Elfborn vs Spell Erosion

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hedna123b14_ESO
hedna123b14_ESO
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As a magicka templar I was wondering if others have done testing to determine the following:
1. In this new patch, while wielding a nirnhoned weapon what is the Elfborn to Spell Erosion ratio you should have. Or if you just need a specific amount of Erosion before putting points into elfborn.
2. Whether you can get better damage by Maxing out Elfborn and putting on a precise weapon instead.

Basically what is the magic number for the focus rating (going by Harven's stats) you should need before Maxing damage, or whether simply Maxing damage will outdo putting points in spell Erosion...
  • hedna123b14_ESO
    hedna123b14_ESO
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  • Asayre
    Asayre
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    I previous showed that

    Base damage = Tooltip * Atk_Cp * Def_Cp * (1 - Mit)

    where tooltip is the tooltip value for the skill, Atk_Cp is like Thaumathurge or Elemental Expert and Def_Cp is like Hardy and Elemental Defender and

    Mit = Defender_Resist * Penetration [Sharpened/Nirnhoned]/ 66000 - Attacker_Focus/66000 - 0.12*Spell Erosion

    If we just roll Atk_Cp*Def_Cp into tooltip to make things easier
    Base damage = Tooltip * (1- Mit" + 0.12*Spell Erosion) = Tooltip * (1-Mit") + 0.12*Tooltip*Spell Erosion
    I've used Mit" to indicate that I have taken out Spell Erosion to make it's impact clearer. Thus every 1% increase in the Spell Erosion tooltip results in Tooltip*0.0012 increase in Base Damage which is pretty much a nothing burger! Note that Penetration from using Nirnhoned does not come into play.

    Note that Attacker_Focus that I used is not the same as that given out by Harven's stats. For my calculations I use a base focus of 100 or 4984 if 5 Light amour pieces are equipped and you have 2 points in the Concentration passive. I am aware that putting 1 point in Spell Erosion massively alters the Focus rating given by Harven's stats but if the Focus provided by Harven's stats is used with the equation I provided for Base damage nothing seems to work out accurately.

    A bit of maths shows that, the extra damage from Spell Erosion is
    Damage_Spell Erosion = Tooltip*0.12*Spell Erosion * (1-Crit chance + Crit Chance * Crit multiplier)

    Elfborn works rather oddly because ZOS has decided that your crit multiplier should be rounded to 2 decimal places. What this means is that there will be critical points when putting points into Elfborn where there is no increase in the Crit multiplier and then a sudden increase. You can see it in the graph below.

    2klggj.png

    The black squares are data points and the blue line is a just a guide for the eye. This graph was based on my Sorcerer but something similar happens for my Templar and the jumps occur at the same location. There is a funky thing for my Templar where there is an 0.02 jump instead of an 0.01 jump but I suspect that this may be due to the Piercing Spear passive.

    Anyway assuming that you get in on this 'jump' points then the extra damage from Elfborn is
    Damage_Elfborn = 0.01*Crit Chance*Tooltip

    To help you put this into perspective, let's take a crit chance of 42% and a crit multiplier of 1.5. The increase in damage from Spell Erosion by increasing it by 1% is
    Damage_Spell Erosion = Tooltip*0.12*0.01*(1-0.42+0.42*1.5) = Tooltip * 0.001452

    Compared to a 'jump' point in Elfborn
    Damage_Elfborn = Tooltip*0.42*0.01 = Tooltip * 0.0042

    So a 'jump' point in Elfborn is better than Spell Erosion. A 'jump' point in Elfborn is equivalent to a 3% increase in Spell Erosion. Thus put points into Spell Erosion if the number of points required to reach a jump will result in at least a 3% increase in Spell Erosion. Let me give you a concrete example.

    Let us say you have 78 points in Elfborn and 0 in Spell Erosion. The next 'jump' is at 89 points in Elfborn that requires another 11 points. But 11 points in Spell Erosion would net you 5.3% since 5.3% is > 3% put those 11 points into Spell Erosion.

    There is a bit of interplay here since with 78 points in Elfborn your crit multipler would be higher than 1.5 thus the effectiveness of Spell Erosion is increased. But I was simplfying things a bit.

    To help with future decisions on this subject, I'll provide all the 'jump' points. They are:
    1, 5, 11, 17, 24, 31, 40, 49, 58, 68, 78 and 89
    There are no 'jump' points after 89.

    And that is the end of your first question
    Edited by Asayre on September 10, 2015 3:38AM
    Reference for any calculation I make Introduction to PvE Damage Calculation
  • Dravecailean
    Asayre wrote: »
    Insightfull stuff

    giphy.gif

    Thank you once again Asayre.
  • YeOldeGamer
    YeOldeGamer
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    Umm... My brain hurts now.
  • hedna123b14_ESO
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    That makes sense, now to figure out the formula for how much CP you need for precise to outperform Nirnhoned...
  • hedna123b14_ESO
    hedna123b14_ESO
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    Also @Asayre in your testing of scathing mage did you find the internal cooldown to be 5 seconds or more?
  • HungryHobo
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    Can I save threads? That is helpful information... *Removed stupid question... lol*
    Edited by HungryHobo on September 10, 2015 7:54PM
  • Kobaal
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  • Asayre
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    Also @Asayre in your testing of scathing mage did you find the internal cooldown to be 5 seconds or more?
    It seems that the internal cooldown is 6 seconds (the duration of the proc). So I could get it to proc almost immediately after the duration of the proc expires but I was unable to refresh the proc while it was up.

    Reference for any calculation I make Introduction to PvE Damage Calculation
  • Uncle_Voodoo
    Uncle_Voodoo
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    About all I can say about this is... you are not a very good carpenter! All of your steps are crooked! :D
  • Asayre
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    I already worked out how to determine when to use Nirnhoned or Precise but I was taking a break from the first question.
    To start off, I’ll begin again with the base damage formula

    Base damage = Tooltip * Atk_Cp * Def_Cp * (1 - Mit)
    where
    Mit = Defender_Resist * (1-Penetration)/ 66000 - Attacker_Focus/66000 - 0.12*Spell Erosion

    Mitigation can be rewritten to separate it into a base and penetration component

    Mit = Defender_Resist/66000 – Attacker_Focus/66000 – 0.12*Spell Erosion – Defender_Resist*Penetration/66000

    Mit = Mit_B – Mit_P

    Where Mit_B is the first 3 terms and Mit_P is the last term.

    The damage with Nirnhoned is then

    Damage = Tooltip*(1-Mit_B + Mit_P)*( 1-Crit chance + Crit Chance * Crit multiplier)
    Thus the damage increase from using Nirnhoned is

    Damage_Nirn = Tooltip*Mit_P*(1-Crit chance + Crit Chance * Crit multiplier)

    In comparison, the damage with Precise is

    Damage = Tooltip*(1-Mit_B)*( 1-(Crit chance +Precise)+ (Crit Chance+Precise) * Crit multiplier)

    The damage increase using Precise is

    Damage_Precise = Tooltip*(1-Mit_B)*Precise*(Crit multiplier – 1)

    To decide which to use, we need to consider Damage_Nirn – Damage_Precise

    Damage_Nirn – Damage_Precise = Tooltip* (Mit_P * (1-Crit chance + Crit Chance * Crit multiplier) – Precise*(1-Mit_B)*(Crit multiplier – 1)

    As you can see, the tooltip value is not important in the evaluation process. Now there are four variables, namely, crit chance, crit multiplier and Mit_P and Mit_B. To simplify it a bit I’ll assume that the attacker has no penetration from any other sources (i.e. Attacker_Focus is 0 and has no champion points in Elfborn. Thus Mit_P and Mit_B can be computer from simply knowing Defender_Resist. Unfortunately this still leaves us with 3 variable which makes creating a graph rather difficult. I’ll provide some slices of Crit chance vs Crit multipler for different armour values. In the following set of graphs, blue means Precise is better and red means nirnhoned is better.

    28bqnwi.png

    2rqf2oj.png

    347jxuf.png

    icv6hc.png

    Below ~10000 resistance, precise is always better and above ~14000 resistance nirnhoned is always superior. Also having a high crit chance favours nirnhoned while having a high crit damage modifier favours precise. Recall that I have for simplication ignored penetration for Attacker Focus, Spell Erosion and Major Breach. Take that into account when fighting in Tamriel.

    I have little understanding of the armour of bosses and it is one of my plans one day to get a group to help me shoot bosses in order to determine their resistance.

    And that is the end of your second question.
    Edited by Asayre on September 11, 2015 2:21AM
    Reference for any calculation I make Introduction to PvE Damage Calculation
  • Cuyler
    Cuyler
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    @Asayre you my fiend, are a gentleman and a scholar
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  • hedna123b14_ESO
    hedna123b14_ESO
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    Asayre wrote: »
    It seems that the internal cooldown is 6 seconds (the duration of the proc). So I could get it to proc almost immediately after the duration of the proc expires but I was unable to refresh the proc while it was up.
    Very helpful thanks!
    Asayre wrote: »
    I already worked out how to determine when to use Nirnhoned or Precise but I was taking a break from the first question.
    To start off, I’ll begin again with the base damage formula

    Base damage = Tooltip * Atk_Cp * Def_Cp * (1 - Mit)
    where
    Mit = Defender_Resist * (1-Penetration)/ 66000 - Attacker_Focus/66000 - 0.12*Spell Erosion

    Mitigation can be rewritten to separate it into a base and penetration component

    Mit = Defender_Resist/66000 – Attacker_Focus/66000 – 0.12*Spell Erosion – Defender_Resist*Penetration/66000

    Mit = Mit_B – Mit_P

    Where Mit_B is the first 3 terms and Mit_P is the last term.

    The damage with Nirnhoned is then

    Damage = Tooltip*(1-Mit_B + Mit_P)*( 1-Crit chance + Crit Chance * Crit multiplier)
    Thus the damage increase from using Nirnhoned is

    Damage_Nirn = Tooltip*Mit_P*(1-Crit chance + Crit Chance * Crit multiplier)

    In comparison, the damage with Precise is

    Damage = Tooltip*(1-Mit_B)*( 1-(Crit chance +Precise)+ (Crit Chance+Precise) * Crit multiplier)

    The damage increase using Precise is

    Damage_Precise = Tooltip*(1-Mit_B)*Precise*(Crit multiplier – 1)

    To decide which to use, we need to consider Damage_Nirn – Damage_Precise

    Damage_Nirn – Damage_Precise = Tooltip* (Mit_P * (1-Crit chance + Crit Chance * Crit multiplier) – Precise*(1-Mit_B)*(Crit multiplier – 1)

    As you can see, the tooltip value is not important in the evaluation process. Now there are four variables, namely, crit chance, crit multiplier and Mit_P and Mit_B. To simplify it a bit I’ll assume that the attacker has no penetration from any other sources (i.e. Attacker_Focus is 0 and has no champion points in Elfborn. Thus Mit_P and Mit_B can be computer from simply knowing Defender_Resist. Unfortunately this still leaves us with 3 variable which makes creating a graph rather difficult. I’ll provide some slices of Crit chance vs Crit multipler for different armour values.

    28bqnwi.png

    2rqf2oj.png

    347jxuf.png

    icv6hc.png

    Below ~10000 resistance, precise is always better and above ~14000 resistance nirnhoned is always superior. Also having a high crit chance favours nirnhoned while having a high crit damage modifier favours precise. Recall that I have for simplication ignored penetration for Attacker Focus, Spell Erosion and Major Breach. Take that into account when fighting in Tamriel.

    I have little understanding of the armour of bosses and it is one of my plans one day to get a group to help me shoot bosses in order to determine their resistance.

    And that is the end of your second question.

    This is helpful, thanks

  • Woman
    Woman
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    @Asayre Thank you so much for doing all the testing for us. It's really appreciated.
    Edited by Woman on September 11, 2015 2:46AM
  • Personofsecrets
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    Asayre wrote: »
    I already worked out how to determine when to use Nirnhoned or Precise but I was taking a break from the first question.
    To start off, I’ll begin again with the base damage formula

    Base damage = Tooltip * Atk_Cp * Def_Cp * (1 - Mit)
    where
    Mit = Defender_Resist * (1-Penetration)/ 66000 - Attacker_Focus/66000 - 0.12*Spell Erosion

    Mitigation can be rewritten to separate it into a base and penetration component

    Mit = Defender_Resist/66000 – Attacker_Focus/66000 – 0.12*Spell Erosion – Defender_Resist*Penetration/66000

    Mit = Mit_B – Mit_P

    Where Mit_B is the first 3 terms and Mit_P is the last term.

    The damage with Nirnhoned is then

    Damage = Tooltip*(1-Mit_B + Mit_P)*( 1-Crit chance + Crit Chance * Crit multiplier)
    Thus the damage increase from using Nirnhoned is

    Damage_Nirn = Tooltip*Mit_P*(1-Crit chance + Crit Chance * Crit multiplier)

    In comparison, the damage with Precise is

    Damage = Tooltip*(1-Mit_B)*( 1-(Crit chance +Precise)+ (Crit Chance+Precise) * Crit multiplier)

    The damage increase using Precise is

    Damage_Precise = Tooltip*(1-Mit_B)*Precise*(Crit multiplier – 1)

    To decide which to use, we need to consider Damage_Nirn – Damage_Precise

    Damage_Nirn – Damage_Precise = Tooltip* (Mit_P * (1-Crit chance + Crit Chance * Crit multiplier) – Precise*(1-Mit_B)*(Crit multiplier – 1)

    As you can see, the tooltip value is not important in the evaluation process. Now there are four variables, namely, crit chance, crit multiplier and Mit_P and Mit_B. To simplify it a bit I’ll assume that the attacker has no penetration from any other sources (i.e. Attacker_Focus is 0 and has no champion points in Elfborn. Thus Mit_P and Mit_B can be computer from simply knowing Defender_Resist. Unfortunately this still leaves us with 3 variable which makes creating a graph rather difficult. I’ll provide some slices of Crit chance vs Crit multipler for different armour values. In the following set of graphs, blue means Precise is better and red means nirnhoned is better.

    28bqnwi.png

    2rqf2oj.png

    347jxuf.png

    icv6hc.png

    Below ~10000 resistance, precise is always better and above ~14000 resistance nirnhoned is always superior. Also having a high crit chance favours nirnhoned while having a high crit damage modifier favours precise. Recall that I have for simplication ignored penetration for Attacker Focus, Spell Erosion and Major Breach. Take that into account when fighting in Tamriel.

    I have little understanding of the armour of bosses and it is one of my plans one day to get a group to help me shoot bosses in order to determine their resistance.

    And that is the end of your second question.

    @Asayre ,

    Are you aware of DOTs (such as eruption) not being increased in damage by nirnhoned? That was an issue for me last patch and I wonder if it still persists.
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  • kaithuzar
    kaithuzar
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    Can a mod author please take these formulas and make a stat calculator out of it where we just input our current numbers & print out what we should do? lol
    (or print to screen efficient build or not efficient)
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  • Asayre
    Asayre
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    @Asayre ,

    Are you aware of DOTs (such as eruption) not being increased in damage by nirnhoned? That was an issue for me last patch and I wonder if it still persists.

    I wasn't aware of such a problem. I tested it against the Mammoths in The Rift and I didn't find any problems. I was using Puncturing Sweep and the damage is within my expectation.

    @kaithuzar, I believe @Soulac has done that for you =). You can find his stat calc at forums.elderscrollsonline.com/en/discussion/169938/stat-calculator-version-1-6-4
    Reference for any calculation I make Introduction to PvE Damage Calculation
  • Personofsecrets
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    Asayre wrote: »

    I wasn't aware of such a problem. I tested it against the Mammoths in The Rift and I didn't find any problems. I was using Puncturing Sweep and the damage is within my expectation.

    @kaithuzar, I believe @Soulac has done that for you =). You can find his stat calc at forums.elderscrollsonline.com/en/discussion/169938/stat-calculator-version-1-6-4

    My post #7 here shows my findings from a couple of months ago.

    I will have to see if this is still happening with the skill I tested.
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  • Shader_Shibes
    Shader_Shibes
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  • Carde
    Carde
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    look at the juicy brain on this science nerd ya'll
    Member of the Psijic Order PTS Group
  • Rune_Relic
    Rune_Relic
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    So that 5280 major ward buff is exactly 8% mitigation then.
    Thanks for the confirmation.

    I have seen 32500 @ 50% or similar mitigation and left me scratching my head.
    Edited by Rune_Relic on September 11, 2015 9:41AM
    Anything that can be exploited will be exploited
  • Leandor
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    Asayre wrote: »
    Below ~10000 resistance, precise is always better and above ~14000 resistance nirnhoned is always superior. Also having a high crit chance favours nirnhoned while having a high crit damage modifier favours precise. Recall that I have for simplication ignored penetration for Attacker Focus, Spell Erosion and Major Breach. Take that into account when fighting in Tamriel.
    Let me start by saying that I am quite impressed by your work, and then continue by asking:

    Doesn't that mean that considering a V16 opponent and the fact that 7 LA do provide more than 14k spell resistance (if the passive is included), and 7 MA close to 14k spell resistance, it is always better to use nirnhoned over precise for magicka damage?

    The next interesting question is whether the additional 2% penetration that sharpened provides (iirc) are worth the lost spell resistance from the nirnhoned weapon.
  • Xantaria
    Xantaria
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    In this precise / Nirnhoned calculation there is one thing that needs to be taken into account when looking at it from the PvE side and that is Agressive Warhorn being up a lot.

    Awesome work there @Asayre Keep it up man!
    Edited by Xantaria on September 11, 2015 11:50AM
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  • Tankqull
    Tankqull
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    Asayre wrote: »
    ...
    Anyway assuming that you get in on this 'jump' points then the extra damage from Elfborn is
    Damage_Elfborn = 0.01*Crit Chance*Tooltip

    To help you put this into perspective, let's take a crit chance of 42% and a crit multiplier of 1.5. The increase in damage from Spell Erosion by increasing it by 1% is
    Damage_Spell Erosion = Tooltip*0.12*0.01*(1-0.42+0.42*1.5) = Tooltip * 0.001452

    Compared to a 'jump' point in Elfborn
    Damage_Elfborn = Tooltip*0.42*0.01 = Tooltip * 0.0042

    So a 'jump' point in Elfborn is better than Spell Erosion. A 'jump' point in Elfborn is equivalent to a 3% increase in Spell Erosion. Thus put points into Spell Erosion if the number of points required to reach a jump will result in at least a 3% increase in Spell Erosion. Let me give you a concrete example.

    Let us say you have 78 points in Elfborn and 0 in Spell Erosion. The next 'jump' is at 89 points in Elfborn that requires another 11 points. But 11 points in Spell Erosion would net you 5.3% since 5.3% is > 3% put those 11 points into Spell Erosion.

    There is a bit of interplay here since with 78 points in Elfborn your crit multipler would be higher than 1.5 thus the effectiveness of Spell Erosion is increased. But I was simplfying things a bit.

    To help with future decisions on this subject, I'll provide all the 'jump' points. They are:
    1, 5, 11, 17, 24, 31, 40, 49, 58, 68, 78 and 89
    There are no 'jump' points after 89.

    And that is the end of your first question

    do you have aswell the jumppoints in spellerosion providing 3% increasement? as its hard to plan your distribution with out it
    using your example going from 78 to 89 but with spell erosion allready within the 40s the 11CP to be spend do not provide 3% more spellerosion, increasing the worthyness of elfborn again...


    spelling and grammar errors are free to be abused

    Sallington wrote: »
    Anything useful that players are wanting added into the game all fall under the category of "Yer ruinin my 'mersion!"


  • Asayre
    Asayre
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    2klggj.png
    About all I can say about this is... you are not a very good carpenter! All of your steps are crooked! :D

    Blame ZOS, they made those steps! I'm just outlining it for you.

    @Shader_Shibes, not a wizard just a Sorcerer and a Templar.
    Rune_Relic wrote: »
    So that 5280 major ward buff is exactly 8% mitigation then.
    Thanks for the confirmation.

    I have seen 32500 @ 50% or similar mitigation and left me scratching my head.

    The 32500 number is from 1.6 where v14 was apparently level 63. I never tested that equation but that is the origin.
    Leandor wrote: »
    do you have aswell the jumppoints in spellerosion providing 3% increasement? as its hard to plan your distribution with out it
    using your example going from 78 to 89 but with spell erosion allready within the 40s the 11CP to be spend do not provide 3% more spellerosion, increasing the worthyness of elfborn again...

    Spell Erosion is linear with no 'jump' points. Going back to my modified example. With 78 points in Elfborn and 40 points in Spell Erosion. You need 11 points to get to the next 'jump' in Elfborn. Raising Spell Erosion from 40 points (13.2%) to 51 points (15.6%) is only an increase of 2.4%. Thus you should put your 11 points into Elfborn and get that 'jump'.

    If you go from 19 points to 30 points you get exactly 3% so you probably never want spell erosion above 19 until you get Elfborn to 89.
    Edited by Asayre on September 11, 2015 1:37PM
    Reference for any calculation I make Introduction to PvE Damage Calculation
  • Tankqull
    Tankqull
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    thx - thats exactly what i wanted to know :D
    spelling and grammar errors are free to be abused

    Sallington wrote: »
    Anything useful that players are wanting added into the game all fall under the category of "Yer ruinin my 'mersion!"


  • YeOldeGamer
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    *brain explodes*
  • monkeymystic
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    Thanks a lot to asayre!

    Edited by monkeymystic on September 11, 2015 2:21PM
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  • Sugram22
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    I recommend 1 point elfborn or 0 to it, 100 ele expert 66 or 67 to erosion, u ask why? cause as mage/sorc u get bit over 40% crit rate (51-52 with some CP perks that activate in certain conditions), no1 can have 100%, so do u want to hit hard always or just sometimes? i want that my awry hit is hard so i wont put much to elfborn, maybe not even 1 point, also with erosion ur spell damage increases, so higher spell damage= Higher crit damage, so in the end u get same crit damage if not better then when u put point to elfborn
    Edited by Sugram22 on February 19, 2016 6:15PM
This discussion has been closed.