Tamriel Foundry

Introduction to PvE damage calculation (Horns of the Reach)

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 @Solinur 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.

About Asayre:

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470 Replies
  1. #41

    Asayre

    Member633 Posts

    It depends how often you have that 17800 penetration really. Would you be able to estimate uptime of Infused Crusher and Alkosh to come up with an average penetration?

    As an aside, my DPS simulations with DW with the gear you mentioned on a Target skeleton with Major Breach suggest a mean DPS of 36617 which I note it close to the value you have in your signature. However, I find that using a Lightning Staff on the front bar produces a mean DPS of 39566. While each ability does less with the staff, perfect light weaving leads to the staff doing substantially more DPS.

    Introduction to PvE Damage Calculation

  2. #42

    Norn

    Member29 Posts

    Looking at my previous combat logs, Alkosh uptime usually seems to be around 65% while Infused Crusher is 70%. If I had to guesstimate I'd take penetration as 16.1K on average.

    I'm actually quite surprised that Lightning Staff did manage to get more DPS than 5P Moondancer. It's understandable that you can get significant DPS increase on your light attacks due to vMA enchant but still I assumed around 40% uptime on Shadow Blessing would be able to crush that in terms of DPS.

    Stamina SorcererRobust Target Argonian Skeleton – Unbuffed DPS: 36,865 (5,745,107 in 2:35.8s)

    Magicka TemplarTarget Argonian Skeleton – Unbuffed DPS: 36,370 (3,015,176 in 1:22.9s)

  3. #43

    Mfool123

    Member2 Posts

    Is it true that all your AOE DAMAGE gets increased by 8% with a lightning staff equipped on your front bar? If so, then this is most likely why a lightning staff could outperform DW on a templar because sweeps, lightning wall & blazing shards are all AOE based. I also believe with the homestead patch DW received a small nerf as ZOS has stated they "Increased the Dual Wield Weapon and Spell Damage penalty by roughly 3%. Weapon and Spell Damage while Dual Wielding (without modifiers) is now equal to using a Two Handed weapon."

  4. #44

    MCGreenLantern

    Member27 Posts

    Awesome Post! Very insightful. Definitely making me rethink my build and my general notion that I will never need to use algebra again in life lol.

  5. #45

    Asayre

    Member633 Posts

    Yes, all AOE damage is increased by 8% with a lightning staff but I do not think that is the main reason for the difference between DW and Lightning staff on your front bar. From looking at the output stats all abilities do less damage with a lightning staff on the front bar and it appears that the only reason a lightning staff is better on the front bar is due to light attacks. Light attacks account for nearly 12% of the DPS.

    Introduction to PvE Damage Calculation

  6. #46

    shredguitargod

    Member33 Posts

    Wonderful work as always Asayre. I was wondering if you have tested 5xBSW+5xNecropotence with a pet constantly active.

    My test so far have been favorable, but I would be interested in what the simulation spits out.

  7. #47

    Asayre

    Member633 Posts

    I've updated the sorcerer calculations because there was a simulation error that resulted in all DPS simulations to be overestimated by around 2k. The error was because sometimes x-x ~ 1e-15 which leads to some abilities triggering twice. I had previously rounded most of these into 0 but I forgot to in one particular section causing an overestimate in the DPS.

    @shredguitargod, I have simulated using Volatile Familiar in place of Inner Light and the results are promising. With 2 Ilambris, 5 Necropotence, 3/4 Moondancer and a Maelstrom staff on the backbar the mean DPS is 42775 compared to 42082 with the usual no pet rotation (2 Ilambris, 5 Necropotence, 3/4 Moondancer, Maelstrom backbar).

    Edit: As an aside it was interesting to note that 2 Ilambris, 5 BSW, 3/4 Moondancer, Maelstrom backbar performs better with a pet build than 5 piece Necropotence. The mean DPS with a pet build with BSW is 43234. My initial inspection of the simulation results suggest that this is mainly caused by LAs scaling more strong off spell damage than abilities.

    Introduction to PvE Damage Calculation

  8. #48

    shredguitargod

    Member33 Posts

    Ah, perhaps I was not clear. I'm asking how 5x BSW + 5x Necropotence at the same time performs. No Ilambris, No Maelstrom weapons.

    I've been running this and it seems quite potent:

    1x Molag Kena

    5x BSW

    5x Necropotence

    Two sharp Necropotence weapon were not easy to farm, but worth it.

  9. #49

    Asayre

    Member633 Posts

    Oh I did not consider that since Ilambris and Minor Slayer from Moondancer are large contributors to DPS. Anyway, I ran your gear setup (5 BSW, 5 Necropotence, 1 Molag Kena) and got a mean DPS of 39623. Is there a reason for not going 5 BSW, 5 Necropotence, Maelstrom staff ?

    Introduction to PvE Damage Calculation

  10. #50

    Norn

    Member29 Posts

    I'd also agree that Maelstrom weapon would be better for that setup. Molag Kena gives you 129 Spell Damage, while vMA weapon gives you 189 plus the enchant. You're probably gonna lose your 6/1 setup but it should still yield way more DPS due to light attacks.

    Stamina SorcererRobust Target Argonian Skeleton – Unbuffed DPS: 36,865 (5,745,107 in 2:35.8s)

    Magicka TemplarTarget Argonian Skeleton – Unbuffed DPS: 36,370 (3,015,176 in 1:22.9s)

  11. #51

    Amasuriel

    Member27 Posts
    Asayre wrote on February 28, 2017

    Oh I did not consider that since Ilambris and Minor Slayer from Moondancer are large contributors to DPS. Anyway, I ran your gear setup (5 BSW, 5 Necropotence, 1 Molag Kena) and got a mean DPS of 39623. Is there a reason for not going 5 BSW, 5 Necropotence, Maelstrom staff ?

    Sharpened vMA staves are very hard to get :)

    Speaking of which, @Asayre, would you be willing to run a set with a non-VMA or moondancer staff (non set / Julianos) to show how much of a difference the hard to get weapons make? Basically a "starter DPS" calc with 5 Julianos, 2 Iambris and 3 Willpower (or blue moondancer / IA, instead of gold)? It would be interesting to know how much theoretical DPS gain several hundred hours of farming get you :)

     

     

  12. #52

    Asayre

    Member633 Posts

    Sure @Amasuriel. So I did two simulations

    Simulation 1

    Gear: 2 Ilambris, 5 Julianos, 3 Willpower, Random sharpened staves

    Mean DPS: 37494 (SD = 712)

    Simulation 2

    Gear: 2 Martial Knowledge, 5 Julianos, 3 Willpower. Martial Knowledge sharpened staves

    Mean DPS: 36126 (SD = 937)

    And just a reminder from previous simulations

    Gear: 2 Ilambris, 5 Julianos, 3 Moondancer, Moondancer front bar and Maelstrom backbar

    Mean DPS: 40598 (SD = 1007)

    Gear: 2 Ilambris, 5 Burning Spellweave, 3 Moondancer, Moondancer front bar and Maelstrom backbar

    Mean DPS: 42082 (SD = 1125)

    So rough summary, you get 36k with easily attainable gear. DPS goes up to 37.5k if you get Ilambris and then an additional 3k DPS with Moondancer and finally another 2k DPS with Burning Spellweave.

    Introduction to PvE Damage Calculation

  13. #53

    Amasuriel

    Member27 Posts

    Amazing, thank you.

    The good news is it means you can be very competitive without the ultra rare drops. The bad news is I am terrible (as is almost everyone apparently to varying degrees) at DPS, since I get literally half this most of the time! But it means I can spend my time working on rotation and make just as much or more progress as grinding for a sharpened vMA staff.

  14. #54

    Bouljig

    Member1 Posts

    Hello,

    first of all thank you for this awesome work.

    i have some questions about the magplar and the DW/lightning staff on front bar.

    can you show us the rotation you used on your simulation ?

  15. #55

    Dezderp

    Member12 Posts

    Can anybody explain how to read the graph on the CP distribution please? I've never seen one like that before and have no idea how to interpret it.

  16. #56

    Kuratius

    Member95 Posts

    @Asayre Quick request:

    sharpened+julianos vs precise+spinner?

    both with IA jewelry and ilambris

  17. #57

    Asayre

    Member633 Posts
    Bouljig wrote on March 8, 2017

    i have some questions about the magplar and the DW/lightning staff on front bar.

    can you show us the rotation you used on your simulation ?

    This was what I was using for DW/Inferno staff

    2 Grothdarr, 5 BSW, 5 Moondancer and VMA Inferno

    A synergy event was provided every 15 seconds and it would only synergise if it did not have the Moondancer Spell Damage buff.

    Bar setup

    1: Blazing Spear, Puncturing Sweeps, Purifying Light, Reflective Light, Inner Light, Shooting Star

    2: Blockade of Fire, Empty, Radiant Oppression, Channeled Focus, Inner Light, Fiery Rage

    Skill rotation was

    Shooting Star > Purifying Light > Blockade of Fire > Blazing Spear > Reflective Light > Radiant Oppression > Puncturing Sweep

    The mean DPS for this setup was 36617 with a SD of 697.

     

    For Lightning Staff/Inferno Staff I was doing this

    2 Grothdarr, 5 BSW, 4 Moondancer (Lightning), VMA Inferno

    Bar setup

    1: Shock Clench, Puncturing Sweeps, Purifying Light, Reflective Light, Inner Light, Shooting Star

    2: Blockade of Fire, Blazing Spear, Radiant Oppression, Channeled Focus, Inner Light, Fiery Rage

    Skill rotation was

    Shooting Star > Purifying Light > Shock Clench > Blockade of Fire > Blazing Spear > Reflective Light > Radiant Oppression > Puncturing Sweeps

    The mean DPS for this setup was 39566 with a SD of 840.

    An example log of what abilities was used for the second setup is shown below

    None

     

    Dezderp wrote on March 8, 2017

    Can anybody explain how to read the graph on the CP distribution please? I’ve never seen one like that before and have no idea how to interpret it.

    If your goal is to learn how to optimise your CP, understanding the graph is not important. The graph is called a ternary plot and is commonly used to plot 3 variables that add up to a certain number. I've included a picture I found from Google on how to read ternary plots

    None

    So if you look at the graph I posted

    None

    The dark red spot is the best CP distribution and corresponds to roughly 50 Elfborn, 40 Spell Erosion, 10 Thaumathurge. The purpose of this plot was to demonstrate that the CP optimisation function is reasonably flat so there is no need to fuss too much over where to put your points. That is to say don't quibble over putting 12 or 15 points in Spell Erosion as it will be close enough it wouldn't matter.

    Kuratius wrote on March 8, 2017

    @Asayre Quick request:

    sharpened+julianos vs precise+spinner?

    both with IA jewelry and ilambris

    Sharpened+Julianos

    Introduction to PvE Damage Calculation

  18. #58

    Kuratius

    Member95 Posts

    Out of curiosity, what was the dps in your simulation? Would it be worth going with that setup if one only has a precise maelstrom weapon?

  19. #59

    Dezderp

    Member12 Posts
    Kuratius wrote on March 9, 2017

    Out of curiosity, what was the dps in your simulation? Would it be worth going with that setup if one only has a precise maelstrom weapon?

    Which Sim? He listed the DPS

     

    @Asayre thank you for explaining that.

  20. #60

    Asayre

    Member633 Posts

    @Kuratius

    Using 2 Ilambris, 5 Julianos, 4 Infallible (Sharpened Inferno), Sharpened Maelstrom Inferno back bar gives a mean DPS of 40779.

    In comparison, 2 Ilambris, 5 Spinner, 4 Infallible (Precise Inferno), Precise Maelstrom Inferno back bar gives a mean DPS of 39536.

    I think I am missing the purpose of your question. If you have a precise maelstrom weapon, you could still use a sharpened staff on your front bar and go with Julianos.

    Introduction to PvE Damage Calculation

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