Replies: 54

Following a few test on the PTS 2.1.2, I would like to share some formulas for a magicka based sorcerer which can be extended to other magicka based classes. Using these formulas, I will suggest desirable equipment in the PTS to increase damage.

All testing was done on the PTS 2.1.2 a few days before the 22nd August 2015. The majority was performed in Cyrodiil with the aid of a second account. Note that all tooltip damage is halved in Cyrodiil because of Battle Spirit. This occurs before any other calculations. Damage was recorded with FTC. My bars are set up similar to that in the thread [2.0.9] Endgame PVE Sorcerer DPS by Dymence.

Stat Pool

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The cumulative percentage increase of pool, %CP, is approximately

Cumulative percentage increase of pool=Number of champion points in 1 colour^0.56

Stat Pool=((Base+AP+Gear)*%CP)+Food+Mundus(Divines))*Skills

AP is the number of points spent in Health, Magicka or Stamina multiplied by 122 for health or 111 for Magicka and Stamina. For Magicka, the following skills have been tested to be additive, Bound Aegis, Inner light, Gift of Magnus, Magicka Controller, Undaunted Mettle.

Base Pool at V16 is 8744 for Health and 7958 for Magicka/Stamina. This value is the same for a V14 on Live.

This formula is the same on Live. Here is an example calculation for my Magicka pool on my V14 Breton Sorcerer on Live. My gear gives me 7410 Magicka. This includes enchantments and set bonuses. I have 62 points in Magicka giving me 6882 Attribute Points. I’m using Lillandril Summer Sausages which increase Magicka by 4635. I have 70 points in the Mage giving me a %CP of 11%. I’m using the Mage mundus stone which provides 1280 Magicka (20 Magicka per level). I have 2 Gold and 2 Purple divines making my divines bonus 1.28. I have Bound Aegis and Inner light activated and I have the passives Gift of Magnus, Magicka Controller and Undaunted Mettle. I have 2 Mages Guild abilities slotted thus

Magicka Pool = ((7958[Base] + 6882[Attribute] + 7410[Gear]) * 1.11 [%CP] ) + 4635[Food] + 1280[Mage mundus] * 1.28 [Divines] ) * ( 1 + 0.08[Bound Aegis] + 0.05 [Inner light] + 0.1 [Gift of Magnus] + 0.04 [Magicka Controller] + 0.06 [Undaunted Mettle]) = 41191

My actual Magicka pool is 41190.

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Spell Damage

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The tooltip spell damage is calculated as follows

Spell damage=(Gear+Apprentice(Divines?)+Molag Kena [2P]+Scathing Mage[5P]*(Surge+Expert Mage+Offensive scroll bonus)

The Apprentice mundus provides 167 spell damage at V16.

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Spell tooltip value

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By testing some spells it seems that the spell tooltip value is approximately

Spell tooltip value = a*(Magicka + b * Spell damage)

Where a varies for different spells and b is roughly 10.5 for a number of spells

Using the equation for Stat Pool and Spell Damage, we can decide on using the Mage or Apprentice Mundus.

The Apprentice Mundus provides 167 Spell Damage. With 2 Mage abilities slotted (Bound Aegis and Crystal Frags) and Surge casted (Surge is on my second bar), this gives 207 Spell damage (167*1.24) which in turn is equivalent to 2174 Magicka.

The Mage Mundus provides 1320 Magicka. Assuming a total bonus of 1.33 from skills and passive, this leads to a Magicka bonus of 1755.

Thus the Apprentice Mundus is preferred.

Since V16 sets offer either 129 Spell Damage or 967 Magicka, following a similar path we end up with conclusion that Spell Damage stacking is still favourable to Magicka stacking

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Spell resistance and penetration

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Your spell resistance as shown in the tooltip can be calculated as follows

Spell resistance=(Gear+Resolve[Heavy Armour Passive])*Spell Resist CP+Spell Resist[Breton Passive]+Spell Warding[Light Armour Passive]+Armour Master [5P]
The amount of mitigation provided by Spell Resistance is as follows

Percentage Mitigation=Spellresistance/(TargetLvl*10)*(Penetrating Magic[Destructive Staff Passive]+?Sharpened trait)-AttackerFocus/(AttackedLvl*10)-c*Spell Erosion CP

I was unable to test whether Penetrating Magic and Sharpened were additive or multiplicative because I did not find a Sharpened staff. I tested with a Sharpened dagger and greatsword. The base focus is 100 and is increased to 4984 with the Concentration passive (Light Armour Passive). The coefficient c appears to be 0.12 and Spell Erosion is the % taken from the tooltip. The effect of Major Breach from Weakness to Elements and its morphs and presumably Pierce Armour is to reduce Spell Resistance by 5280. The passive Shield Expert increases the tooltip value of your shield.

The focus value provided by Harven’s Extended Stats did not prove correct when even one point was put into Spell Erosion.

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Spell cost reduction

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Spell cost=(Base*(1-Magician)-Flat CR)*(1+0.0025*(Lvl-1)-Skill_CR+Molag Kena[2P])

Again level is 66 for a V16. For Skill_CR, I have tested Evocation (Light Armour passive), Magicka mastery (Breton passive), Unholy knowledge (Sorcerer passive, Dark Magic) and Mage adept (Mages Guild passive, only applies to Mages Guild ability). The base value is the value when naked and without champion points divided by (1+0.0025*(Lvl-1)).

As an example, consider Funnel Health (NB class ability). The cost at V16 when naked and with no champion points is 1233. The Base value however should be 1060 = 1233/1.1625. For our example, we shall assume a Breton with 3 points in Magicka Mastery (3% Cost reduction) with 5 pieces of light armour equipped for 15% cost reduction via the Evocation passive and 46 points in Magician (10%) and a flat cost reduction of 558. The spell cost is then

Spell cost = (Base*(1-Magician)-Flat CR)*(1+0.0025*(Lvl-1)-Skills_CR)
Spell cost = (1060*(1-0.1)-558)*(1.1625-0.03-0.15)
Spell cost = 389

The tooltip value is 391.

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Magicka recovery

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Magicka recovery=((Base+Gear+Atronach Mundus*Divines)*Arcanist*(Magicka Aid[Support Passive]+Recover[Light Armour Passive])+Drink)*(Spellcharge[Altmer Passive]+Major Intellect+Magicka Controller)

where the Base Magicka recovery is 514 at V16. I was unable to test the Magicka recovery provided by Vampirism as it is unlevelled in the PTS.

In order to determine the balance between Arcanist and Magician, you must first determine your average Magicka usage per second and subtract your Magicka recovery. This can be accomplished by fighting a long boss and looking at your combat log to determine the number of spells casted and the cost of each. Naturally, it is desirable to obtain a positive value (net Magicka drain per second) that allows your Magicka to completely empty in approximately 90 seconds (the length of the majority of boss fights). Additional Magicka recovery or Spell cost reduction is then superfluous. Note that in longer boss fights your healers will most likely support you with either Elemental Drain or Siphon Spirit thereby alleviating any Magicka problems.

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Critical damage Modifier

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The base critical damage modifier is 0.5 and is raised by the Shadow mundus (+12% Critical damage modifier) and Elfborn which stack additively. This formula may require correction.

Critical damage=1.5+Shadow+0.5*Elfborn

Critical damage modifier is rounded to decimal places.

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Elemental Expert and Thaumathurge

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Elemental Expert and Thaumaturge are multiplied to the tooltip value. Elemental Expert and Elemental Talent (Altmer passive) stack multiplicatively. Hardy, Elemental Defender and thick skinned are applied after mitigation. Thick Skinned stacks additively with Elemental Defender and Hardy

Here is an example in Cyrodiil. I am using a V16 Altmer sorcerer and casting force pulse on a target with 21511 spell resistance and 40 points in Elemental Defender(13.2%). The tooltip value of force pulse is 2058. I have 75 points in Elemental Expert (20.4%) and 25 points in Spell Erosion (9.5%). I also have 3 points in Elemental Talent and 2 points in penetrating magic. My focus is 4984 (2 points in Concentration)

Damage=2058/2[Battle Spirit] *1.204[Elemental Expert]*1.04[Elemental Talent]*(1-%Mitigation)*(1-0.132[Elemental Defender])=887

where

%Mitigation=21511/660*0.9[Penetrating Magic]-4984/660-0.12*9.5

The actual damage is 890.

These equations can be used to decide on how to spread out points in the Warrior and Mage constellations.

[IMG]http://i62.tinypic.com/16hk8d5.png[/IMG]

Above, I have drawn a surface plot of the damage as a function of Elemental Expert and Spell Erosion. The damage points are only calculated for valid percentages. If you are focused on maximizing elemental or magical damage, it is always better to put points into Thaumaturge or Elemental Expert instead of Spell Erosion irrespective if you are playing an Altmer. If you are intending to optimise both your elemental and magic damage then things get trickier because you need to first determine the ratio of elemental to magic damage and optimise between the two. Note that 1 point into Elemental Expert and Thaumaturge is at worst equal to 2 points into Spell Erosion. Thus never put points into Spell Erosion. As a rough estimate, the damage contribution of Crystal Fragments and occasionally Velocious Curse is around 15-20% thus the majority of points should be placed in Elemental Expert.

It is reasonably clear that Hardy and Elemental Defender are much more efficient than points in Spell Resist. I cannot think of many strong DOT spells so would not recommend Thick Skinned. In PVE, Bastion is superfluous though it is favoured in PVP but I did not test the impact of Battle Spirit on Bastion.

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Elfborn vs Spell Erosion

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

where tooltip is the tooltip value for the skill, Atk_Cp islike 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 times 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.

[IMG]http://i61.tinypic.com/2klggj.png[/IMG]

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% 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.

Note that 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.

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Reinforced and Impenetrable

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I know that this is a bit of an unusual topic give the topic title and the focus on PVE but a guild mate asked me this and I thought I would lump all my calculations together.

To begin an understanding of how Impenetrable works is needed. A gold impenetrable piece claims to ‘Increase resistance to Critical hits by 250’. This does not seem very informative. My testing suggests that a gold impenetrable piece reduces the critical damage multiplier by approximately 3.5%. Thus without any pieces of impenetrable the base critical damage multiplier is 1.5 but with 2 pieces of impenetrable this is reduced to 1.43. As an aside this stacks additively with Resilient. With this information the analysis can continue.

Let the base damage without taking into account critical damage be, D. From my previous testing

D = Tooltip * Battle Spirit * Attacker CP * Defender CP*(1-Mitigation)

Attacker CP here includes Thaumathurge or Elemental Expert and Defender CP refers to Elemental Defender. The first four terms can be combined together into a single parameter, T, for this analysis. Mitigation is given by the following formula

Mitigation = (Base Armour + Reinforced Armour)*Penetration/66000 – Focus/66000

Mitigation = Base Armour*Penetration/66000 – Focus/66000 + Reinforced Armour*Penetration/66000

Mitigation = Base Mitigation + Reinforced mitigation

where I am assuming that both the attacker and target are V16. I’ve explicitly neglected additional penetration from Spell Erosion and Piercing.

Then

D = T * (1-Base Mitigation + Reinforced Mitigation)

Now let us consider the damage done while taking in account critical damage, D1.

Reinforced

D_reinforced = (1-C)*D + C*M*D

where C is the Critical Chance and M is the critical damage multiplier

D_reinforced = D (1 – C + C*M )

D_reinforced = T ( 1 – Base_mitigation – Reinforced_mitigation ) ( 1 – C + C*M )

Impenetrable

D_impenetrable = ( 1 – C ) * D + C * ( M – I ) * D

where I is the reduction of the critical damage multiplier.

D_ impenetrable = D ( 1 – C + C * ( M – I ) )

D_impenetrable  = T ( 1 – Base_mitigation) ( 1 – C + C*M – C*I )

Reinforced – Impenetrable

If (Reinforced – Impenetrable) is positive this means that Impenetrable is favoured. The converse is true.

Reinforced – Impenetrable = T ( C*I*( 1 – Base_mitigation ) – Reinforced_mitigation ( 1 – C + C*M) )

From this, the following observations can be made

• Impenetrable is more effective at lower base mitigation (i.e. light armour wearers benefit more)
• A higher critical damage multiplier results in benefits only for reinforced

I’ll calculate (Reinforced – Impenetrable) for a range of Reinforced Armour and Critical Chance. To put into perspective the range of Reinforced Armour. The reinforced traits gives 16% increased armour for a legendary item. The lowest armour piece at V14 is a light armour sash with a base armour of 511. Thus for this particular item, reinforcing it would increase Reinforced Armour by about 82.

Using a critical damage multiplier of 1.5 and an extra reinforced mitigation of 100/66000 the following is calculated

[IMG]http://i59.tinypic.com/odyiv.png[/IMG]

This shows that impenetrable is always preferred when comparing between 250 increased critical damage resistance and 100 bonus armour from reinforced.

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Infused and Divine

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It is commonly know that Infused should be used on large pieces (i.e. Head, Chest, Legs and Shield) and divines on small pieces (Shoulders, Waist, Hands and Feet). This is based on the assumption that the Mage or Apprentice mundus is being utilised. However, is this still true with the increasing use of the Thief and Shadow mundus? In this section, I’ll show what conditions are required to favour infused or divines when using the Thief or Shadow mundus.

The amount of Magicka gained from using infused on a legendary large piece, Inf, is

Magicka from Infused on large legendary piece = 0.2*868*%CP*Skills

The base and average damage when using

Base damage_Inf = a*(Mag+Inf+b*SD)*(1-Mit)

Damage_Inf = a*(Mag+Inf+b*SD)*(1-C+C*M)*(1-Mit)

Damage_Inf = a*(Mag+b*SD)*(1-C+C*M)*(1-Mit) + a*Inf*(1-C+C*M)*(1-Mit)

In comparison, the base and average damage when using a legendary divines large piece along with the Thief mundus is

Base damage_Div = a*(Mag+b*SD)*(1-Mit)

Damage_Div = a*(Mag+b*SD)*(1-C-T*0.075+C*M+T*M*0.075)*(1-Mit)

Damage_Div = a*(Mag+b*SD)*(1-C+C*M)*(1-Mit) + a*(Mag+b*SD)*T*0.075*(M-1)*(1-Mit)

Then

Damage_Inf – Damage_Div = a*(1-Mit)*[Inf*(1-C+C*M) – (Mag+b*SD)*T*0.075*(M-1)]

As an example, let us consider a Sorcerer with 70 points in the Mage constellations (%CP=1.11) with a critical chance, C, of 0.54 and a critical multiplier, M, of 1.51. We’ll also use a Magicka pool, Mag, of 40000 and let SD be 2000. Also, the sorcerer in this example will have skills which boost Magicka by 33%. In which case,

Inf = 0.2*868*1.11*1.33 = 256

And

Damage_Inf – Damage_Div = 256*(1-0.54+0.54*1.51) – (40000+10.5*2000)*0.118*0.075*(1.51-1)

Damage_Inf – Damage_Div = 326 – 275 = 51

Note that I’ve ignored a*(1-Mit) since it is always positive.

So in this example, Infused is still preferred on large pieces. Since 0.54 is the lower end of critical chance when the Thief mundus is used it would seem that infused is always preferred on large pieces when the Thief is used.

The base and average damage when using a legendary divines large piece along with the Shadow mundus is

Base damage_Div = a*(Mag+b*SD)*(1-Mit)

Damage_Div = a*(Mag+b*SD)*(1-C+C*M+C*S*0.075)*(1-Mit)

Damage_Div = a*(Mag+b*SD)*(1-C+C*M)*(1-Mit) + a*(Mag+b*SD)*C*S*0.075*(1-Mit)

Then

Damage_Inf – Damage_Div = a*(1-Mit)*[Inf*(1-C+C*M) – (Mag+b*SD)*C*S*0.075]

Using the same numbers from the previous example, we obtain

Damage_Inf – Damage_Div = 256*(1-0.42+0.42*1.63) – (40000+10.5*2000)*0.42*0.12*0.075

Damage_Inf – Damage_Div = 323 – 230 = 93

Again Infused is preferred on large pieces.

Conclusion: Infused on large pieces still seems favourable for most cases. This might be different with the Scathing Mage set though.

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Precise or Nirnhoned

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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.
[IMG]http://i57.tinypic.com/28bqnwi.png[/IMG]

[IMG]http://i60.tinypic.com/2rqf2oj.png[/IMG]

[IMG]http://i62.tinypic.com/347jxuf.png[/IMG]

[IMG]http://i62.tinypic.com/icv6hc.png[/IMG]

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.

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2H and Dual Wield

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A 2H sword with 2 points in the Heavy Weapons passive results in 5% increased damage reflected in the spell tooltip.

Dual wielding swords with 2 points in blade and blunt leads to a 5% increase in the spell damage component for the swords.

For example, using two swords with a tooltip value of damage of 442 each results in 530 Spell Damage (442*1.2) on the Character sheet. But with 2 points in blade and blunt this is increased to 556 Spell Damage (442*1.2*1.05).

While 2H Greatsword offers the greatest increase to Spell Damage the extra set bonuses possible with dual wielding must be considered. This consideration can be made as follows

DW Tooltip=a (M+10.5*SD_DW)
2H Tooltip=1.05*a (M+10.5*SD_2H)

where

SD_DW=SD_gear+(DW_dmg*1.2*1.05+129)*Boost
SD_2H=SD_gear+2H_dmg*Boost

and Boost=Surge+Expert Mage

Using arithmagic

2H Tooltip-DW Tooltip=0.05aM+0.525a*SD_gear+11.025a*Boost(2H_dmg-(DW_dmg*1.2+129/1.05)

Note that the value of a is positive and can be ignored in determining whether 2H Tooltip – DW Tooltip is positive or negative

Giving some exemplary values for legendary equipment at V16, M ~ 40000, SD_Gear ~ 1300, 2H_dmg = 1571, DW_dmg = 1335, Boost = 1.3 shows that 2H provides superior tooltip values.

This judgement depends on the variables put into the equation. If we keep the same 2H_dmg, DW_dmg and Boost then we can obtain the figure below which suggest that dual wielding outperforms 2H at lower magicka values (magenta area)

[IMG]http://i62.tinypic.com/n3nujl.png[/IMG]

If you didn’t understand that then you can do the following

• Unequip your weapon and boost yourself appropriately with food and Major Sorcery buff
• Open your character sheet and record your Magicka and Spell Damage
• Calculate the following
  0.05*Magicka + 0.525*Spell damage
• If it is higher than 2035 go for a V16 Legendary Greatsword
  If not, dual wield V16 swords

If you want an even simpler threshold, here it is

Use a 2H greatsword (and put 2 points into Heavy Weapons) if you have more than 40,000 Magicka.

Final note: This only applied to damaging abilities and does not work for healing abilities with the exception of puncturing sweep since the heal is based on damage done.

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Mundus Stone: Apprentice, Shadow and Thief

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The base damage formula is
Base damage = a*(Mag+b*S)(1-Mit)*Attacker_CP * Defender_CP
where a and b are coefficients with b~10.5, S is your spell damage and Mit is the mitigation. We can roll the Attacker_CP and Defender_CP into the coefficient a without any worries for the analysis. The mitigation is also not important but I’ll keep it here for the moment to show you that it can evetually be neglected

The base damage when using the Apprentice stone is
Base damage_Apprentice = a*(Mag+b(S0+S1))(1-Mit)
Here I have separated your spell damage component into spell damage from Apprentice stone and associated buffs, S1, and spell damage from everything else, S0

The average damage with the Apprentice stone is
Damage_Apprentice = (1-C)*Base damage_Apprentice + C*M*Base damage_Apprentice
where C and M are your critical chance and critical damage modifier, respectively. With some arithmetic, we obtained
Damage_Apprentice = a*(Mag+b*S0)(1-Mit)(1-C+C*M) + a*b*S1*(1-Mit)*(1-C+C*M)

The base damage when using the Shadow stone is simply
Base Damage_Shadow = A*(Mag+b*S0)*(1-Mit)
From this, we can obtain the average damage
Damage_Shadow = (1-C)*Base damage_Shadow + C*(M+S)*Base damage_Shadow
where I have used S for the Shadow stone. Again some maths leads to
Damage_Shadow = a*(Mag+b*S0)(1-Mit)(1-C+C*M) + a*(Mag+b*S0)(1-Mit)*C*S

In order to figure out when the Apprentice mundus is preferred over the Shadow mundus, I shall just subtract Damage_Shadow from Damage_Apprentice

Damage_Apprentice – Damage_Shadow = a*(1-Mit)* [ b*S1*(1-C+C*M) – (Mag+b*S0)*C*S]
a and (1-Mit) are always positive so you simply need to evaluate the second term. I’ll put in some typical values for a Sorc to show you an example

The Apprentice confers 167 Spell damage. S1 includes all Spell damage buffs as well so as a Sorcerer I typically run a 26% buff due to Expert Mage and Surge. Thus S1 = 167*1.26=210. We’ll stick with a b value of 10.5. My crit chance, C, is 0.42 and my critical damage modifier, M, is 1.51 (I have 1 point in Elfborn). My Magicka is about 40k and my Spell damage from other stuff is around 2k. So my calculation would be

10.5*210*(1-0.42+0.42*1.51) – (40000+10.5*2000)*0.42*0.12 = -397

in my example I should use the Shadow stone. You don’t have to take into account divines since it can be factored out.

We can do a similar calculation to compare the Shadow and Thief mundus stone

Rather briefly the maths is as follows
Damage_Shadow = (1-C)*Base Damage + C*(M+S)*Base Damage
Damage_Thief = (1-C-T)*Base Damage + (C+T)*M*Base Damage

Damage_Thief – Damage_Shadow = Base Damage ( T*(M-1) – C*S )

Thief is better than Shadow when, T*(M-1) – C*S > 0
This is equivalent to fulfilling the equation below
(M-1) / C > 60/59

Back to my example,
(1.51-1) / 0.42 > 60/59 is true thus the Thief is better for me.

For completeness I have also listed the condition for Apprentence and Thief in the summary.

Summary:
If [ b*S1*(1-C+C*M) – (Mag+b*S0)*C*S] > 0, use Apprentice, otherwise use Shadow
where b = 10.5, S1 is Spell damage from Apprentice stone including any buffs, C is crit chance, M is crit modifier, Mag is your Magicka, S0 is spell damage from everything else and S is the Shadow mundus stone (0.12)

If [ b*S1*(1-C+C*M) – (Mag+b*S0)*T*(M-1)] > 0, use Apprentice, otherwise use Thief
where b = 10.5, S1 is Spell damage from Apprentice stone including any buffs, C is crit chance, M is crit modifier, Mag is your Magicka, S0 is spell damage from everything else and T is the Thief mundus stone (0.118)

If (M-1) / C > 60/59 is true, then use Thief otherwise use Shadow.
where M is crit modifier and C is crit chance
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Gear choice

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It would seem the PTS offers a few suggestive sets to the calculative Sorcerer

A

2 piece Molag Kena
4 piece Overwhelming Surge
3 piece Willpower jewellery
2 piece Torug (1 Armour, 1 Weapon)
Weapons are a destruction staff and 2H Greatsword
I do not feel that the 5 piece Overwhelming Surge bonus is beneficial for a Sorcerer since Sorcerers typically weave Force Pulse with an attack and only occasionally cast Crystal Fragments or swap to their secondary bar for buffs and DOTs. But the Overwhelming Surge 5 piece set bonus seems extremely promising for the Magicka Templar that spams Puncturing Sweep and in general uses a lot more Class skills.

The Spell Damage of this set is estimated to be 2275 without casting Surge and the Molag Kena 2 Piece bonus activated.

It appears that the Molag Kena 2 piece set bonus can be procced while weaving Force pulse, leading to 100% uptime of the Molag Kena bonus.

[IMG]http://i57.tinypic.com/2hcg2m1.gif[/IMG]

Thus the expected Spell Damage with the Molag Kena 2 piece set bonus constantly active with Surge is 3572. This can be increased further with spell power enchantments on the jewellery. Magicka and Health should be approximately 40.3k and 14.4k, respectively. This is estimated using the Crown Fortifying Meal which provides 3885 Health and 3570 Magicka/Stamina.

B

2 piece Molag Kena
5 piece Scathing Mage
3 piece Willpower
Non-set staff and 2H Greatsword

This set yields around 14.4k Health and 40.3K Magicka at 100 CP. Again higher Spell Damage is possible by using spell power enchantments on the jewellery. With the Molag Kena and Scathing Mage set bonuses activated this leads to 3524 Spell Damage.

For this set, we need to choose between the Thief, Apprentice and Shadow mundus stones. In addition to deciding between Nirnhoned and Precise. Nirnhoned always gives larger Spell Penetration values than Sharpened and is preferred. Here, I am assuming that the Spell Penetration conferred by Nirnhoned and Sharpened work in the same way.

Let us begin by estimating the proc chance of the Scathing Mage by obtaining the highest possible spell critical. The maximum spell critical achievable is most likely 67.1% (10% base + 10% Prodigy + 10% Inner light + 6.3% Scathing Mage set bonus + 11.8% Thief mundus + 12% Spell precision + 7% Precise trait).

It appears that the Scathing Mage set cannot be proced by DOTs and cannot be re-proced while it is active. It can be proced by the initial cast by subsequents DOTs do not seem to proc it.

A rough test suggest that I can accomplish 14 Force Pulse and 13 light attacks in 18 seconds without doing any other things like proccing Crystal Frags or swapping to my secondary bar to buff myself or drop some DOTs. This turns out to be about ~1.5 attacks per second. The probability that any attack will proc Scathing Mage is 0.1*Spell Critical. This means that in 50% of all cases the Scathing mage set will proc in

Time_50% = 0.66 s * ln(0.5) / ln (1-0.1*SC) = 6.58 s

The proc duration for the Scathing Mage is 6 seconds. Based on this estimate, the average Spell Damage is 3184 (Max SD is 3524 when proced and 2874 when not proced).

If we swap to the Shadow or Apprentice stones, Time_50% is increased to 8.04 s. The average Spell Damage for the Shadow stone is 3151 and 3361 for the Apprentice stone (Max SD 3734, Min SD 3084). But here we have neglected the role of the increased critical damage and the possibility that Elfborn will surpass the effectiveness of Thaumaturge or Elemental Expert.

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• This topic was modified 1 week, 2 days ago by  Asayre.