Introduction to PvE damage calculation (Horns of the Reach)

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    Tabatta

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    Altmer Sorcerer

    Latin said on October 12, 2017 :

    Tabatta said on October 11, 2017 :

    Dear @Asayre, I’ve been re-doing mundus stone calculations, and I’d like to point out (what I think are) two mistakes in the formulas you showed in this section.
    First, in the calculation of the damage boost created by the Mage mundus, it seems to me that the CPI factor disappears from your analytical expression to your numerical expression. Indeed, the analytical expressions show the product CPI x Skills, and you specify underneath that CPI = 1.2 while Skills is between 1.2 and 1.4 (I assume you took 1.3 as a representative value). The numerical estimation, however, shows only a factor 1.3.
    Second, in the calculation of the damage boost created by the Thief mundus, I think you used 9% for the Thief boost in critical rate, while the live version in Horns of the Reach is only 7%.
    Correcting these two mistakes, and keeping the other values you used unchanged, it seems that the Mage is better than the Thief.

    Thank you for all your work !

    Actually, the absence of CPI in the Mage mundus calculation makes sense. The mundus magicka of 2028 is not modified by CPI – it is actually just additive with the base pool. So whether you incorporate 1.2 into your calculation or not will not affect the result of that comparison, because it only modifies the base pool. Either way, the mage mundus with zero divine pieces works out to be 1.0349 when using the same 75500 effective magicka as benchmark.

    Consider thief, using 0.07 as it is on Live,while retaining 0.5 crit chance and 0.7 crit mod in Asayre’s example. we get 1.0363.

    If we drop the crit mod to 0.6, the differenceis reduced to 1.0323, at which point the Mage becomes favourable.

    Thanks you for your answer ! My bad, I didn’t see that the Mage mundus wasn’t modified by CPI. Still, there remains this inconsistency between the analytical formula he uses and the numerical one underneath, as the analytical one shows the CPI factor :). I agree with the rest of the computation done. And indeed, I’m assuming the value he uses are the PTS ones … Likewise, I found that on the computation divines vs infused, he uses 11% critical rate for the Thief. Adjusting the value to 7%, I find that infused on big pieces is better than divines for pretty much any major force uptime.

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    Tabatta

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    Altmer Sorcerer

    For those who might be interested, I did a little script to test some optimization for pet magsorc, in particular to test mundus stones and 4-pieces set (mainly Moondancer vs. Infaillible Aether), in a group PVE environment.

    I considered the stats I would have on my magsorc (Necropotence, Ilambris, 4 pieces set and vMA staff back) without mundus and without the 1-item bonus for the 4-pieces set, and then computed the damage increase compared to these previous stats, obtained with the Mage and the Thief along with the 1-item set bonus from MD or IA. I didn’t include the Apprentice, as I found that, considering that pets does approximatively 10% of the total damage, its bonus was smaller than the Mage’s. Given that I found that infused on big pieces was better with the Thief (and obviously with the Mage), independently of the major force uptime, I considered that we were using 3 infused pieces and 4 divines. Then, I plotted these damage increases as function of the major force uptime in the group. Please note that I considered a fix aggressive horn uptime, either equal to 100% uptime or a bit lower, which corresponds to what I have in group usually. Therefore, the part of the plot with a low major force uptime is “artificial” as it is not possible to have 100% uptime on horn and less than around 30% major force uptime … :)

    The results I found were the following :
    http://hpics.li/45d48a1

    Basically, I found that the Thief+MD is always better than the Mage or than Thief+IA.

    While I did my best to re-read it multiple times, I cannot claim that my script is free of any mistakes. I uploaded it here http://textuploader.com/d4q2w, it is written in Python and I did my best to make it readable. Please feel free to read it and comment :D.

    One of the reasonning I have made that were not made by others, and on which I’d love to have some feedback, is the following. In many posts I found that do the same kind of calculations, to compute the boost in damage brought by a piece that brings max magicka (or spell damage), the formula used is basically

    http://hpics.li/78076aa

    where the Modifiers comes from different skills, and in particular horn, and CPI, and where the effective pool is taken as

    http://hpics.li/9e316d6

    However, while the max magicka here is often taken as the value buffed by all passives and by CPI, most calculations I saw didn’t take into account the fact that it also should be buffed by the 10% of horn (with an uptime of 100%). This is why, in my calculations, I added multiplied the max magicka in the effective pool by roughly 1.4/1.3, which corresponds to the increase due to horn. As I said, all feedback is welcomed !

     

    • This reply was modified 1 week ago by Profile photo of Tabatta Tabatta. Reason: Cleaned the code and added some more details
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    Latin

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    Floliroy said on October 12, 2017 :

    I think the Mage can only be usefull on Sorc wich have a lot of Magicka Bonus ^^

    And pets are more affected by Magicka than by Spell Damage, it seems to me.

    Not necessarily. Since you have other skills that do damage, where spell damage is worth a lot more to your effective magicka, and thus the power of your skills. Since you are using sorc as example, let’s use Liquid Lightning to illustrate; using the Mage with 1.33 multiplier gives an increase in damage of around 5.3% compared to the control, Apprentice with 1.25 multiplier gives an increase in damage of around 6.1% compared to the control. Unless pets do an overwhelming proportion of your overall damage, it would be unwise to pick the Mage.

     

    Pets are affected more by magicka because they have near zero skill coefficient with spell damage (< 1e-4) – the most straightforward way to observe this is by checking the tooltip.

     

    @Tabatta

    Nice plot, script seems okay at first glance but you should note that Major Force is 0.15 and not 0.3 since 2.7.

    Yes, you can definitely include warhorn boost to max magicka by factoring into your skills multiplier. What I tend to do is to use a scaled average based on the uptime (similar to the way you would factor Major Force) in my usual sub-optimal groups, but you could go with whatever is applicable to you. I am curious though, why the constant of 1.4/1.3 specifically – is that just the output of an unspecified function dealing with warhorn uptime? Would it not be simpler just to add 0.1 (or adjusted based on whatever uptime you have) into the skills multiplier?

    It may have been left out depending on the target audience and the purpose of the analysis. Other skills multipliers (e.g. Magicka Controller, Inner Light) are easily accessible outside of organised group content, which makes those analysis more widely applicable. But obviously, if one foresees himself/herself doing trials or something, then it would make sense to incorporate into his/her own calculation.

     

    e pluribus unum

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    Floliroy

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    Latin said on October 12, 2017 :

    Not necessarily. Since you have other skills that do damage, where spell damage is worth a lot more to your effective magicka, and thus the power of your skills. Since you are using sorc as example, let’s use Liquid Lightning to illustrate; using the Mage with 1.33 multiplier gives an increase in damage of around 5.3% compared to the control, Apprentice with 1.25 multiplier gives an increase in damage of around 6.1% compared to the control. Unless pets do an overwhelming proportion of your overall damage, it would be unwise to pick the Mage.

    I agree i play my Magsorc with Julianos and Apprentice xD

    Arkadium_Floliroy

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    Tabatta

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    Latin said on October 12, 2017 :

    @Latin Thanks for pointing out this mistake, I guess the website I used was really outdated and I didn’t think about double crossing the values … The 1.4/1.3 comes from the fact that for me, Skills=1+Passives+Horn, where Passives includes bound aegis, inner light, mage’s guild, undaunted, racial passive, and is roughly 0.3, while Horn is the bonus from horn, so 0.1 with 100% uptime. The quantity I used for max_magicka was the one printed by the game in the attribute window, so already took into account Passives, that is max_magicka = base *(1+Passives), so base = max_magicka/(1+Passives). Therefore, the max magicka boosted by Skills (including horn) is base*Skills=base*(1+Passives+Horn)/(1+Passives) approx base*1.4/1.3. I think just multiplying it by 1.1 would be like considering the horn is multiplicative with the other passives, so that’s why I used this factor.
    Thanks a lot for your answer tho, I was suspecting people were just not specifying that they did it, but wasn’t sure :) !

    @Floliroy I found that, considering 10% of the damage done with pet, the mage (and then the thief) was actually better than the apprentice. I made the calculation with Necropotence bonuses tho, not sure if the results would still be valid for Julianos !

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    Latin

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    Thanks for your elaboration.

    Tabatta said on October 12, 2017 :

    I think just multiplying it by 1.1 would be like considering the horn is multiplicative with the other passives, so that’s why I used this factor.

    You have probably misinterpreted me.

    Latin said on October 12, 2017 :

    Would it not be simpler just to add 0.1

    What I meant was to add 0.1 to your skills modifier with 100% warhorn uptime, i.e. if your skills modifier pre-warhorn is 1.33, you’d just add 0.1 so the skills modifier becomes 1.43.

    For example, on Sorc, with Undaunted Mettle II using 5/1/1 (3*0.02), 2 skills for Magicka Controller (2*0.02), Gift of Magnus (0.1), Bound Aegis (0.08) and Inner Light (0.05), you get a total skill modifier of 1.33. Having 10% increase in max magicka from warhorn means adding 0.1 to the modifier for 1.43.

    Tabatta said on October 12, 2017 :

    The quantity I used for max_magicka was the one printed by the game in the attribute window, so already took into account Passives, that is max_magicka = base *(1+Passives), so base = max_magicka/(1+Passives). Therefore, the max magicka boosted by Skills (including horn) is base*Skills=base*(1+Passives+Horn)/(1+Passives) approx base*1.4/1.3.

    The displayed max magicka already accounts for warhorn buff, if it is active. There is no need to make a separate account for it. I am not sure what you are trying to determine when looking for “the max magicka boosted by skills”.

    If you are attempting to calculate the max magicka value before the skill modifier (which includes the warhorn 10% buff) is applied, couldn’t you just use the following:

    (level base + attribute + gear) * CPI + food + mage (if applicable) + necro 5p bonus (if applicable) = pre-skill modified max magicka

    I noticed that you are distinguishing Passives and Horn modifiers, but there is no real need to do so. They work the same way – additive with each other, and their sum is multiplicative with the pre-skill modified max magicka as determined from the relation above.

     

    I take that 1.4/1.3 is used to indicate the proportion of buffed magicka between having a warhorn buff and not having one, but I am unsure what it is indicative of.

    For instance, it doesn’t really provide a good approximation of the damage increase from skills, because the coefficients of magicka for skills vary. 1.4/1.3 is around 1.0769; with a pre-warhorn modifier of 1.33, having the 10% max magicka increase will lead to modifier of 1.43. In this case, Liquid Lightning will be doing only 1.0501 more damage, and Crystal Fragment doing 1.0508 more damage. In this example, my reference benchmark for the pre-skill modified magicka is 32927, everything else held constant.

     

    If I’m missing something, please don’t hesitate to point out.

    e pluribus unum

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    Tabatta

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    Latin said on October 12, 2017 :

    What I meant was to add 0.1 to your skills modifier with 100% warhorn uptime, i.e. if your skills modifier pre-warhorn is 1.33, you’d just add 0.1 so the skills modifier becomes 1.43.

    For example, on Sorc, with Undaunted Mettle II using 5/1/1 (3*0.02), 2 skills for Magicka Controller (2*0.02), Gift of Magnus (0.1), Bound Aegis (0.08) and Inner Light (0.05), you get a total skill modifier of 1.33. Having 10% increase in max magicka from warhorn means adding 0.1 to the modifier for 1.43.

    The displayed max magicka already accounts for warhorn buff, if it is active. There is no need to make a separate account for it. I am not sure what you are trying to determine when looking for “the max magicka boosted by skills”.

    I think we mean the same thing but maybe I didn’t explain myself very well, sorry. I used as base stats the one I have without warhorn, so basically stats that are already increased by passives, skills and all, but not by horn, so that’s why. Indeed, 1.4/1.3 should be really Skills/(Skills-0.1), it’s just that I was a bit lazy when I wrote this part in the script and didn’t correct it later on :). (To be clearer, I started writing the script when I was away from home and had no access to the game, the only thing that I had was a few Superstar screenshots that I took with different mundus and different jewels, without any horn on)

    As for the last part of your answer, I considered the damage boost for one specific skill so that the proportionality factor that is skill-dependent is washed away.

    • This reply was modified 1 week ago by Profile photo of Tabatta Tabatta.
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    InfiniteXavier

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    Latin said on October 6, 2017 :

    This is the case. So it is imperative for others not to use non-infused crusher if there is already an infused crusher user (tank) on a single target.

    Rather than changing their enchant, couldn’t they also just substitute poisons so they can have their crusher available for vMA, Parses, or general activities and then just use a poison for damage in a trial where a tank has crusher?

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    InfiniteXavier

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    Floliroy said on October 12, 2017 :

    I think the Mage can only be usefull on Sorc wich have a lot of Magicka Bonus

    MagBlades also get Max Magicka.

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    HelpFromAbove

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    @InfiniteXavier

    This is what my trial group does sometimes. Minor Breach poisons to overwrite the glyph. Helps with keeping a good spell pen debuf up-time. Though, only one or two really need to do this, and any extras can switch their enchantment for increased DPS.

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    InfiniteXavier

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    @Latin and @Tabatta

    So what was the conclusion after the adjustments to the formulas?

    If you are going for a max mag build, what Mundus should you take?

    If you are going for max spell damage build, what Mundus should take?

     

     

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    Latin

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    @InfiniteXavier

    There was no adjustment to the formula. The preceding discussion with @Tabatta was purely related to the approximation of modifiers in the comparison between 4p IA and MD, in the python script.

    The script itself considers given variables and implements known relationships in damage calculation. You could modify it to account for different mundus, buff uptime, stat benchmark and traits, to produce a similar graph.

     

    Not really sure about your questions. What is the salient difference in purpose between a max mag and a max spell damage build? What is the difference in percentage or absolute value (in effective magicka or another common denominator), before you can tell one from the other?

    e pluribus unum

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