposes and not meant for day to day play.
    Reference for any calculation I make Introduction to PvE Damage Calculation
  • Ixtyr
    Ixtyr
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    Holy *** @Asayre this is insane. Thank you.
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    Rhys Falavir - Orc Sorcerer - Aldmeri Dominion
    Rhiannon Falavir - Altmer Templar - Aldmeri Dominion
    Nenara Falavir - Argonian Warden - Aldmeri Dominion
    Neera Falavir - Orc Warden - Aldmeri Dominion
    ---
    The Ska'vyn Exchange & Bazaar - Guild Master
    Ømni - Guild Master
    Vanquish - Officer
    Nightfighters - Member
    Vehemence - Officer
    ---
    Moderator of /r/elderscrollsonline
  • AzuraKin
    AzuraKin
    ✭✭✭✭✭
    utilzing base crit damage boost (actual boost used dont matter to compare thief and shadow if stats otherwise are same):

    a 1000 damage skill will RMS for 1350 with thief mundus at 1.5% damage boost (assuming 70% crit chance)
    a 1000 damage skill will RMS for 1374 with shadow mundus at 1.5% base damage boost (assuming 55% crit chance)

    this is based on thief is 12% crit 15% at full divine
    this is based on shadow is 15% crit boost 18% at full divine
    v160 spellsword (nightblade)
    v160 restoration archmage (Templar)
    v160 battlemage (sorcerer)
    v160 restoration archmage (Templar)
    v160 warrior (DragonKnight)
    v160 assassin (nightblade)
    v160 swordsman (sorcerer)
    v160 spellsword (nightblade)
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