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Introduction to PvE damage calculation (Homestead)

Asayre
Asayre
✭✭✭✭✭
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
  • Asayre
    Asayre
    ✭✭✭✭✭
    DAMAGE EQUATIONS
    2.1 - Resource pool
    1d46adc87bbb1fe9a5d019fd29dc0ea8.png
    The Base value at CP160 is 8744 for Health and 7958 for Magicka and Stamina. Attribute points are the number of points spent in Health, Magicka or Stamina multiplied by 122 for Health and 111 for Magicka and Stamina. While Gear covers the vast majority of set bonuses and enchants, certain set bonuses fall under Gear1, most notable are the 5 piece bonus of Destruction Mastery and Necropotence. CPI is a cumulative percentage increase due to points spent in the corresponding constellation and can be calculated as follow
    a8d38a0c92a6b149c304c9f8e70321b4.png
    The Lord Mundus gives 1452 Health. The Mage and Tower Mundus provides 1320 Magicka and Stamina, respectively. Mundus values should be multiplied by the 1 + sum of Divines. Skills refer to the sum of stat boosting skills.

    2.2 - Spell damage
    690b428ec27f32f434eb88f475a2712f.png
    The Apprentice Mundus provides 166 Spell damage at CP160.

    2.3 - Recovery
    4878711bd7ac361df53260ae19f9cae5.png
    Base Magicka and Stamina recovery at CP160 is 514. Base Health recovery at CP160 is 309. The Atronach mundus provides 198 Magicka recovery at CP160.

    2.4 - Spell Cost
    5273a604acf0f802da9337889aa1f62f.png
    The Base Cost of a spell is the tooltip cost value, without any points in Magician and without any equipment or skills that provide either a percentage or flat cost reduction. Flat Cost Reduction is typically in the form of enchantments on jewellery and % Cost Reduction comes from skills and passives. Note that the 2 piece Molag Kena is a 33% cost increase when activated.

    2.5 - Spell Critical
    Simply add up all sources that increase Spell Critical. 219 Spell Critical rating is equivalent to 1% Spell Critical. There is a base critical chance of 10% or 2191.

    2.6 - Critical modifier
    The additional percentage of damage done on a critical hit can be calculated as follows
    ab38da5a571d8f6afa8d397a89ee035a.png
    where Floor is the floor function, Round is the round function and Elfborn<sub>Real</sub> is similar to the tooltip value of Elfborn but when it is used no unexpected rounding errors are found.
    8800f24b5ccb844d41ddaad853c14473.png
    Round(x, 2) rounds a number to 2 decimal places and Floor(x, 0.01) truncates a number at the 2nd decimal places. Here are examples of both functions in action, Round(23.458,2) = 23.46, Floor(23.458,0.01) = 23.45.
    Due to rounding of Elfborn there are jumps. Points spent in between jumps do not increase critical modifier. The Elfborn jump points are at
    1, 2, 4, 7, 9, 12, 15, 18, 22, 26, 29, 33, 38, 42, 46, 51, 56, 61, 66, 71, 76, 81, 87, 92, 98.

    2.7 - Damage calculation
    2.7.1 - Base ability tooltip
    7d9438b8efa8c6454186aa7e541c99ff.png
    where a, b, and c are coefficients. Skill coefficients can be found at ESO: Skill Browser. Since the ratio of b/a is around 10.5 for most abilities, a close approximation to the spell tooltip is
    59b1bcc84155404d462759599127c519.png
    where with a’ approximately equal to a and b’ is roughly 10.5. Since the ratio b/a is mostly constant, it is common to use the notion of an effective max magicka, defined below, to quickly evaluate builds with varying Magicka and Spell Damage.
    820e9554b0976ea0d32542c3ba50aedf.png
    The tooltip calculated in this manner will typically differ from in-game tooltips as the latter sometimes shows the influence of CP and damage done multipliers.

    2.7.2 - Base damage
    The base damage formula is
    41c98d207c329db53642eeefcc88124f.png
    where
    455306b9965ad480fef2b302fc54b7dd.png
    Attacker Bonus has three components
    45c432977344b74870d7dee3073ce05d.png
    CP Bonus is typically Elemental Expert for direct damage abilities or the sum of Elemental Expert and Thaumathurge for damage over time abilities. While the majority of damage increases bonuses fall under Damage Done, such as Minor Berserk and Elemental Talent. A sizable number fall under Damage Taken. Resistance is the relevant physical or spell resistance. Since OneTamriel, dungeon mobs have a resistance of 18200 while overworld mobs have a resistance of 9100. A notable exception being Maelstrom Arena. There is a base Flat Penetration of 100. While CP160 players are considered level 66, mobs are level 50.

    2.7.3 - Average damage
    The average damage done when taking into account critical chance is
    c143ecf6a9f6dfa452287172d98255fa.png

    2.7.4 - Ability Metric
    It is often useful to calculate all factors in the average damage equation except for the base tooltip as this provides an efficient method to compare builds. The ability metric can be defined as
    51f4704dc70bc75358c8243c41e66b7f.png

    Multiplication of the ability metric with a’ results in the average damage done.
    Edited by Asayre on February 5, 2017 2:20AM
    Reference for any calculation I make Introduction to PvE Damage Calculation
  • Asayre
    Asayre
    ✭✭✭✭✭
    ANALYTICAL RESULTS

    3.1 - Champion Point System

    3.1.1 - Thief
    In previous patches, it was necessary to choose between spending points in Magician or Acanist. The optimal allocation could be found by finding the minimum of
    0e9b819bf447b2b726e9defabae648c0.png
    A strong preference for Magician over Arcanist was found. However, with the current CP cap, this issue is no longer present.

    3.1.2 - Mage
    For magicka damage dealers, there are five signs of interest: Elemental Expert, Thaumathurge, Spell Erosion, Elfborn and Staff Expert. Essentially, we wish to find the maximum of
    6742bacaf5215aedb52660c11144a13e.png
    My approach to find the maximum is to begin with 0 champion points allocated and evaluate the function for an increase of 1 point in each star. The allocation corresponding to the highest function is then used as the next starting point. A webpage with the solver implemented can be found here. If you encounter problems, there is a ‘Help’ tab. Also @Jeckll has a comprehensive guide on how to use the calculator for stamina characters.

    In practice, most magicka classes allocate 100 points in Elemental Expert and (practically) 0 in Staff Expert. Thus we only actually need to consider how to allocate 100 points amongst Thaumathurge, Spell Erosion and Elfborn. The ternary contour diagram below shows the function evaluation for all possible combinations as the sum of CP anywhere within the triangle is 100. The function is reasonably flat near the maximum. It varies by around 2% within 20 points of the maximum. Therefore, while some accuracy in the values used in the solver is desirable, there is no need to be overly pedantic as the function is rather flat.
    620fd36108b8729a7b166e04f64d247b.png

    3.2 - Mundus: Mage, Apprentice, Thief and Shadow
    There are four mundus stones of interest for PvE Magicka based damage dealers. They are the Apprentice, Mage, Thief and Shadow. The average damage increase for each mundus can be determine by calculating the quotient of the damage with and without the mundus. The impact of Divines can be neglected for this section.

    For the Mage, this is
    95adc9907f0e16700a7cde74c09044be.png
    where CPI and Skill were define in Resource Pool. For endgame characters Magicka and Spell Damage are in the vicinity of 40000 and 3000 respectively. For CP 600 players, CPI is 1.199 and Skills of 1.2 to 1.4 is typical. From this, it is concluded that the Mage mundus will increase damage by around 2.9%.
    e2525fbf04873d8640fb74fd4e908329.png
    Similarly, with the Apprentice mundus, the damage increase is
    775a12c19f7fc0c356c34936120e510a.png
    The Skill multiplier for Spell Damage is usually 1.25 due to Major and Minor Sorcery. Thus, the Apprentice mundus increases damage by approximately 3.1%
    b5c4337009cbadb8b25e8344b7732d43.png
    With the Thief mundus, the damage increase is
    7e2db092a40c7194ec46a5d475bc6997.png
    Endgame characters will have a critical chance in the region of 40 to 60 % and a critical modifier of 60 to 80%. I expect the Thief mundus to increase damage by about 5.9%
    f178468fbefea682852b68df97b8ca87.png
    Similarly, with the Shadow mundus, the damage increase is
    3b84f2fbc4cc8e342df418b7573c13d6.png
    Using identical values to the Thief section, I conclude that the Shadow increases damage by 4.1%
    5cce83ccbbcd0c1908910dbe497a64c1.png
    In general, the preferred mundus order is
    f5911830b1acac30bfc149d5bebf3658.png
    There are some situations where the Apprentice or Mage is preferred, notably for skills that scale strongly or solely of magicka or spell damage. There are occasional questions on the relative merit of Shadow over the Thief, it can be demonstrated that the Thief is better than Shadow when
    36c2f46bef874aa88ebc51f64e827baf.png

    3.3 - Armour Trait: Divines and Infused
    The Mundus section concludes that in the majority of cases, PvE magicka damage dealers tend to benefit the most from the Thief mundus. Based on the assumption that the Thief mundus is used, I calculate the damage increase with Divines and Infused on large and small gear.

    Each legendary Divines gear increases Critical Chance by 0.825 with the Thief mundus. This represents a damage increase of
    adb4357c8b1870c558c441529463727f.png
    On a large piece (Head, Chest, Legs), Infused increases magicka by 173. Assuming CP 600 and a Skill multiplier of 1.3. The damage increase from a large infused piece
    ec5ea0382e27fbac2fd4ba6da20ac996.png
    On a small piece, Infused increase magicka by 70. This is increased by CP and Skill multipliers. Thus, the damage increase from a small infused piece is
    5d145ea358559db07e519568e3e10fd5.png
    In conclusion, each piece of Divines increases damage by 0.41% and is slightly better than a large Infused piece by 0.04% and a small Infused piece by 0.26%.

    3.4 Weapon Trait: Nirnhoned, Precise and Sharpened
    In this section, we use the same method of evaluation as in the Mundus and Armour Trait section to determine the ideal weapon trait.

    A legendary Nirnhoned staff has 146 extra spell damage. This is increased by Major and Minor Sorcery thus the damage increase expected from using Nirnhoned for endgame builds is about 2.7%
    c13cab9c0d4829504f3dedf1ef6c2cd7.png
    For Precise, we can evaluate it in a similar manner to the Thief mundus. A higher critical chance is assumed as the Thief mundus is use with Divines pieces and a few gear sets that increase critical chance. The damage increase from Precise is around 3.4%
    8007f81e86f85ba4a6dac46554147fa5.png
    Finally, the damage increase from Sharpened is
    2a78ee3b73c55139694f232ac8e0d281.png
    Resistance is the base resistance less armour debuffs and other sources of armour penetration. Assuming only Major Breach is consistently applied and that magicka classes will have an additional 4884 spell penetration from Concentration, 100 from base penetration and around 1000 from Spell Erosion, the damage increase from Sharpened is
    340e2ab46b27667a979b70c2b4e94bcf.png
    Sharpened is significantly better than Nirnhoned and Precise. Although its effectiveness decreases with increasing spell resistance debuffs. Under ideal conditions, it is possible to reduce dungeon mob resistance to 0 where Sharpened is not effective at all. The threshold where this occurs is when the target only has 1700 resistance remaining ( 1000 * Level * Damage_Precise) in which case Precise will outperform Sharpened.
    Edited by Asayre on February 4, 2017 1:02PM
    Reference for any calculation I make Introduction to PvE Damage Calculation
  • Asayre
    Asayre
    ✭✭✭✭✭
    NUMERICAL RESULTS
    4.1 - Introduction
    This section summaries my attempts at creating a combat simulator in order to answer some of the trickier questions such as proc based mechanics that are inadequately handled by analytical methods relying on average statistical behaviour.

    The combat simulator is coded in Matlab.

    4.2 - Details of simulation algorithm
    Essentially, my combat simulator takes an ordered list of abilities and executes it. To provide further details, the main simulation loop does the following
    1. Applies any Buffs/Debuffs when mod( time, refresh) = 0
    2. Allows the casting of ultimates if you have enough ultimate
    3. Determine which ability from the ordered list to execute. It goes for the highest priority with a few requirements such as if a specified amount of time has passed since it was last cast (useful for controlling damage over time abilities) or certain health thresholds are fulfilled.
    4. Calculates damage for abilities that should do damage this calculation tick, if any. Also applies any applicable buffs, debuffs or proc events.
    5. Calculates resource recovery for this particular calculation tick, if any.
    6. Determines the next calculation tick.
    7. Calculation ticks can be for damage event, resource recovery events, buff events (both new buffs and expiring buffs) and debuff events.

    4.2.1 - Supported Skills

    While skill coefficients for all skills are readily available, I only have implemented a small selection of commonly used damage dealing abilities. A complete list of supported abilities is listed here.
    https://docs.google.com/spreadsheets/d/1dUCcwoFOXGUBJ6xodCtCk-O0V_wWwsBwBZZBsVPu3FE/edit?usp=sharing

    4.2.2 - Supported Sets

    The following sets with unusual bonuses are implemented in my simulator
    • Ilambris
    • Valkyn Skoria
    • Nerien’eth
    • Grothdarr
    • Molag Kena
    • Scathing Mage
    • Burning Spellweave
    • Silks of the Sun
    • Moondancer (Smart – only synergises if you don’t have the spell damage buff)
    • Moondancer (Random – always synergises)

    4.3 - Simulation Interface
    To aid with the flow of simulation, I have built a rough interface. It contains four panels.

    4.3.1 - Stats
    This panel allows for calculation of key stats on both bars and includes inputs for certain passive calculation, special proc sets and champion point allocation.
    169cd7234b20ff628c8ebe09edc940f5.png

    4.3.2 - Skills
    This panel is primarily for inputting the ordered list of abilities. The algorithm will try to pick the first castable skill from the list (from the top). Once an ability is used, it is not allowed to be cast again for time, t_Period. This time is tracked by cooldown, CD. The time needed to execute the ability is controlled by t_Execute. There is an option to weave a light attack with the ability. Heavy attacks are not implemented due to varying charging times. Min Health and Max Health control the health thresholds when an ability should be used. SD is an unused column.

    The panel on the right controls periodic buffs and debuffs. In the picture below, a magicka potion (with Major Sorcery and Major Intellect) is drank every 45 seconds starting at 0 seconds and the buff last for 48 seconds.

    Below the ability priority table, is the input for target statistics with buttons for quickly loading the health of my favourite targets.

    The panels around the bottom are for saving and loading files as well as simulation details.
    a18c7abb1226da3df32eb95e727018a2.png

    4.3.3 - Results
    The third tab outputs a single damage parse. It contains a damage log and damage summary. There are additional buttons that plots selected stats.
    2d9ff49fa0c8125db0aec2c3812a86a2.png
    An example plot showing magicka related stats
    b310eafe9a0246a20caabf3987d966c7.png
    Note that there is no restriction on current magicka thus it can be negative.

    4.3.4 - Average Results
    The final tab aggregates all the simulation results and calculates some statistics. There are also additional buttons to plot some stats.
    d01baf05104121083340f4119559dd53.png
    An example showing histograms of total damage and contribution of the top nine highest damage dealing abilities is shown below.
    37d8b40f9b9828349aec1d926572ff79.png

    4.4 - Normal approximation of damage distribution
    Since a hit either crits or not, the total damage distribution conforms to a binomial distribution. This can be approximated with a normal distribution with the following statistics
    8e3007e8e6873f0e15be199776613a46.png
    where n is the number of events. Assuming that k attacks occurs per second, the normal distribution for damage per second is
    57e26b6488a86fef658f6159aad18ea1.png
    Since Time is proportional to health, the standard deviation can be decreased by increasing the health of the target.

    In order to reduce the standard error of the mean, we can either decrease the standard deviation or increase the number of simulations. I have found that the most computationally efficient way is to increase the number of simulations as it leverages parallel computing.

    4.5 - Simulation accuracy
    The accuracy of damage calculation is usually within 10 point of the observed in game value with the exception of the damage of Burning, Chilled and Concussed as well as the second direct damage component of Rearming Trap. An example of my accuracy for some abilities is shown below
    a57994664e3db7861222d8e012e81659.png
    A source of error in my simulation is when the game decides to apply on cast buffs. For example, Minor Sorcery is applied after the initial hit of Reflective Light and Purifying Light but before the initial hit of Radiant Oppression. In my simulation, all buffs on ability cast are granted prior to damage calculation.

    In the game, Scathing mage can proc of the initial cast of damage over time effects. This is not reproduced in the simulator. The simulation only allows direct damage abilities and Twisting Path to proc Scathing Mage.

    4.6 - Simulation Results for Magicka Sorcerer
    I have ran a few simulations for magicka sorcerers. To keep things rather compact, I will only report some key parameters. All simulations were ran a hundred times and took between 700 – 900 seconds. This was done via parallel computation on an i5-3570k. Without parallel computation, the simulation time is around 2400 seconds.

    4.6.1 - Sets
    Assumes the same rotation namely
    0a9316f26c6afb942e7debde73e310d7.png
    The race is set to Altmer and champion point distribution is kept constant at 100, 46, 46 and 8 in Elemental Expert, Elfborn, Spell Erosion and Thaumathurge, respectively. Synergies are activated every 15 seconds. This is primarily for allowing the 5 piece bonus of Moondancer to proc.
    5b648d91c51c57b711a7ef610282a1ae.png
    Note that (5) uses Blockade of Storms instead of Blockade of Fire thus the higher Minor Vulnerability uptime and lower Burning Spellweave uptime.

    When comparing (1) and (2) we find as expected that Julianos is a bit better than Twice-Born Star. From the ability metric, we would have predicted that Julianos is about 0.2% better than Twice-Born Star but this neglects the different metric for light attacks. Light attacks with Julianos are almost 5% greater than Twice-Born Star. Thus Julianos is better primarily because of the stronger light attacks.

    Of the sets considered, the simulation is most favourable for (4). Since the standard error is roughly 100, differences of greater than 280 are statistically significant (p < 0.05). Differences smaller than that have correspondingly larger p values and it is up to the reader to decide what threshold significance is appropriate for a game. Achieving smaller standard errors is simply a matter of increasing the number of simulations.

    It is interesting to note that the uptime on my Burning Spellweave is quite high. After some consideration, I belief this is due to the nature of my simulation putting most damaging abilities near the start of a second right after Burning Spellweave comes after cooldown. If we were to analyse the number of flame-based attacks in an example parse we would get the following
    b40766f7f0532124567a30ac243e5e3b.png

    A geometric distribution would suggest that the median number of attacks needed to proc Burning Spellweave is 3.1. This suggest that it would take about 1 second to proc Burning Spellweave when it comes of cool down giving an uptime of 61.5%. But this is based on the assumption that the 3.5 flame-based attacks are equally distributed over a second. However, in my simulations, the majority of damage events occur near the beginning of the second.
    d034571dc64c111061d55e5133e3e1e4.png

    This means that the time to proc burning spellweave is usually 0 as seen in the histogram below
    bb343e286cbdee2906fcdd5a946c958a.png

    4.6.2 - Effect of Race
    Using set (4), I simulated the effect changing the race from Altmer to both Dunmer and Breton. The difference between Altmer and Dunmer is too small to be determined with this number of simulation. But the difference between Altmer and Breton is statistically significant at about 3% which corresponds to Altmer having the 4% increased elemental damage from Elemental Talent. The difference is less than 4% due to the additive nature of damage multipliers.

    4.6.3 - Rotational changes
    My simulation allows for evaluation of difference rotations. This is something that is a big difficult to do analytically. In comparison to the rotation described in Sets, replacing Boundless Storm with Haunting Curse results in a small change (mean = 41026, SD = 1089) but a higher Minor Vulnerability uptime of 55% but of course this is at the cost of having to stay close to the target.

    If we were to be lazy and recast all DoTs every 12.1 seconds that is after the second explosion of Haunting Curse, mean DPS decreases by around 3% (mean = 40631, SD = 905). Also recasting Haunting Curse every 3.6 seconds (after the first explosion) results in a DPS loss of approximately 4% (mean = 40597, SD = 999).

    4.6.4 - Modelling user error
    I have also played with variables that might better model in-game situations. All comparisons are made to that of (4) in Sets where the mean DPS is 42082.

    Normal Error for damage over time
    Instead of casting damage over time abilities like Blockade of Fire immediately after 8 seconds, I tried recasting at 8 seconds with a standard deviation of 0.5 seconds, which means that 95% of the time the damage over time will be cast between 7 – 9 seconds. This results in a DPS loss of about 1.3% (mean = 41536, SD = 921). I believe this is mainly from accidentally casting Curse too early and skipping the second explosion. The DPS loss is less than recasting Curse every 3.6 seconds because half the time the second explosion does occur. If the standard deviation is increased to 1 s the DPS loss is 1.0% (mean = 41659, SD = 1146). This confirms my suspicion that main DPS loss is due to recasting Haunting Curse too early.

    Execute Time

    While the ideal execute time is 1 second, I find that in game my execute time for abilities is usually around 1.1 seconds and a bit higher during more intensive fight sequences. Increasing the execution time for ability to 1.1 results in a significant DPS loss of 5% (mean = 4010, SD = 917). Further increasing the execution time to 1.2 results in a DPS loss of 11% (mean = 37845, SD = 814).

    Missing Light Attacks

    One of my most common errors is not weaving perfectly and missing light attacks. If I were to allow only 50% of light attacks to occur this results in a DPS loss of 10 % (mean = 38027, SD = 1111).

    A table summarising all these individual effects is shown below
    cc7b7a20c54f14307a00bf3b50f98e22.png
    Edited by Asayre on March 3, 2017 3:45AM
    Reference for any calculation I make Introduction to PvE Damage Calculation
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    <3
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    Zenimax hire this guy!
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  • Izaki
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    :heart:
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    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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    Thanks again! <3
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    Saving, in hopes of one day being able to comprehend this!

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

    Anyway, thanks once again for the insane amount of information!
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    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

    All Trial Trifecta Titles Done!

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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

    All Trial Trifecta Titles Done!

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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.
    Nightfighters ― PC/NA and PC/EU

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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
    ✭✭✭✭
    Amazing job! You are the hero we need in these dark times.
    NA-PC

    Kaineth - Stamina Nightblade (Weakest Player Ever!)
    Elena Stormwood - Magicka Sorcerer (vMA no Death 12/21/15 Score 401148)
    Sheila Feyrondas - Magicka Dragonknight Tank (Frost staves are gonna be fun!)

    *Disclaimer* I fail at emotional communication, so assume what I say is NOT meant to be offensive.
  • LorDrek
    LorDrek
    ✭✭✭
    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
    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.
  • YoshinJaa
    YoshinJaa
    ✭✭✭
    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
    ✭✭✭
    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

    PC/NA - Trueflame

    One zerg to rule them all, one zerg to find them. One zerg to bring them all and in the darkness bind them.
  • 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.

    Guides and other fun videos at https://youtube.com/c/gilliamtherogue
  • 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.
    Quoted for truth
    "In my experience, the elite ones have not been very toxic, and the toxic ones not very elite." WrathOfInnos
  • 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.
  • 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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  • AzuraKin
    AzuraKin
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    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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