[PTS 2.3.x] Sorcerer arithmagic
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Asayre
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PTS 2.3.x Changes
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INTRODUCTION
This post is divided into two main sections: Fundamental Equations and Application of Equations. Fundamental Equations covers the majority of calculations in the game while Application of Equations uses the derived equations to draw conclusions regarding what trait or mundus to use. While my initial focus was on Magicka Sorcerers, the focus has spread a bit and is probably of interest to most Magicka based classes. Note that a large number of equations can be applied to Stamina builds as well by simply substituting for the relevant stamina analogue. At the end of this post, are spreadsheets that implements the Fundamental Equations as well as Application of Equations. The spreadsheets can be used to determine the relative strengths of different sets. The spreadsheets are view only to prevent tampering but please feel free to make a copy for your own calculations. If you do use the spreadsheets I would appreciate feedback in terms of accuracy or ease of use.
FUNDAMENTAL EQUATIONS
Stat pool
The Base value at V16 is 8744 for Health and 7958 for Magicka and Stamina. Attribute points is the number of points spent in Health, Magicka or Stamina multiplied by 122 for Health and 111 for Magicka and Stamina. CPI is a cumulative percentage increase due to points spent in the corresponding constellation and can be calculated as follow
The Lord Mundus gives 1452 Health. The Mage and Tower Mundus gives 1320 Magicka and Stamina, respectively. Divines is the sum of divines. For example 4 pieces of green equipment with divines (4.5% each) means Divines = 1.18. Limited testing on the PTS suggest that Divines is rounded to 2 decimal places.
Example
I have a V16 Breton Sorcerer on the PTS. My gear gives me 7924 Magicka. This includes enchantments and gear bonuses. I have 64 points in Magicka, thus Attribute Points is 7104. I have 100 Champion Points in the Mage constellation which means that CPI is 1.134. I am using the Crown Fortifying Meal which gives 3617 Magicka. Skills is 1.31 (8% Bound Aegis, 5% Inner light, 2% Magicka Controller, 10% Gift of Magnus, 6% Undaunted Mettle). Putting this all into the formula, My in-game Magicka pool in the PTS is 38899.
Spell damage
The Apprentice Mundus provides 166 Spell damage at V16.
Ability tooltip value
The tooltip value for the majority of skill conforms to where a and b are coefficients. b is typically around 10.5 and a varies for each skill. The range of a is typically between 0.02 to 0.2. It is quite challenging to get extremely accurate values for a even with plane fitting over a large data range. We can fix b without much loss in the fitting for a thus we can introduce to concept of effective pool
This allows a fast evaluation method for different builds with varying Magicka and Spell Damage.
A technically more accurate estimate can be obtained by using
However the first formula presented in this section usually provides sufficient accuracy and will be used for the remainder of this post.
Some skills notably Hardened Ward and Annulment scale of only Magicka. In some cases the coefficient a is modified by Champion Points, at the time of writing, Thaumathurge appears to increase the tooltip for all abilities even non-DoTs while Elemental Expert does not increase the tooltip of any ability. In the remainder of this post, it will be assumed that tooltip refers to the base tooltip unmodified by Champion Points.
A list of skill coefficients for the PTS 2.3.2 can be found at
https://docs.google.com/spreadsheets/d/1YN8YWDpi1-d4CfoagRy1F9ath2w2nb-TniL4MjdJdz4/edit?usp=sharing
Recovery
Base Magicka and Stamina recovery at V16 is 514. Base Health recovery at V16 is 309. The Atronach mundus provides 198 Magicka recovery at V16. Other skills include Magicka Aid [Support Passive]. Skills include Magicka Controller [Mages’ Guild Passive], Major Intellect, Recovery [Light Armour Passive], and Spellcharge [Altmer Passive].
Example
I’m using a V16 Altmer with 765 Magicka Recovery from Gear and have the Atronach mundus but no divines pieces equipped. I have 30 points in Arcanist (10.8%). I have two Support skills slotted with 2 points in Magicka Aid so Other skills is 1.2. I am using a Crown Refreshing Drink which provides 361 Magicka Recovery. Skills is 1.55, 6% from Magicka Controller, 20% from Major Intellect, 20% from Recovery and 9% from Spellcharge. This yields My in-game Magicka Recovery in the PTS is 3602.
Spell Cost
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, divided by 1.1625. For instance, the tooltip cost value for Fire Rune is 3654. The Base Cost for Fire Rune is then 3143. 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.
Example
I am calculating the cost to cast Fire Rune. The Base Cost is 3141 at V16. I have 70 points in Magician (12.9%) and 3 legendary reduce spell cost enchantment (203 each). %Cost Reduction is 0.33, 15% from Evocation [Light Armour Passive], 15% from Mage Adept [Mages’ Guild Passive] and 3% from Magicka Mastery [Breton Passive]. The cost for casting Fire Rune is This matches the in-game cost for Fire Rune in the PTS.
If I was to activate the 2 piece bonus of Molag Kena the cost for Fire Rune will be
The in-game cost for Fire Rune on the PTS is 2475.
Spell Critical
Simply add up all sources that increase Spell Critical. 219 Spell Critical rating is equivalent to 1% Spell Critical
Critical modifier
This formula has been updated due to changes in [2.2.4]
where Fl is the floor function, Rd is the round function and Elfborn_Real is similar to the tooltip value of Elfborn but when it is used no unexpected rounding errors are found. Rd(x, 2) rounds a number to 2 decimal places and Fl(x, 0.01) truncates a number at the 2nd decimal places. Here are examples of both functions in action, Rd(23.458,2) = 23.46, Fl(23.458,0.01) = 23.45. Skills tested were the Piercing Spear passive and Trap Beast (Minor Force). Aggressive Horn (Major Force) is multiplicative. Thanks to @Beltan3 and @hofawd with some help in getting this formula down.
By the way, if you don't mind some error in your calculation, a simpler formula is
Due to rounding errors, Elfborn still suffers from jump. Any points in between jumps do not increase your critical modifier. @Erraln has kindly listed all the jump points in this thread but for convenience, I'll put them here as well. 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, and 98.
Resistance
Your spell resistance can be calculated with the following formula
where Gear is the sum of tooltip armour values, Resolve is a Heavy Armour Passive, Defending is a weapon trait. Other includes Breton Spell Resistance Passive, Balanced Warrior Passive (Templars), Major Ward, Spell Warding and Spell Shield CP.
Similarly, physical resistance is calculated as follows
The Lady mundus provides 1980 Physical Resistance at V16 and is put into the variable Other. The Reinforced trait increases the tooltip armour value and will be included when calculating Gear. The Shield Expert passive under the Steed increases the tooltip value of the shield thus is also included in Gear.
Example
I have 5 pieces of heavy armour, 1 medium and 1 light. The sum of all my tooltip armour values, Gear, is 16666. Resolves grants 1811 resistance and Spell Warding grants 363 Spell Resistance. I have a legendary defending weapon equipped (6%). My set bonus for physical resistance is 5805. I have 100 points in Heavy Armour Focus (5281). I also have the Spell Resistance (Breton passive) and Balanced Warrior (Templar passive) passives. With Major Resolve and Ward active, I estimate my physical and spell resistance to be
My actual physical and spell resistance are 35951 and 31828, respectively.
Critical resistance
Critical resistance is not needed in PvE since monsters do not do critical damage. An enemies’ critical modifier can be reduced by equipping gear with the Impenetrable trait or by spending points in the Resilient champion point sign. Every percent in Resilient decreases the enemies’ critical modifier by the same amount and every 250 points of critical resistance reduces an enemies’ critical modifier by 3.5%
Example
If you are PvP’ing against an enemy with a critical modifier of 0.5 and you have 500 critical resistance (2 legendary equipment) and 48 points (15%) in Resilient, then
Miscellaneous equations
Bash Cost
Bash cost reduction comes from the Shield-Play enchantment. The effect of the enchantment should be multiplied by 1.1625 to get the Bash Cost Reduction. Bashing Focus has no impact on Bash Cost.
Block Cost
Skills tested were Absorb Magicka, Bracing and Fortress.
Block Mitigation
Skills tested were Spear Wall, Deflect Bolts, Footman, Absorb Magicka and Sword and Board. There are some tooltip inconsistencies with Spear Wall and Deflect bolts but the error is not large.
Dodge Cost
Heavy Attack Resource Return
Cycle of Life is a Restoration Staff passive. I only tested this briefly but for some reason Lightning staves was returning ~12.6% additional resources.
Sneak Cost
Sprint Cost
DAMAGE CALCULATION
Base damage
The base damage formula is where
Attacker Bonus includes relevant champion point signs, Minor Berserk [Combat Prayer] and Elemental Talent [Altmer Passive]. These stack multiplicatively. Defender bonus refers to relevant champion point signs. Battle Spirit can be included by simply multiplying by 0.5. In 2.2.3, the impact of Thaumathurge is included in the tooltip but the impact of Elemental Expert is not included in the tooltip, so be wary you’re not double counting Thaumathurge. Resistance is the relevant physical or spell resistance. Penetration is the sum of percentage based penetration. For magicka builds, this is either 18% for a legendary nirnhoned weapon or 28% when using a legendary nirnhoned weapon and casting a Destruction Staff spell due to the Penetrating Magic passive. Examples of Flat Penetration are Concentration for Light Armour users, Spell Erosion and Piercing. The base Flat Penetration is 100. Veteran rank 16 corresponds to level 66. For PvE, most mobs have a level of 50. Examples of Armour Debuff are Major and Minor Fracture and Breach, 5 piece bonus of Night Mother's Gaze and Glyphs of Crushing. The resistance of some bosses in 2.1.x can be found at [2.1] Project Resistance.
PvP Example
A V16 Altmer cast Force Pulse on a target with 22354 spell resistance and 40 points in Elemental Defender (13.2%). The tooltip value of Force Pulse is 1354. I have put 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. I am using a precise staff. My focus is 4984. Given these parameters and The actual damage recorded is 576.
Average damage
The average damage when taking into account critical damage is
HEALING CALCULATION
Base Healing
The base healing formula for a healer using a variety of sources of Healing Done and Healing Taken and Healing Received isThe Tooltip value is increased by Restoration Master, Soul Siphoner, Major Mending and the Ritual Mundus. These add additively. Healing Done was tested with Blessed. Healing Taken was tested with Tormentor and Leeching sets. Healing Received was tested to be additive with Quick Recovery [Champion Point], Rapid Mending [Heavy Armour Passive], Minor Vitality [Swallow Soul & Coagulating Blood], Burning Heart [Draconic Power Passive] and Quick to Mend [Argonian Passive].
Example
A V16 Argonian cast Healing Springs. This character has 12% Healing Taken from the Tormentor and Leeching Sets and has 100 points in Blessed (25% Healing Done) and 100 points in Quick Recovery (16% Healing Received). In addition, this character is wearing 7 Heavy armour pieces (7% Healing Received), has the Minor Vitality buff, has a Draconic Power ability active and has 3 points in the Quick to Mend passive. This tooltip value includes the bonuses from Restoration Master, Major Mending and the Ritual Mundus.
The recorded in-game healing is 3264.
APPLICATION OF EQUATIONS
Champion Point System
WARRIOR
Most players will be looking to spend points in either Hardy, Elemental Defender or Thick-Skinned. Sorcerers will also be looking to spend points into Bastion. Not much can be said for Armour Focus or Spell Shield as a 100 points provides only 5281 resistance which corresponds to 8% mitigation at V16 which corresponds to 20 points in Hardy or Elemental Defender. In addition, Armour Focus and Spell Shield are affected by percentage penetration and are not taken into account when a damage shield is used.
THIEF
For Magicka builds, the decision is on how to spread points between Magician and Arcanist. I approach this problem with a brute force method. I enumerate all possible combination of champion points and calculate the function The Recovery equation is used as is in the section Recovery. The other variables are Cast per 2 seconds which I conservatively estimate at around 1.5. For Spell Cost, I estimate an average Base Spell cost of around 2000 for Sorcerers as well as Templars. The calculation can be repeated for Cost Reduction, Magicka Recovery or Spell Damage enchantments. In the cases that I experimented with I found a strong bias in favour of Magician of around 9:1 ratio for Cost Reduction/Spell Damage jewellery and 4:1 for Magicka Recovery jewellery. I was testing a Breton with 100 CP in the Thief, the ratios are probably significantly different for an Altmer.
MAGE
For a Magicka damage dealer, there are five signs of interest, Elemental Expert, Thaumathurge, Spell Erosion, Elfborn and Staff Expert.
The mechanics of all these except Staff Expert have been discussed in the sections on Critical Modifier and Base Damage. Staff expert increases the damage of light and medium attacks that is your weaving damage. Light and medium staff attacks are also increased by Elemental Expert.
In order to determine the optimal Champion Point distribution, we first need to consider the ratio of Elemental, DoT and Staff attacks. Then we can optimise the following function
One way to approach this is to enumerate all possible CP distributions and then calculate the function. However, this is quite a challenging task since with 167 Mage CP and 5 CP stars to consider the total possible of combinations is 30507895 (166C4). Although, some of these can be eliminated through some insight on the relative strengths of the CP stars. While this can be done, I have decided to make the equation a bit more accessible with the loss of a tiny amount of accuracy. I've included a spreadsheet that will do this
https://docs.google.com/spreadsheets/d/1Zp9v1Vp4Z7X6zfDfcxTwyAnejv-tEC5LujbXYBiVMDk/edit?usp=sharing
On the first sheet you'll see a range of inputs including
Number of Champion Points
Critical Chance
Critical Modifier
Defined as Critical Damage/Non-Critical Damage - 1
Target Resistance
Target Level
Percentage Penetration
Flat Penetration
Elemental Ratio
DoT Ratio
Staff Ratio
It will output the ideal CP distribution in Elemental Expert, Thaumathurge, Staff Expert, Elfborn and Spell Erosion. It does not take into account the Elfborn jump points in the calculation so if it suggest a non-Elfborn jump point it will also display the nearest Elfborn jump points. Also all CP passives are ignored. This means that there may be situations where it will not recommend putting 30 points into the Apprentice first.
How it works?
It starts by assuming you have 0 in all 5 CP stars. It then calculates the following function
for an increase of 1 point in each star. It selects the optimum distribution then keeps going until it reaches your stated number of Champion Points. I had to use a continuous equation to model how the CP stars vary with points spent. The equation used can be seen in Sheet 3. Because a continuous equation was used some deviation from my previous discrete optimisation will be present. In addition, I could not include the impact of Elfborn jump points thus jump points are suggested at the end of the optimisation. While the previous discrete optimisation is probably better to model the jump points, I hope that this method of presenting the ideal mage CP distribution for magicka builds will be easier to use thus increasing it's accuracy as you can put in your own relevant values instead of looking for the closest table match.
Precise and Nirnhoned
Recall that the average damage equation is
where
For the purpose of this analysis, it is possible to ignore the Tooltip, Attacker Bonus and Defender Bonus. But for completeness, I’ll combine it all into a coefficient, k, that I will show later that it can be eliminated for this assessment. This discussion assumes a PvE situation thus the level is set to 50.
It is clear that we can separate Mitigation into two parts, one containing the ‘Base’, Mit_Base, and the other the ‘Penetration’, Mit_Pen, component
The average damage with Nirnhoned, Dmg_N, is then
In comparison the average damage with Precise, Dmg_P, is
To decide which is preferable, we will subtract the average damage with Precise, Dmg_P, from the average damage with Nirnhoned, Dmg_N,
The coefficient k is always positive so we can ignore it when determining if the equation is positive, that is favouring Nirnhoned, or negative, that is favouring Precise. For simplicity, I’ll assume that 0 points are placed in Spell Erosion. Flat Penetration is assumed to be 4984. Then for select values of Resistance we can create graphs showing when Nirnhoned or Precise is better. In the graphs below, blue means Precise is better and red implies Nirnhoned is better.
Below ~8000 resistance, precise is always better and above ~14000 resistance nirnhoned is always superior. Also having a high critical chance favours Nirnhoned while having a high critical modifier favours Precise.
To help with your decision between Nirnhoned and Precise, I have included an additional calculator in my latest spreadsheet. It uses the critical chance, critical modifier, points in spell erosion, focus, and monster resistance to determine which is preferred.
Divines and Infused
The current meta advice suggest using Infused on large pieces (Head, Chest, Legs and Shield) and Divines on small pieces (Shoulders, Waist, Hands and Feet). There are no other viable traits for optimising damage. However, with the buffs to the Thief and Shadow mundus stones this advice is called into question. In this section, I will derive the conditions where Infused or Divines should be used. It is quite laborious mathematics and this section has been implemented in my spreadsheet. The equations here are to explain how the calculation is done.
The amount of magicka gained from using Infused on a legendary large piece instead of Divines, Inf, is173 is the difference between in enchantment of a V16 legendary Magicka enchant on an Infused large piece compared to a non-Infused large piece. CPI and Skills were defined in Stat Pool.
The average damage when using an Infused piece is
The coefficient, k, in this section isDmg_Inf can be separated into two parts, Dmg_Base and Dmg’_Inf. The former is the damage component from not using any trait and the latter is the bonus damage coming from using infused
The average damage increase when using Divines depends on the mundus stone. For completeness, I’ll analyse the Apprentice, Mage, Thief and Shadow mundus stones.
Apprentice
The average damage increase when using Divines with the Apprentice mundus isSkill_SD refers to abilities and buffs that increase spell damage, notably Minor and Major Sorcery and the Expert Mage passive.
Again this can be separated into two components, Dmg_Base and Dmg_Divine^App’
Mage
The average damage increase when using Divines with the Mage mundus isSkills refers to abilities and passives that increase maximum Magicka and was defined in more detail in <b>Stat Pool</b>.
Again this can be separated into two components, Dmg_Base and Dmg_Divine^Mage’
Thief
The average damage increase when using Divines with the Thief mundus is
Again this can be separated into two components, Dmg_Base and Dmg_Divine^Thief’
Shadow
The average damage increase when using Divines with the Shadow mundus is
I’m using a simplified form of the Critical Modifier equation here but in my implementation of the equation in my spreadsheet I use the more exact form of the Critical Modifier. Skill_S refers to skills that increase the critical modifier such as Piercing Spear [Templar passive], Hemorrhage [Nightblade passive], Trap Beast [Minor Force] and Aggressive Warhorn [Major Force].
This can be separated into two components, Dmg_Base and Dmg_Divine^Shadow’
The way to decide between Infused and Divines is then to evaluate Dmg_Inf’ - Dmg_Divine’ with the corresponding mundus stone. Since several variables need to be taken into account, I’ve simply implemented my calculation into my spreadsheets. On a personal note, in the majority of calculations that I have performed Divines with Thief or Shadow outperforms Infused. However, if the Apprentice or Mageis used then Infused on large pieces is preferred.
Mundus stone: Apprentice, Mage, Thief and Shadow
There are four mundus stones of interest to optimising Magicka based damage dealers. They are the Apprentice, Mage, Thief and Shadow. I’ll begin with the average damage equation for each mundus. Astute readers might notice a striking similarity with the section <b>Divines and Infused</b>.
ApprenticeIn this section, the coefficient, k, is defined to be
Skill_SD refers to abilities and buffs that increase spell damage, notably Minor and Major Sorcery and the Expert Mage passive.
Dmg_App can be separated into two components, Dmg_Base and Dmg_App’. The former is the damage component without any mundus active and the latter is the damage from using the Apprentice mundus.Mage
Skills refers to abilities and passives that increase maximum Magicka and was defined in more detail in Stat Pool. Separating into a base and Mage component yieldsThiefOnce again, this can be separated into a base and Thief component.
Shadow
I’m using a simplified form of the Critical Modifier equation here but in my implementation of the equation in my spreadsheet I use the more exact form of the Critical Modifier. Skill_S refers to skills that increase the critical modifier such as Piercing Spear [Templar passive], Hemorrhage [Nightblade passive], Trap Beast [Minor Force] and Aggressive Warhorn [Major Force].
This can be separated into two components, Dmg_Base and Dmg_Shadow’From this, we can easily conclude that the Apprentice mundus is preferred to the Mage mundus in nearly all cases for increasing damage sincewhereAt V16 the Apprentice provides 166 Spell Damage, <i>b</i> is approximately 10.5 and Skill_SD is typically 1.2 due to the Major Sorcery buff. The Mage gives 1320 Magicka at V16 and Skills is typically around 1.31 for a Sorcerer and is lower for Templars. Putting this into the equation, we obtainThus the Apprentice is preferred. The Mage mundus is sometimes preferred due to increasing Magicka pool for stronger shields and higher pet damage as these scale solely off Magicka.
For the comparison between the Apprentice and Thief there are no easy simplifications and one is left to evaluateThere are many variables and no obvious simplifications thus I have simply implemented the laborious calculation in my spreadsheet. Similarly the comparison between Apprentice and Shadow is very involved and is implemented in the spreadsheet.
While the equations presented for the Thief are a crude approximation due to the complicated rounding in the more accurate formula for Critical Modifier, it is possible to make a rough comparison between the Thief and Shadow mundus stones.Thus the Thief is better ifThis is equivalent toIn the Orsinium PTS, the Shadow mundus increases Critical Modifier by 12% and the Thief increases Critical Chance by 11%. Putting this values in, we get the following inequalitywhich means that Thief is better than Shadow if your Critical Modifier is at least ~10% greater than your Critical Chance.
Percentage Penetration and Spell Damage Equivalence
Since Maelstrom weapons cannot come in Nirnhoned, it is natural to ask how does a non-set Nirnhoned destruction staff compare to a Sharpened Maelstrom destruction staff.
To evaluate this, let us consider T1 and T2, where T1 is the base damage with S1 extra spell damage and T2 be the base damage with no extra spell damage but 4% extra penetration. Then
where M is Max Magicka, S0 is the base spell damage, S1 is the extra spell damage for T1 and
Note that any penetration that is common to T1 and T2 can be seen as just a reduction in the Resistance.
We then proceed to solve T1-T2=0 for S1
We can rearrange this to get
Now we have to put some typical endgame values, I'll let M=43487, S_0=3764 and Mit=0.19 (17k boss resistance, 14% penetration, 4984 Focus, 0 Spell Erosion). Mit'=0.04*0.34
Thus for the stats assumed a Sharpened Maelstrom Destruction Staff is better than a non-set Nirnhoned Destruction Staff as the 4% additional penetration is equivalent to 133 Spell Damage which is less than the Maelstrom enchantment of 189 Spell Damage
Julianos and Twice-Born Star
Due to changes to Elfborn and skills that increase critical damage, TBS is no longer optimal from a DPS point of view. In the spreadsheets below, I have introduced a new metric called the Combined Metric. This metric was introduced because staff attacks scale differently from abilities. For most abilities 10.5 Max Magicka ~ 1 Spell Damage but for staff attacks 40 Max Magicka ~ 1 Spell Damage. To obtain the Combined Metric, I assume approximately 15% of total dps comes from Heavy (Medium Attacks) and 85% comes from abilities, then the weighted average of the Ability and Attack metric results in the Combined Metric.
We see then that for the Combined Metric on staffs, Law of Julianos is better by about 1.5%. Previously, my calculations showed that Law of Julianos was ~0.5% better than TBS but that was without taking into account the higher Attack Metric. On the dual wield bar, we should use the Ability Metric since no weaves are used and in this situation Julianos is better by around 0.5%.
If you were to replace one magicka enchantment on a large piece in favour of health so that the Health with Julianos and Twice-Born Star are comparable then on the staff bar Julianos is better by 0.1% but worse by 0.1% on the dual wield bar. To help put all these percentage differences into context, my rough calculations suggest that not having Divines on one piece (maybe you have been unlucky and have a bank full of Well-Fitted Molag Kena shoulders/helm) equates to a loss of ~0.5%
I've heard of people saying that Twice-Born Star is better with lower CP but I have yet to see extensive calculations that demonstrate this. Using the spreadsheets below, I varied the amount of CP by adjusting both the number of points invested into the Mage Tree and assumed that the first 100 points will be put into Elemental Expert followed by all points (up to 66) into Elfborn. While this CP distribution is not absolutely optimal, it is reasonably close. In this case, even with 100 Mage CP (300 total CP) Julianos is better than Twice-Born Star on the staff bar (0.3%). On the Dual-Wield bar, Julianos outperforms Twice-Born Star at 129 Mage CP (387 total CP)
Note: Ignore the Magicka Recovery and Spell Cost boxes. I was too lazy to move them away before I took the pictures.
Twice-Born Star Staff
Twice-Born Star Dual Wield
Law of Julianos Staff
Law of Julianos Dual Wield
CHARACTER SPREADSHEETS
Only made them for Sorcerers, Templar and Nightblades at the moment.Feel free to make a copy for your own calculations.
https://docs.google.com/spreadsheets/d/1e2M7ZU9ZKBxCNhDmvfS4GKPs_Nx7YLUny9vBmPaUmgA/edit?usp=sharing
@Beltan3 has made an awesome calculator. The post is at
http://tamrielfoundry.com/topic/stats-calculator/
and the calculator itself can be found at
https://docs.google.com/spreadsheets/d/12-_behjvbr6L0e2F3pge5aumfKInY6rsqv61x27JHic/edit#gid=1127244779
Edited by Asayre on February 23, 2016 9:53PM [/list]
- Ability tooltip value
- List of skill coefficients for PTS 2.3.2
- Resistance
- Changed how armour focus was being applied
- Critical modifier
- Major Force is multiplicative
- New Section: Miscellaneous equations
- Champion Point System: Warrior
- Made recommendations in favour of Hardy and Elemental Defender over Armour Focus and Spell Shield
- Champion Point System: Mage
- Changed the function to optimise for ideal CP distribution and provided a spreadsheet
- Precise and Nirnhoned
- Changed from a PvP setting to a PvE setting
INTRODUCTION
This post is divided into two main sections: Fundamental Equations and Application of Equations. Fundamental Equations covers the majority of calculations in the game while Application of Equations uses the derived equations to draw conclusions regarding what trait or mundus to use. While my initial focus was on Magicka Sorcerers, the focus has spread a bit and is probably of interest to most Magicka based classes. Note that a large number of equations can be applied to Stamina builds as well by simply substituting for the relevant stamina analogue. At the end of this post, are spreadsheets that implements the Fundamental Equations as well as Application of Equations. The spreadsheets can be used to determine the relative strengths of different sets. The spreadsheets are view only to prevent tampering but please feel free to make a copy for your own calculations. If you do use the spreadsheets I would appreciate feedback in terms of accuracy or ease of use.
FUNDAMENTAL EQUATIONS
Stat pool
Spoiler
The Base value at V16 is 8744 for Health and 7958 for Magicka and Stamina. Attribute points is the number of points spent in Health, Magicka or Stamina multiplied by 122 for Health and 111 for Magicka and Stamina. CPI is a cumulative percentage increase due to points spent in the corresponding constellation and can be calculated as follow
The Lord Mundus gives 1452 Health. The Mage and Tower Mundus gives 1320 Magicka and Stamina, respectively. Divines is the sum of divines. For example 4 pieces of green equipment with divines (4.5% each) means Divines = 1.18. Limited testing on the PTS suggest that Divines is rounded to 2 decimal places.
Example
I have a V16 Breton Sorcerer on the PTS. My gear gives me 7924 Magicka. This includes enchantments and gear bonuses. I have 64 points in Magicka, thus Attribute Points is 7104. I have 100 Champion Points in the Mage constellation which means that CPI is 1.134. I am using the Crown Fortifying Meal which gives 3617 Magicka. Skills is 1.31 (8% Bound Aegis, 5% Inner light, 2% Magicka Controller, 10% Gift of Magnus, 6% Undaunted Mettle). Putting this all into the formula, My in-game Magicka pool in the PTS is 38899.
Spell damage
Spoiler
The Apprentice Mundus provides 166 Spell damage at V16.
Ability tooltip value
Spoiler
The tooltip value for the majority of skill conforms to where a and b are coefficients. b is typically around 10.5 and a varies for each skill. The range of a is typically between 0.02 to 0.2. It is quite challenging to get extremely accurate values for a even with plane fitting over a large data range. We can fix b without much loss in the fitting for a thus we can introduce to concept of effective pool
This allows a fast evaluation method for different builds with varying Magicka and Spell Damage.
A technically more accurate estimate can be obtained by using
However the first formula presented in this section usually provides sufficient accuracy and will be used for the remainder of this post.
Some skills notably Hardened Ward and Annulment scale of only Magicka. In some cases the coefficient a is modified by Champion Points, at the time of writing, Thaumathurge appears to increase the tooltip for all abilities even non-DoTs while Elemental Expert does not increase the tooltip of any ability. In the remainder of this post, it will be assumed that tooltip refers to the base tooltip unmodified by Champion Points.
A list of skill coefficients for the PTS 2.3.2 can be found at
https://docs.google.com/spreadsheets/d/1YN8YWDpi1-d4CfoagRy1F9ath2w2nb-TniL4MjdJdz4/edit?usp=sharing
Recovery
Spoiler
Base Magicka and Stamina recovery at V16 is 514. Base Health recovery at V16 is 309. The Atronach mundus provides 198 Magicka recovery at V16. Other skills include Magicka Aid [Support Passive]. Skills include Magicka Controller [Mages’ Guild Passive], Major Intellect, Recovery [Light Armour Passive], and Spellcharge [Altmer Passive].
Example
I’m using a V16 Altmer with 765 Magicka Recovery from Gear and have the Atronach mundus but no divines pieces equipped. I have 30 points in Arcanist (10.8%). I have two Support skills slotted with 2 points in Magicka Aid so Other skills is 1.2. I am using a Crown Refreshing Drink which provides 361 Magicka Recovery. Skills is 1.55, 6% from Magicka Controller, 20% from Major Intellect, 20% from Recovery and 9% from Spellcharge. This yields My in-game Magicka Recovery in the PTS is 3602.
Spell Cost
Spoiler
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, divided by 1.1625. For instance, the tooltip cost value for Fire Rune is 3654. The Base Cost for Fire Rune is then 3143. 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.
Example
I am calculating the cost to cast Fire Rune. The Base Cost is 3141 at V16. I have 70 points in Magician (12.9%) and 3 legendary reduce spell cost enchantment (203 each). %Cost Reduction is 0.33, 15% from Evocation [Light Armour Passive], 15% from Mage Adept [Mages’ Guild Passive] and 3% from Magicka Mastery [Breton Passive]. The cost for casting Fire Rune is This matches the in-game cost for Fire Rune in the PTS.
If I was to activate the 2 piece bonus of Molag Kena the cost for Fire Rune will be
The in-game cost for Fire Rune on the PTS is 2475.
Spell Critical
Spoiler
Simply add up all sources that increase Spell Critical. 219 Spell Critical rating is equivalent to 1% Spell Critical
Critical modifier
Spoiler
This formula has been updated due to changes in [2.2.4]
where Fl is the floor function, Rd is the round function and Elfborn_Real is similar to the tooltip value of Elfborn but when it is used no unexpected rounding errors are found. Rd(x, 2) rounds a number to 2 decimal places and Fl(x, 0.01) truncates a number at the 2nd decimal places. Here are examples of both functions in action, Rd(23.458,2) = 23.46, Fl(23.458,0.01) = 23.45. Skills tested were the Piercing Spear passive and Trap Beast (Minor Force). Aggressive Horn (Major Force) is multiplicative. Thanks to @Beltan3 and @hofawd with some help in getting this formula down.
By the way, if you don't mind some error in your calculation, a simpler formula is
Due to rounding errors, Elfborn still suffers from jump. Any points in between jumps do not increase your critical modifier. @Erraln has kindly listed all the jump points in this thread but for convenience, I'll put them here as well. 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, and 98.
Resistance
Spoiler
Your spell resistance can be calculated with the following formula
where Gear is the sum of tooltip armour values, Resolve is a Heavy Armour Passive, Defending is a weapon trait. Other includes Breton Spell Resistance Passive, Balanced Warrior Passive (Templars), Major Ward, Spell Warding and Spell Shield CP.
Similarly, physical resistance is calculated as follows
The Lady mundus provides 1980 Physical Resistance at V16 and is put into the variable Other. The Reinforced trait increases the tooltip armour value and will be included when calculating Gear. The Shield Expert passive under the Steed increases the tooltip value of the shield thus is also included in Gear.
Example
I have 5 pieces of heavy armour, 1 medium and 1 light. The sum of all my tooltip armour values, Gear, is 16666. Resolves grants 1811 resistance and Spell Warding grants 363 Spell Resistance. I have a legendary defending weapon equipped (6%). My set bonus for physical resistance is 5805. I have 100 points in Heavy Armour Focus (5281). I also have the Spell Resistance (Breton passive) and Balanced Warrior (Templar passive) passives. With Major Resolve and Ward active, I estimate my physical and spell resistance to be
My actual physical and spell resistance are 35951 and 31828, respectively.
Critical resistance
Spoiler
Critical resistance is not needed in PvE since monsters do not do critical damage. An enemies’ critical modifier can be reduced by equipping gear with the Impenetrable trait or by spending points in the Resilient champion point sign. Every percent in Resilient decreases the enemies’ critical modifier by the same amount and every 250 points of critical resistance reduces an enemies’ critical modifier by 3.5%
Example
If you are PvP’ing against an enemy with a critical modifier of 0.5 and you have 500 critical resistance (2 legendary equipment) and 48 points (15%) in Resilient, then
Miscellaneous equations
Spoiler
Bash Cost
Bash cost reduction comes from the Shield-Play enchantment. The effect of the enchantment should be multiplied by 1.1625 to get the Bash Cost Reduction. Bashing Focus has no impact on Bash Cost.
Block Cost
Skills tested were Absorb Magicka, Bracing and Fortress.
Block Mitigation
Skills tested were Spear Wall, Deflect Bolts, Footman, Absorb Magicka and Sword and Board. There are some tooltip inconsistencies with Spear Wall and Deflect bolts but the error is not large.
Dodge Cost
Heavy Attack Resource Return
Cycle of Life is a Restoration Staff passive. I only tested this briefly but for some reason Lightning staves was returning ~12.6% additional resources.
Sneak Cost
Sprint Cost
DAMAGE CALCULATION
Base damage
Spoiler
The base damage formula is where
Attacker Bonus includes relevant champion point signs, Minor Berserk [Combat Prayer] and Elemental Talent [Altmer Passive]. These stack multiplicatively. Defender bonus refers to relevant champion point signs. Battle Spirit can be included by simply multiplying by 0.5. In 2.2.3, the impact of Thaumathurge is included in the tooltip but the impact of Elemental Expert is not included in the tooltip, so be wary you’re not double counting Thaumathurge. Resistance is the relevant physical or spell resistance. Penetration is the sum of percentage based penetration. For magicka builds, this is either 18% for a legendary nirnhoned weapon or 28% when using a legendary nirnhoned weapon and casting a Destruction Staff spell due to the Penetrating Magic passive. Examples of Flat Penetration are Concentration for Light Armour users, Spell Erosion and Piercing. The base Flat Penetration is 100. Veteran rank 16 corresponds to level 66. For PvE, most mobs have a level of 50. Examples of Armour Debuff are Major and Minor Fracture and Breach, 5 piece bonus of Night Mother's Gaze and Glyphs of Crushing. The resistance of some bosses in 2.1.x can be found at [2.1] Project Resistance.
PvP Example
A V16 Altmer cast Force Pulse on a target with 22354 spell resistance and 40 points in Elemental Defender (13.2%). The tooltip value of Force Pulse is 1354. I have put 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. I am using a precise staff. My focus is 4984. Given these parameters and The actual damage recorded is 576.
Average damage
Spoiler
The average damage when taking into account critical damage is
HEALING CALCULATION
Base Healing
Spoiler
The base healing formula for a healer using a variety of sources of Healing Done and Healing Taken and Healing Received isThe Tooltip value is increased by Restoration Master, Soul Siphoner, Major Mending and the Ritual Mundus. These add additively. Healing Done was tested with Blessed. Healing Taken was tested with Tormentor and Leeching sets. Healing Received was tested to be additive with Quick Recovery [Champion Point], Rapid Mending [Heavy Armour Passive], Minor Vitality [Swallow Soul & Coagulating Blood], Burning Heart [Draconic Power Passive] and Quick to Mend [Argonian Passive].
Example
A V16 Argonian cast Healing Springs. This character has 12% Healing Taken from the Tormentor and Leeching Sets and has 100 points in Blessed (25% Healing Done) and 100 points in Quick Recovery (16% Healing Received). In addition, this character is wearing 7 Heavy armour pieces (7% Healing Received), has the Minor Vitality buff, has a Draconic Power ability active and has 3 points in the Quick to Mend passive. This tooltip value includes the bonuses from Restoration Master, Major Mending and the Ritual Mundus.
The recorded in-game healing is 3264.
APPLICATION OF EQUATIONS
Champion Point System
WARRIOR
Spoiler
Most players will be looking to spend points in either Hardy, Elemental Defender or Thick-Skinned. Sorcerers will also be looking to spend points into Bastion. Not much can be said for Armour Focus or Spell Shield as a 100 points provides only 5281 resistance which corresponds to 8% mitigation at V16 which corresponds to 20 points in Hardy or Elemental Defender. In addition, Armour Focus and Spell Shield are affected by percentage penetration and are not taken into account when a damage shield is used.
THIEF
Spoiler
For Magicka builds, the decision is on how to spread points between Magician and Arcanist. I approach this problem with a brute force method. I enumerate all possible combination of champion points and calculate the function The Recovery equation is used as is in the section Recovery. The other variables are Cast per 2 seconds which I conservatively estimate at around 1.5. For Spell Cost, I estimate an average Base Spell cost of around 2000 for Sorcerers as well as Templars. The calculation can be repeated for Cost Reduction, Magicka Recovery or Spell Damage enchantments. In the cases that I experimented with I found a strong bias in favour of Magician of around 9:1 ratio for Cost Reduction/Spell Damage jewellery and 4:1 for Magicka Recovery jewellery. I was testing a Breton with 100 CP in the Thief, the ratios are probably significantly different for an Altmer.
MAGE
Spoiler
For a Magicka damage dealer, there are five signs of interest, Elemental Expert, Thaumathurge, Spell Erosion, Elfborn and Staff Expert.
The mechanics of all these except Staff Expert have been discussed in the sections on Critical Modifier and Base Damage. Staff expert increases the damage of light and medium attacks that is your weaving damage. Light and medium staff attacks are also increased by Elemental Expert.
In order to determine the optimal Champion Point distribution, we first need to consider the ratio of Elemental, DoT and Staff attacks. Then we can optimise the following function
One way to approach this is to enumerate all possible CP distributions and then calculate the function. However, this is quite a challenging task since with 167 Mage CP and 5 CP stars to consider the total possible of combinations is 30507895 (166C4). Although, some of these can be eliminated through some insight on the relative strengths of the CP stars. While this can be done, I have decided to make the equation a bit more accessible with the loss of a tiny amount of accuracy. I've included a spreadsheet that will do this
https://docs.google.com/spreadsheets/d/1Zp9v1Vp4Z7X6zfDfcxTwyAnejv-tEC5LujbXYBiVMDk/edit?usp=sharing
On the first sheet you'll see a range of inputs including
Number of Champion Points
Critical Chance
Critical Modifier
Defined as Critical Damage/Non-Critical Damage - 1
Target Resistance
Target Level
Percentage Penetration
Flat Penetration
Elemental Ratio
DoT Ratio
Staff Ratio
It will output the ideal CP distribution in Elemental Expert, Thaumathurge, Staff Expert, Elfborn and Spell Erosion. It does not take into account the Elfborn jump points in the calculation so if it suggest a non-Elfborn jump point it will also display the nearest Elfborn jump points. Also all CP passives are ignored. This means that there may be situations where it will not recommend putting 30 points into the Apprentice first.
How it works?
It starts by assuming you have 0 in all 5 CP stars. It then calculates the following function
for an increase of 1 point in each star. It selects the optimum distribution then keeps going until it reaches your stated number of Champion Points. I had to use a continuous equation to model how the CP stars vary with points spent. The equation used can be seen in Sheet 3. Because a continuous equation was used some deviation from my previous discrete optimisation will be present. In addition, I could not include the impact of Elfborn jump points thus jump points are suggested at the end of the optimisation. While the previous discrete optimisation is probably better to model the jump points, I hope that this method of presenting the ideal mage CP distribution for magicka builds will be easier to use thus increasing it's accuracy as you can put in your own relevant values instead of looking for the closest table match.
Precise and Nirnhoned
Spoiler
Recall that the average damage equation is
where
For the purpose of this analysis, it is possible to ignore the Tooltip, Attacker Bonus and Defender Bonus. But for completeness, I’ll combine it all into a coefficient, k, that I will show later that it can be eliminated for this assessment. This discussion assumes a PvE situation thus the level is set to 50.
It is clear that we can separate Mitigation into two parts, one containing the ‘Base’, Mit_Base, and the other the ‘Penetration’, Mit_Pen, component
The average damage with Nirnhoned, Dmg_N, is then
In comparison the average damage with Precise, Dmg_P, is
To decide which is preferable, we will subtract the average damage with Precise, Dmg_P, from the average damage with Nirnhoned, Dmg_N,
The coefficient k is always positive so we can ignore it when determining if the equation is positive, that is favouring Nirnhoned, or negative, that is favouring Precise. For simplicity, I’ll assume that 0 points are placed in Spell Erosion. Flat Penetration is assumed to be 4984. Then for select values of Resistance we can create graphs showing when Nirnhoned or Precise is better. In the graphs below, blue means Precise is better and red implies Nirnhoned is better.
Below ~8000 resistance, precise is always better and above ~14000 resistance nirnhoned is always superior. Also having a high critical chance favours Nirnhoned while having a high critical modifier favours Precise.
To help with your decision between Nirnhoned and Precise, I have included an additional calculator in my latest spreadsheet. It uses the critical chance, critical modifier, points in spell erosion, focus, and monster resistance to determine which is preferred.
Divines and Infused
Spoiler
The current meta advice suggest using Infused on large pieces (Head, Chest, Legs and Shield) and Divines on small pieces (Shoulders, Waist, Hands and Feet). There are no other viable traits for optimising damage. However, with the buffs to the Thief and Shadow mundus stones this advice is called into question. In this section, I will derive the conditions where Infused or Divines should be used. It is quite laborious mathematics and this section has been implemented in my spreadsheet. The equations here are to explain how the calculation is done.
The amount of magicka gained from using Infused on a legendary large piece instead of Divines, Inf, is173 is the difference between in enchantment of a V16 legendary Magicka enchant on an Infused large piece compared to a non-Infused large piece. CPI and Skills were defined in Stat Pool.
The average damage when using an Infused piece is
The coefficient, k, in this section isDmg_Inf can be separated into two parts, Dmg_Base and Dmg’_Inf. The former is the damage component from not using any trait and the latter is the bonus damage coming from using infused
The average damage increase when using Divines depends on the mundus stone. For completeness, I’ll analyse the Apprentice, Mage, Thief and Shadow mundus stones.
Apprentice
The average damage increase when using Divines with the Apprentice mundus isSkill_SD refers to abilities and buffs that increase spell damage, notably Minor and Major Sorcery and the Expert Mage passive.
Again this can be separated into two components, Dmg_Base and Dmg_Divine^App’
Mage
The average damage increase when using Divines with the Mage mundus isSkills refers to abilities and passives that increase maximum Magicka and was defined in more detail in <b>Stat Pool</b>.
Again this can be separated into two components, Dmg_Base and Dmg_Divine^Mage’
Thief
The average damage increase when using Divines with the Thief mundus is
Again this can be separated into two components, Dmg_Base and Dmg_Divine^Thief’
Shadow
The average damage increase when using Divines with the Shadow mundus is
I’m using a simplified form of the Critical Modifier equation here but in my implementation of the equation in my spreadsheet I use the more exact form of the Critical Modifier. Skill_S refers to skills that increase the critical modifier such as Piercing Spear [Templar passive], Hemorrhage [Nightblade passive], Trap Beast [Minor Force] and Aggressive Warhorn [Major Force].
This can be separated into two components, Dmg_Base and Dmg_Divine^Shadow’
The way to decide between Infused and Divines is then to evaluate Dmg_Inf’ - Dmg_Divine’ with the corresponding mundus stone. Since several variables need to be taken into account, I’ve simply implemented my calculation into my spreadsheets. On a personal note, in the majority of calculations that I have performed Divines with Thief or Shadow outperforms Infused. However, if the Apprentice or Mageis used then Infused on large pieces is preferred.
Mundus stone: Apprentice, Mage, Thief and Shadow
Spoiler
There are four mundus stones of interest to optimising Magicka based damage dealers. They are the Apprentice, Mage, Thief and Shadow. I’ll begin with the average damage equation for each mundus. Astute readers might notice a striking similarity with the section <b>Divines and Infused</b>.
ApprenticeIn this section, the coefficient, k, is defined to be
Skill_SD refers to abilities and buffs that increase spell damage, notably Minor and Major Sorcery and the Expert Mage passive.
Dmg_App can be separated into two components, Dmg_Base and Dmg_App’. The former is the damage component without any mundus active and the latter is the damage from using the Apprentice mundus.Mage
Skills refers to abilities and passives that increase maximum Magicka and was defined in more detail in Stat Pool. Separating into a base and Mage component yieldsThiefOnce again, this can be separated into a base and Thief component.
Shadow
I’m using a simplified form of the Critical Modifier equation here but in my implementation of the equation in my spreadsheet I use the more exact form of the Critical Modifier. Skill_S refers to skills that increase the critical modifier such as Piercing Spear [Templar passive], Hemorrhage [Nightblade passive], Trap Beast [Minor Force] and Aggressive Warhorn [Major Force].
This can be separated into two components, Dmg_Base and Dmg_Shadow’From this, we can easily conclude that the Apprentice mundus is preferred to the Mage mundus in nearly all cases for increasing damage sincewhereAt V16 the Apprentice provides 166 Spell Damage, <i>b</i> is approximately 10.5 and Skill_SD is typically 1.2 due to the Major Sorcery buff. The Mage gives 1320 Magicka at V16 and Skills is typically around 1.31 for a Sorcerer and is lower for Templars. Putting this into the equation, we obtainThus the Apprentice is preferred. The Mage mundus is sometimes preferred due to increasing Magicka pool for stronger shields and higher pet damage as these scale solely off Magicka.
For the comparison between the Apprentice and Thief there are no easy simplifications and one is left to evaluateThere are many variables and no obvious simplifications thus I have simply implemented the laborious calculation in my spreadsheet. Similarly the comparison between Apprentice and Shadow is very involved and is implemented in the spreadsheet.
While the equations presented for the Thief are a crude approximation due to the complicated rounding in the more accurate formula for Critical Modifier, it is possible to make a rough comparison between the Thief and Shadow mundus stones.Thus the Thief is better ifThis is equivalent toIn the Orsinium PTS, the Shadow mundus increases Critical Modifier by 12% and the Thief increases Critical Chance by 11%. Putting this values in, we get the following inequalitywhich means that Thief is better than Shadow if your Critical Modifier is at least ~10% greater than your Critical Chance.
Percentage Penetration and Spell Damage Equivalence
Spoiler
Since Maelstrom weapons cannot come in Nirnhoned, it is natural to ask how does a non-set Nirnhoned destruction staff compare to a Sharpened Maelstrom destruction staff.
To evaluate this, let us consider T1 and T2, where T1 is the base damage with S1 extra spell damage and T2 be the base damage with no extra spell damage but 4% extra penetration. Then
where M is Max Magicka, S0 is the base spell damage, S1 is the extra spell damage for T1 and
Note that any penetration that is common to T1 and T2 can be seen as just a reduction in the Resistance.
We then proceed to solve T1-T2=0 for S1
We can rearrange this to get
Now we have to put some typical endgame values, I'll let M=43487, S_0=3764 and Mit=0.19 (17k boss resistance, 14% penetration, 4984 Focus, 0 Spell Erosion). Mit'=0.04*0.34
Thus for the stats assumed a Sharpened Maelstrom Destruction Staff is better than a non-set Nirnhoned Destruction Staff as the 4% additional penetration is equivalent to 133 Spell Damage which is less than the Maelstrom enchantment of 189 Spell Damage
Julianos and Twice-Born Star
Spoiler
Due to changes to Elfborn and skills that increase critical damage, TBS is no longer optimal from a DPS point of view. In the spreadsheets below, I have introduced a new metric called the Combined Metric. This metric was introduced because staff attacks scale differently from abilities. For most abilities 10.5 Max Magicka ~ 1 Spell Damage but for staff attacks 40 Max Magicka ~ 1 Spell Damage. To obtain the Combined Metric, I assume approximately 15% of total dps comes from Heavy (Medium Attacks) and 85% comes from abilities, then the weighted average of the Ability and Attack metric results in the Combined Metric.
We see then that for the Combined Metric on staffs, Law of Julianos is better by about 1.5%. Previously, my calculations showed that Law of Julianos was ~0.5% better than TBS but that was without taking into account the higher Attack Metric. On the dual wield bar, we should use the Ability Metric since no weaves are used and in this situation Julianos is better by around 0.5%.
If you were to replace one magicka enchantment on a large piece in favour of health so that the Health with Julianos and Twice-Born Star are comparable then on the staff bar Julianos is better by 0.1% but worse by 0.1% on the dual wield bar. To help put all these percentage differences into context, my rough calculations suggest that not having Divines on one piece (maybe you have been unlucky and have a bank full of Well-Fitted Molag Kena shoulders/helm) equates to a loss of ~0.5%
I've heard of people saying that Twice-Born Star is better with lower CP but I have yet to see extensive calculations that demonstrate this. Using the spreadsheets below, I varied the amount of CP by adjusting both the number of points invested into the Mage Tree and assumed that the first 100 points will be put into Elemental Expert followed by all points (up to 66) into Elfborn. While this CP distribution is not absolutely optimal, it is reasonably close. In this case, even with 100 Mage CP (300 total CP) Julianos is better than Twice-Born Star on the staff bar (0.3%). On the Dual-Wield bar, Julianos outperforms Twice-Born Star at 129 Mage CP (387 total CP)
Note: Ignore the Magicka Recovery and Spell Cost boxes. I was too lazy to move them away before I took the pictures.
Twice-Born Star Staff
Twice-Born Star Dual Wield
Law of Julianos Staff
Law of Julianos Dual Wield
CHARACTER SPREADSHEETS
Spoiler
Only made them for Sorcerers, Templar and Nightblades at the moment.Feel free to make a copy for your own calculations.
https://docs.google.com/spreadsheets/d/1e2M7ZU9ZKBxCNhDmvfS4GKPs_Nx7YLUny9vBmPaUmgA/edit?usp=sharing
@Beltan3 has made an awesome calculator. The post is at
http://tamrielfoundry.com/topic/stats-calculator/
and the calculator itself can be found at
https://docs.google.com/spreadsheets/d/12-_behjvbr6L0e2F3pge5aumfKInY6rsqv61x27JHic/edit#gid=1127244779
Reference for any calculation I make Introduction to PvE Damage Calculation
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RoxyPhoenix✭✭✭✭Dude, you should be working at NASA.. or maybe you already are...and all those calculations mean nothing when you got a 3 year old on your back yelling I WANT A DINOSAUR!
But.. good job I suppose.9 -
Mojmir✭✭✭✭✭
✭✭✭✭✭RoxyPhoenix wrote: »Dude, you should be working at NASA.. or maybe you already are...and all those calculations mean nothing when you got a 3 year old on your back yelling I WANT A DINOSAUR!
But.. good job I suppose.
he should be working over eric wrobel. :P15 -
RoxyPhoenix✭✭✭✭
he should be working over eric wrobel. :P
Eric is a Lead Combat Designer, which means he makes up all the skills and combat interactions, however I don't think he got diagrams popping up in his head. That job relays on the shoulders of all the coders, IT brainiacs trying to fallow their boss instructions, sometimes resulting in errors.
Funny... just like for most of us: you work your hands to the bone for 8h a day and your boss sits there thinking of new ways to make your job harder
2 -
hammayolettuce✭✭✭✭✭
✭Thank you for all of the time you put into this post. I found it very useful.♥ Snü (Magicka DK) ♥ Thnu (Stamplar) ♥ Pizza for Breakfast (Magplar) ♥ Sparklefingers (Magicka Sorc) ♥♥ Bean and Cheese Burrito (Magicka DK) ♥ Snurrito (Stamplar) ♥DARFAL COVANT2 -
Septimus_Magna✭✭✭✭✭
✭✭Amazing work, this gives a lot of insight in the right gear and CPs for magicka builds!
One thing you might have overlooked is the use of a master destro staff for the scalding mages setup. This lowers the spell dmg a bit because its max v14 instead of v16 and you need to sacrifice the weapon enchant, but it increases max magicka which will increase dmg. Again, great stuff! I hope the combat team sees this.PC - EU (AD)SpoilerSeptimus Mezar - Altmer Sorcerer
Septimus Rulanir - Orsimer Templar
Septimus Desmoru - Khajiit Necromancer
Septimus Iroh - Dunmer Dragon Knight
Septimus Thragar - Dunmer Nightblade
Septimus Jah'zar - Khajiit Nightblade
Septimus Nerox - Redguard Warden
Septimus Ozurk - Orsimer Sorcerer1 -
Xeven✭✭✭✭✭
✭OP confirming that the most intelligent people among our community don't post that much. Awesome post and all that...
I almost stopped reading when you said bastion was superfluous. It would have been a lot more interesting from a PvP point of view.Edited by Xeven on August 23, 2015 7:54AM1 -
Mojmir✭✭✭✭✭
✭✭✭✭✭RoxyPhoenix wrote: »
Eric is a Lead Combat Designer, which means he makes up all the skills and combat interactions, however I don't think he got diagrams popping up in his head. That job relays on the shoulders of all the coders, IT brainiacs trying to fallow their boss instructions, sometimes resulting in errors.
Funny... just like for most of us: you work your hands to the bone for 8h a day and your boss sits there thinking of new ways to make your job harder
exactly my point,meaning technically this guy would probably get things done because he speaks the language, after watching some ESO lives, these guys dont seem to take what they do serious. the OP shows passion, i dig that.2 -
Asayre✭✭✭✭✭
✭Septimus_Magna wrote: »Amazing work, this gives a lot of insight in the right gear and CPs for magicka builds!
One thing you might have overlooked is the use of a master destro staff for the scalding mages setup. This lowers the spell dmg a bit because its max v14 instead of v16 and you need to sacrifice the weapon enchant, but it increases max magicka which will increase dmg. Again, great stuff! I hope the combat team sees this.
Unfortunately we don't get free master weapons in the PTS thus I have no idea what the stats are. If you happen to have the stats for it could you please let me know?Reference for any calculation I make Introduction to PvE Damage Calculation0 -
Ahzek✭✭✭✭✭
✭The master staff gets you ~900 magicka. However you loose over 200 spelldamage in the process. In my opinion that is hardly worth it.
Edit: Its even worse for phisical weapons, such as the masters GS, since those enchantments can simply be replaced with the new weapon damage on hit enchants.Edited by Ahzek on August 23, 2015 11:27AMJo'Khaljor0 -
Asayre✭✭✭✭✭
✭CheeseDivinity wrote: »Meanwhile I dual wield on my sorc because it looks cool..
It depends on your Magicka pool and the spell damage of the rest of your stuff. My purpose was to illustrate how one would go about deciding between 2H and DW where the assumption is that with DW you get a bonus of 129 SD from one set bonus and with some assumptions on magicka and spell damage.
As you can see in the figure below at lower Magicka values, dual wielding is preferable. Magenta means 2H is favourable and cyan indicates a preference for dual wielding
Reference for any calculation I make Introduction to PvE Damage Calculation4 -
Septimus_Magna✭✭✭✭✭
✭✭
Unfortunately we don't get free master weapons in the PTS thus I have no idea what the stats are. If you happen to have the stats for it could you please let me know?
As mentioned by Ahzek above the loss of 200 spell dmg wont make up for 900 increased magicka. Im kinda surprised the difference between spell dmg from v14 and v16 weapons is so big tbh.
For max spell dmg on the DW bar you could also consider:
2x molag kena's
5x scalding mage
2x cyrodiil's light (rings)
3x willpower (2x sword/staff + necklace)
This would reduce spell dmg and magicka by a bit (diff between v16 and v14 jewelry) on the destro staff bar but you would get an extra spell dmg bonus on the DW bar.
PC - EU (AD)SpoilerSeptimus Mezar - Altmer Sorcerer
Septimus Rulanir - Orsimer Templar
Septimus Desmoru - Khajiit Necromancer
Septimus Iroh - Dunmer Dragon Knight
Septimus Thragar - Dunmer Nightblade
Septimus Jah'zar - Khajiit Nightblade
Septimus Nerox - Redguard Warden
Septimus Ozurk - Orsimer Sorcerer0 -
ToRelax✭✭✭✭✭
✭✭Septimus_Magna wrote: »
As mentioned by Ahzek above the loss of 200 spell dmg wont make up for 900 increased magicka. Im kinda surprised the difference between spell dmg from v14 and v16 weapons is so big tbh.
For max spell dmg on the DW bar you could also consider:
2x molag kena's
5x scalding mage
2x cyrodiil's light (rings)
3x willpower (2x sword/staff + necklace)
This would reduce spell dmg and magicka by a bit (diff between v16 and v14 jewelry) on the destro staff bar but you would get an extra spell dmg bonus on the DW bar.
As was already stated in the post above yours, DW will give another SD bonus anyway, using Torug's Pact swords.DAGON - ALTADOON - CHIM - GHARTOK
The Covenant is broken. The Enemy has won...
Elo'dryel - Sorc - AR 50 - Hopesfire - EP EU0 -
Septimus_Magna✭✭✭✭✭
✭✭
As was already stated in the post above yours, DW will give another SD bonus anyway, using Torug's Pact swords.
The spell dmg value on Torugs Pact 2pc has been nerfed so this combination would offer more spell dmg, although the difference probably wont be too big.
PC - EU (AD)SpoilerSeptimus Mezar - Altmer Sorcerer
Septimus Rulanir - Orsimer Templar
Septimus Desmoru - Khajiit Necromancer
Septimus Iroh - Dunmer Dragon Knight
Septimus Thragar - Dunmer Nightblade
Septimus Jah'zar - Khajiit Nightblade
Septimus Nerox - Redguard Warden
Septimus Ozurk - Orsimer Sorcerer0 -
Asayre✭✭✭✭✭
✭For players with high magicka 2H will offer better results than dual wielding even taking into the account a set bonus of 129 SD.
It seems that the previous post is suggesting taking 2 Cyrodiil rings and 3 Willpower (1 necklace, 2 swords) over my proposed 3 Willpower and 1 non-set greastsword. The former setup confers 2 SD and 1 Magicka set bonus. The latter provides 1 Magicka and 1 SD set bonus. Note that since Cyrodiil rings will only come in V14, 2 Torugs sword and 3 Willpower will be preferred over 2 Cyrodiil rings and 3 Willpower. I believe the crafting bonus is being removed ie. crafted and dropped gear will have equivalent set bonuses.
Then the question is how does a 2H compare to DW with that extra 129 spell damage (1 SD set bonus). I calculated that in my original post where I have taken into account the passive Blade and Blunt (DW) and Heavy Weapons (2H)
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
I estimate that at V16, Magicka will be about 40K and SD_Gear (the spell damage from other sources not including your weapon) is around 1900( = 1.3 [Surge+5 Expert Mage] * (129*2 (Willpower,Molag Kena 1P] + 688 [Molag Kena, 2P] + 516 [Scathing Mage, 5P]) at this values 2H is outperforms dual wielding.
Dual wielding with the extra 129 spell damage becomes preferred at lower Magicka. As example, dual wielding is preferred over 2H when you have 27K magicka and 1327 SD.
The figure I generated above shows the cutoff point. If your spell damage and magicka is in the magenta then you should consider 2H. If it is in the cyan then maybe try out dual wieldingReference for any calculation I make Introduction to PvE Damage Calculation3 -
Soulac✭✭✭✭✭
✭✭I tested StamReg and MagReg Formulas the last Patch, but with the new one it seems that Champion Passives doesn´t increase the boost of used drinks.
Stamina Reg:
(514+247)*1.63*1.216+(463*1.63)
(Base + Set) * Passives * ChampionPassives + (Drink * Passives)
Staminareg formula is different from magickareg formula.
It´s a nerf!
Edited by Soulac on August 23, 2015 2:42PMR.I.P Dawnbreaker / Auriel´s Bow
Member of the Arena Guild and the overpowered Banana Squad.
Nathaerizh aka Cat - Nightblade V16 - EU
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Ludof✭✭✭Well done
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 22<sup>nd</sup> 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.
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<sub>Gear</sub> ~ 1300, 2H<sub>dmg</sub> = 1571, DW<sub>dmg</sub> = 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.
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.
Well done!!
Thanks for sharing [EP-EU]
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hammayolettuce✭✭✭✭✭
✭
Unfortunately we don't get free master weapons in the PTS thus I have no idea what the stats are. If you happen to have the stats for it could you please let me know?
Making a V14 template will give you most of the masters weapons and a few other sets you don't get on the V16 templates.♥ Snü (Magicka DK) ♥ Thnu (Stamplar) ♥ Pizza for Breakfast (Magplar) ♥ Sparklefingers (Magicka Sorc) ♥♥ Bean and Cheese Burrito (Magicka DK) ♥ Snurrito (Stamplar) ♥DARFAL COVANT0 -
Asayre✭✭✭✭✭
✭I tested StamReg and MagReg Formulas the last Patch, but with the new one it seems that Champion Passives doesn´t increase the boost of used drinks.
Stamina Reg:
(514+247)*1.63*1.216+(463*1.63)
(Base + Set) * Passives * ChampionPassives + (Drink * Passives)
Staminareg formula is different from magickareg formula.
It´s a nerf!
I totally forgot about drink haha.
I added the new formula including drinks
Magicka recovery=((Base+Gear)*Arcanist*(Magicka Aid[Support Passive]+Recover[Light Armour Passive])+Drink)*(Spellcharge[Altmer Passive]+Major Intellect+Magicka Controller)
Yea drinks are not boosted by Arcanist.Reference for any calculation I make Introduction to PvE Damage Calculation1 -
Asayre✭✭✭✭✭
✭hammayolettuce wrote: »Making a V14 template will give you most of the masters weapons and a few other sets you don't get on the V16 templates.
I only got 2 master greatswords and 2 master daggers. The light armaments bag gives me a bunch of torug staffs. But thanks for letting me know about those bags. I didn't realise I could get a nirn staff. It allowed me to test the relationship between nirnhoned and penetrating magic. They are additive.
If they keep master weapons at V14 they will never be attractive at V16. A V16 legendary staff gives 1335 spell damage while a V14 legenday staff gives 1144 spell damage. The difference is 191 Spell damage or 240 effective spell damage (with a 1.24[Surge+3*Expert Mage] boost). This is equivalent to having approximately 2526 Magicka.
To compete with this the magicka provided by the enchantment must be reasonably large. With 70 champion points in the mage giving a 11% boost and a 33% boost from skills then it would require that the enchantment provide 1711 Magicka.Reference for any calculation I make Introduction to PvE Damage Calculation0 -
Soulac✭✭✭✭✭
✭✭
I totally forgot about drink haha.
I added the new formula including drinks
Magicka recovery=((Base+Gear)*Arcanist*(Magicka Aid[Support Passive]+Recover[Light Armour Passive])+Drink)*(Spellcharge[Altmer Passive]+Major Intellect+Magicka Controller + Vampire)
Yea drinks are not boosted by Arcanist.
Added Vamp for you :P
R.I.P Dawnbreaker / Auriel´s Bow
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AssaultLemming✭✭✭✭Dual wielding swords with 2 points in blade and blunt leads to a 5% increase in the spell damage component for the swords.
Can you check this? Blade and blunt tooltip was changed in 1.5 to only provide a damage increase to dual wield abilities. Does this still provide a 5% increase to all damage?1 -
Junkogen✭✭✭✭✭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 22<sup>nd</sup> 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 (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.
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*(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.
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<sub>Gear</sub> ~ 1300, 2H<sub>dmg</sub> = 1571, DW<sub>dmg</sub> = 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.
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.
Could you please use your powers of mathematics to analyze the racial passives and prove to ZOS that the Argonian racial passives are, in fact, the worst passives compared to all the others? Pretty please? The lizards need your help. You're our only hope.Edited by Junkogen on August 23, 2015 10:20PM2 -
Erock25✭✭✭✭✭
✭✭Good topic and I'm loving the amount of people quoting the entire original post just to write a few words.You earned the 500 LOLs badge.
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Septimus_Magna✭✭✭✭✭
✭✭For players with high magicka 2H will offer better results than dual wielding even taking into the account a set bonus of 129 SD.
It seems that the previous post is suggesting taking 2 Cyrodiil rings and 3 Willpower (1 necklace, 2 swords) over my proposed 3 Willpower and 1 non-set greastsword. The former setup confers 2 SD and 1 Magicka set bonus. The latter provides 1 Magicka and 1 SD set bonus. Note that since Cyrodiil rings will only come in V14, 2 Torugs sword and 3 Willpower will be preferred over 2 Cyrodiil rings and 3 Willpower. I believe the crafting bonus is being removed ie. crafted and dropped gear will have equivalent set bonuses.
Then the question is how does a 2H compare to DW with that extra 129 spell damage (1 SD set bonus). I calculated that in my original post where I have taken into account the passive Blade and Blunt (DW) and Heavy Weapons (2H)
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
I estimate that at V16, Magicka will be about 40K and SD_Gear (the spell damage from other sources not including your weapon) is around 1900( = 1.3 [Surge+5 Expert Mage] * (129*2 (Willpower,Molag Kena 1P] + 688 [Molag Kena, 2P] + 516 [Scathing Mage, 5P]) at this values 2H is outperforms dual wielding.
Dual wielding with the extra 129 spell damage becomes preferred at lower Magicka. As example, dual wielding is preferred over 2H when you have 27K magicka and 1327 SD.
The figure I generated above shows the cutoff point. If your spell damage and magicka is in the magenta then you should consider 2H. If it is in the cyan then maybe try out dual wielding
Thanks for clearing that up.
To my knowledge the stats of dropped sets will have +1 vr stats compared to crafted set, currently its the other way around. In addition, the weapon and spell dmg boni on sets with 4 traits or less are reduced. This makes the spell dmg bonus from Torugs Pact lower than the spell dmg bonus from Cyrodiils Light (res. 129 vs 170 if I remember correct). 2H would probably still be prefered on high spell dmg builds because the difference is pretty small.
I cant wait for IC to go live, it seems like it will take a while to get all the desired gear.
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