Replies: 7

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

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.

Spell Damage

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. Since I did not have access to divines equipment I could not verify where the Divines bonus occurs.

Spell tooltip value

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

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

Spell resistance and penetration

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.

Effect of other CPs on damage

Elemental Expert and Thaumaturge are multiplied to the tooltip value before mitigation. 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 (no 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.

Spell cost reduction

Spell cost=(Base-Flat CR)*(1+0.25*(Lvl-1)-%CR+Molag Kena[2P])*(1-Magician)

Again level is 66 for a V16. For skills, 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).

Magicka recovery

Magicka recovery=(Base+Gear)*(Arcanist)*(Spellcharge[Altmer Passive]+Major Intellect)*Magicka Controoler*(Magicka Aid[Support Passive]+Recover[Light Armour Passive])

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.

Other Passives

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.

Gear choice

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.

Critical damage

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

Critical damage=1.5+Shadow+0.5*Elfborn

Critical damage is the final calculation thus is applied after all forms of mitigation making it much more effective against targets with low resistance.

Let us suppose we have no points in Elfborn to evaluate the effectiveness of the Apprentice, Shadow and Thief Mundus stones. The the average spell damage as calculated above is used and a Magicka of 40k is assumed.

Avg Dmg_App=a(M+10.5*SD_App )+0.5*SC*a(M+10.5*SD_App )
=96108a

Avg Dmg_Sha=a(M+10.5*SD_Sha )+0.5*SC*a(M+10.5*SD_Sha )+SC*Shadow*a(M+10.5*SD_Sha )
=98143a

Avg Dmg_Thf=a(M+10.5*SD_Thf )+0.5*SC_T*a(M+10.5*SD_Thf )
=98068a

Thus the Shadow mundus stone appears to be the most effective for the Scathing mage set for the given parameters.

How does the Scathing Mage set with the Shadow mundus compare to the Overwhelming Surge Set (OSS) and the Apprentice Stone?

Avg Dmg_OSS=a(M+10.5*SD_OSS )+0.5*SC_OSS*a(M+10.5*SD_OSS )
=96494a

where SC_OSS = 0.49

As for the calculations for the Scathing Mage set, we have assumed the use of a Precise weapon. Thus the Scathing Mage set appears to be the most promising set in the PTS.

Precise or Nirnhoned?

Based on the previous conclusion that the Scathing Mage is the most promising set, we set out to decide whether a Nirnhoned or Precise weapon is favoured. This is a rather tedious section where the Damage with a Nirnhoned and Precise weapon are calculated and then the Average damage is taken into account to include the spell critical rating and finally this is performed for a range of tooltip damage values on a broad range of spell resistance. The preceeding formulas should allow anyone to recreate the following result for some typically encountered values. It shows that nirnhoned is superior when the target’s spell resistance is high and the tooltip damage is high.

[IMG]http://i57.tinypic.com/2wcfb0p.jpg[/IMG]

• This topic was modified 5 hours, 39 minutes ago by  Asayre.