How Spell Damage is calculated

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mortimer_85
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How Spell Damage is calculated


Why this post?

If you want to optimize/min-max your (caster)-build or to gear your A3 merc properly, it would be really nice to know how the total damage output of a certain spell is calculated.
This may be common knowledge to experienced players but I think this can help new players.

What kind of Spells are out there?

  • Spells that scale only with hard points of stats like Psicrown or Psionic Storm
  • Spells that has to be cast but actually do wdm Damage like Fairy Ring
  • Spells that scale with at least one type of Spell Damage and Synergies (and may have to be triggered by attacks)
  • ...

:!: This post concentrates on the latter ones

Of course most of the Spells if not all get better with base points and soft points put into the skill.

What is the big Formula?

I really appreciate the presence of the skill calculator but unfortunately it is outdated.
I assumed, that the overall mechanic did not change and played around with numbers on many skills and came up with following result:
Image

TD: Total Damage of Spell per cast/projectile/missile/arbitrary time-unit
BD: Base Damage that depends on skill level and char lvl (only devs and smarter people know those numbers and its progression)
SD: The Spell Damage Bonus of the corresponding type (fire, cold, light, ...) in %
Synergie: The Sum of all Synergies to the Spell in %


Some skill descriptions (e.g. Witchblood) sounds like a third overall multiplier is applied to the Formula but the only way to do this is equipping an item with an Orange Modifier that does so.

[edit] the numbers from the following tests I got from Median 2017 but the mechanics did not change [edit]
I made a test sorc on SP to get in-game numbers. I only skilled Flamefront to 22 and crafted test-gear to get the following max Damage numbers:

Image

so apart from some strange small offsets and rounding issues due to d2 engine number handling, the formula seems to be right.
I did this with several other spells on different chars and got similar results.

What does affect the SD and Synergy ?

SD:
  • Modifier + xx% to corresponding Spell damage
  • Buffing auras like Demon Blood Aura from Flayers or Avenging Aura from SoV
  • Buffing Skills that can be cast on players like Bloodlust, MotW, ...
  • Buffing Skills like Superbeast morph or Symbiosis
  • Some Passives that add Damage Bonus to corresponding Skill like Life and Death/Solstice and Equinox
  • ...

Synergy:
  • Synergies from Stats and Spell Damage Factors Like EF and SF
  • Synergy Skills like Bachanallia or Nightwalker or Witch Blood
  • ...

:!: Since wordings regarding Spell damage in skill descriptions are not consistent, a simple rule:
:!: Test it! You never know whether it adds to the SD percentage, the Synergy percentage or even applies an overall multiplier

Other things:
Of course there are other things that actually increase the DPS like less frames per cast, more missiles of spell, pierce (in case of elemental spells) and more, but they do not change the displayed number.
Increased Poison skill duration certainly increases the total damage output but not per second.

► Show Spoiler


Nice theory, but what shall I do?

I will only give an advice in terms of balancing Synergy and Spell Damage. I assume that in this process the skill level,the pierce (in case of elemental spells) and the achieved speed breakpoints will not suffer.
There is a simple rule:
If possible, keep both multipliers on the same level

speaking in numbers:
SD=Synergy=400 is better than SD=500 and Synergy=300. It is total factor of 25 against total factor of 24 so a real TD increase of 4.16%. So it can be good to sacrifice some SD to increase Synergy.
Or to rephrase it: when you have the choice of either increasing SD or Synergy by the same amount, always increase the lower stat of both.


List of SD Bonuses


Besides the modifier xx % to yy Spell Damage there are quite some pasives and buffs/auras that affect the SD percentage.

[edit] After Party Buff nerfs this section needs some rework [edit]

Assassin:
Way of the Spider: adds Poison Spell Damage per Skill level
Way of the Phoenix: adds Fire Spell Damage per Skill level

Amazon:
Innate skill Bloodlust increases Spell damage (excluding Poison) by 10%.
This Value can be changed by equipping items with xx % Elemental Damage to Bloodlust
Aura from Uber Skill SoV gives 10% +3% per additional skill level to fire and phys/mag Spell Damage.
Barbarian:
Protector Spirits Bloodlust gives 10% + 2.5%(skill level-2) to elemental Spell Damages.
Druid:
Innate Skill Mark of the Wild: Increases Elemental Spell Damages by 10%. This Value can be changed by equipping items with xx % Elemental Damage to Mark of the Wild
Aura from Acid Fiends: Aura of the Acid Fiends increases Spell Damage depending on base and skill lvl with Diminshing returns.
Symbiosys/Mythal: Full skilled Symbiosys will add 5% Ligthning and Cold Spell Damage per Mythal Base level.
Necromancer:
[edit] 1.1.0 changes will be added soon[edit]
Paladin:
Life and Death adds 10% on first +6% per additional skill level to phys Spell Damage of Vessel of Justice.
Solstice and Equinox adds 10% on first +6% per additional skill to phys Spell Damage of Vessel of Retribution.
Superbeast adds xx% to Spell Damage depending on skill level with diminishing returns
Solar Flare adds 5% to Fire, Cold and phys/mag Spell Damage per Incarnation base level but locks out all non Dragon Tree Spells.
Sorceress:
Firedance: Buffing Ring of Fire that increases Spell Damage by 20% on first +2 % per every additional skill level.
O-Skills
The O-Skill versions of the Innate Buffing skills often scale with skill level and can be better buffing options in late game.
Mark of the Wild:
Bloodlust:
Elemental Totem:
Raven Heart:



List of Synergy Bonuses


I am aware of the fact that SD is much more present than the synergy bonus. So I try to compile a list with all Synergies to spell damages.

Stat Synergy:

Take a look at the skill description of your spell. At the bottom you might find a line stat: xx % Increased Damage where stat can be one or two of (ene,str,dex).
Examples for not(only) ene:
► Show Spoiler

The Stat Synergy Bonus in % is calculated with 260*(10+stat)/(250+stat).
In case of two stats granting the synergy, stat has to be replaced by the sum of them.
Early on this Synergy is probably the highest one:
stat = 140 gives 100 %
stat = 790 gives 200 %
It has heavy diminishing returns and only in theory can be pushed to 259 % ( @stat = 62150 )
:!: Note that the displayed number always is the sum of the Stat Synergy and the Factor Synergy what may be confusing.

Factor Synergy:

The Factor Synergy in % is calculated the following way min[(str*SF+ene*EF)/15000 , 200].
So Factor parts adds and scale linear in the stat and factor itself but the sum has a hard cap at 200%. In other words: If you have 4000 Energy and 750 EF getting SF will do nothing.

Getting EF:
Most common ways are MOs on weaopns ( 8 EF for 4 req lvls) and jewels that can spawn with up to 15 EF.
EF can spawn as an affix on many other items
EF is a modifier of Eerie Shrines
EF can be found as an modifier on many Sacred Uniques
Some Charms (
Hammer of the Taan Judges
Hammer of the Taan Judges
Keep in Inventory to Gain Bonus
Required Level: 115
+(21 to 25) Energy Factor to Spell Damage
+1 to All Skills
+1 Extra Totems
Enhanced Weapon Damage +(0.25 per level)% (Based on Character Level)

,
Silver Seal of Ureh
Silver Seal of Ureh
Keep in Inventory to Gain Bonus
Required Level: 120
+(21 to 30) Energy Factor to Spell Damage
+1 to All Skills
+(21 to 25)% to Summoned Minion Damage
+(11 to 15)% to Summoned Minion Resistances
+(11 to 20) to Strength
+(11 to 20) to Dexterity
+(11 to 20) to Vitality
+(11 to 20) to Energy

,
Moon of the Spider
Moon of the Spider
Keep in Inventory to Gain Bonus
Required Level: 110
+(21 to 25) Energy Factor to Spell Damage
+1 to Jitan's Gate
Maximum Skill Level Increased by 1
Half Freeze Duration

,
The Sleep
The Sleep
Cube with Trophy to Add Bonus
Keep in Inventory to Gain Bonus
Required Level: 125

with CoL trophy,
Nexus Crystal
Nexus Crystal
(Sorceress Challenge Item)

Keep in Inventory to Gain Bonus
(Sorceress Only)
Required Level: 90
Unlocks your Ennead Skill
+15% Bonus to Energy Factor
+2 to Sorceress Skill Levels
+15% to Spell Damage
Poison Length Reduced by 33%

)
Items with the modifier xx% Bonus to Energy Factor (
Wake of Destruction
Wake of Destruction
Greaves (4)

Required Level: 9
Required Strength: 60
Defense: (90-102) to (135-152)
+(3 to 5)% Bonus to Energy Factor
(0 to 40)% Movement Speed
+(6 to 8)% to Fire Spell Damage
+(6 to 8)% to Poison Spell Damage
+(11 to 13)% to Physical/Magic Spell Damage
+(24 to 40)% Enhanced Defense
+(21 to 25) to Energy
Requirements -20%
Socketed (1)

Required Level: 27
Required Strength: 84
Defense: (333-369) to (462-512)
+(9 to 11)% Bonus to Energy Factor
(0 to 40)% Movement Speed
+(10 to 12)% to Fire Spell Damage
+(10 to 12)% to Poison Spell Damage
+(15 to 17)% to Physical/Magic Spell Damage
+(58 to 75)% Enhanced Defense
+(26 to 30) to Energy
Requirements -25%
Socketed (2)

Required Level: 44
Required Strength: 164
Defense: (854-930) to (1152-1254)
+(15 to 17)% Bonus to Energy Factor
(0 to 40)% Movement Speed
+(14 to 16)% to Fire Spell Damage
+(14 to 16)% to Poison Spell Damage
+(19 to 21)% to Physical/Magic Spell Damage
+(92 to 109)% Enhanced Defense
+(31 to 35) to Energy
Requirements -30%
Socketed (3)

Required Level: 52
Required Strength: 292
Defense: (1274-1378) to (1713-1853)
+(18 to 20)% Bonus to Energy Factor
(0 to 40)% Movement Speed
+(18 to 20)% to Fire Spell Damage
+(18 to 20)% to Poison Spell Damage
+(23 to 25)% to Physical/Magic Spell Damage
+(109 to 126)% Enhanced Defense
+(36 to 40) to Energy
Requirements -40%
Socketed (4)

,
Robe of Steel
Robe of Steel
Full Plate Mail (Sacred)

Required Level: 100
Required Strength: 428
Defense: (6084-6876) to (7456-8427)
+(11 to 20)% Bonus to Energy Factor
25% Cast Speed
+(21 to 30)% to Spell Damage
+(115 to 143)% Enhanced Defense
+100 to Strength
+100 to Energy
Elemental Resists +20%
Total Character Defense 50%
+250 Life after each Demon Kill
Requirements -33%
Socketed (6)

,
Auriel's Focus
Auriel's Focus
Mystic Orb

Cube Reagent

Cube with Any Armor to Add Bonus

+2% Bonus to Energy Factor
+25% Enhanced Defense
+20 to Energy
Poison Length Reduced by 5%
+10 Required Level
,...)

Getting SF:
SF is much rarer and can be found on some Sacred Uniques,
Uldyssian's Spirit
Uldyssian's Spirit
Mystic Orb

Cube Reagent

Cube with Any Weapon to Add Bonus

+10 Strength Factor to Spell Damage
+10 Energy Factor to Spell Damage
+50% Damage to Demons
+3% to Spell Damage
+10 Required Level
,
Lone Wolf's Path
Lone Wolf's Path
Druid Elemental Set

Lone Wolf's Maul
Lone Wolf's Fur
Lone Wolf's Gaze
Lone Wolf's Claws
Lone Wolf's Track

Set Bonus with 2 or more set items:
+150 Strength Factor to Spell Damage
Set Bonus with 3 or more set items:
+14 to Firedance
Set Bonus with 4 or more set items:
+50% to Poison Spell Damage
Poison Resist +20%

Set Bonus with complete set:
+1 Hunting Banshee/Elemental Projectile
+6 to Druid Skill Levels
-30% to Enemy Fire Resistance
-30% to Enemy Cold Resistance
+19 to Nova Charge
+400 to Life

and on
Yaerius' Xyston
Yaerius' Xyston
Yaerius' Grey Omen Set
Spear (Sacred)

(Paladin Only)
Required Level: 100
Required Strength: 376
Required Dexterity: 376
Two-Hand Damage: 284 to 296
Dexterity Damage Bonus: (30/256 per Dexterity)%
+(101 to 150) Strength Factor to Spell Damage
+(1 to 7) to Paladin Skill Levels
+200% Enhanced Damage
+125 damage
-(14 to 15)% to Enemy Fire Resistance
-(14 to 15)% to Enemy Cold Resistance
+(101 to 500) to Strength
Elemental Resists +100%
Socketed (6)
.
Barb (Shamanic Trance) and Druid (Force of Nature) however have access to this modifier due to a skill.

:!:Apart from Synergy skills and orange modifiers spells can have a maximum Spell Synergy percentage of 459%.

char specific Synergy Skills

Amazon:
The Bachanallia skill of the blood tree. It adds 6% to the synergy bonus to Blood skills per base level if below 2/3 of max life or when Blood Fury is active.

► Show Spoiler


Assassin:
Tiefling Form adds 3 Energy Factor to Spell Damage per skill level.

Barbarian:
Shamanic Trance in Spirit tree adds 5 SF for every Base level in Spirit tree.

Druid:
Uber Skill Force of Nature adds SF with diminishing returns
► Show Spoiler



Necromancer:
Nightwalker in Malice tree adds 4% to Synergy Bonus of Malice Spells per Base lvl.

Paladin:
No skills that affect Synergy percentage.

Sorceress:
Vengeful Power in Poison Tree adds 2% to Synergy Bonus per level for 5 seconds after being hit
Uber Skill Witch Blood gives you 4% Synergy Bonus to sorc spells per level if your HP is above 90%.


Orange Text Modifiers on Items



I will only give some examples on how those modifiers work/intended to work or what I think they do

There are many new items in Sigma with modifiers that cannot be obtained by 'regular' gear. If they are kind of unique they are written in Orange. The following list tries to give an overview over Modifiers that affect Spell Damages.

SU
Adjudicator
Adjudicator
Goedendag (Sacred)

(Paladin Only)
Required Level: 100
Required Strength: 574
One-Hand Damage: 53 to 54
Strength Damage Bonus: (20/256 per Strength)%
Holy: Plague Deals 150% More Total Damage
Unholy: Blood Thorns Deal 40% More Total Damage
Neutrality: Vessel Damage Bonus from Passives is Doubled

+50% Damage to Undead
Adds 350-650 fire damage
Adds 1-1200 lightning damage
Adds 400-500 cold damage
Adds 800 poison damage over 1 seconds
-(15 to 25)% to Enemy Elemental Resistances
Socketed (3)


  • adds 40% Total Bonus to Blood Thorns if you go Unholy.
  • Doubles the Bonus of Vessel Passives (S&E, L&D) if you go neutral.
SU
Gromotvod
Gromotvod
Coronet (Sacred)

(Amazon Only)
Required Level: 100
Required Dexterity: 327
Defense: (605 to 684)
+3% Lightning Spell Damage per Spirit of Vengeance Skill Level
+(2 to 3) to Amazon Skill Levels
(20 to 40)% Cast Speed
-(5 to 15)% to Enemy Lightning Resistance
Maximum Lightning Resist +(1 to 2)%
Physical Resist (5 to 10)%
+(20 to 60) Life after each Kill
Socketed (4)


  • adds 3% Lightning Spell Damage per SoV Skill level
    ► Show Spoiler



How to Gear my A3 merc?


► Show Spoiler





thanks to:
suchbalance for the skill calculator
the whole mxl dev team for this mod
the people who made the wiki that unfortunately is out of date at some points (but someday will be great)
Edited by mortimer_85 1 month.
Ethario
Stygian Watcher
43 | 0
Thanks alot for this. You blew my mind talking about the Abjurer merc having buff duration instead of just spell damage.
mortimer_85
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Ethario wrote:Thanks alot for this. You blew my mind talking about the Abjurer merc having buff duration instead of just spell damage.


I have to test it in Sigma whether Buff Duration still affect the Superbeast morph of the Abjurer. In the last version it was the case, but idk what they changed for the merc mechanics
tranvanhieu
Cog
246 | -1
I am wondering: are there any other equipments with + to Y to X skills that benefit Mers (I only know +Hailstorm (rare amulet) for Necrolyte and +Ancient Hand (weapon runeword) for Barb mers)
LovBetween2Dogs
Fallen
1 | 0
Thank you so much
Mxl wouldn't be this fun without a little bit of math
mortimer_85
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Glad that you like it. Really appreciate it.
As soon as BBCode for new items work I will ad more (useful) stuff. I am open to suggestions/critics whatever.

Happy number juggling!!
vpk79
Prowler
16 | 0
I wonder if my merc have an item with bonus - %monster elemental resist, whether these bonuses are added to mine or they not?
mortimer_85
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-enemy resist is calculated separately, for you and your merc. The only stacking modifier that comes to my mind is Magic Find.
You need a good farming caster merc ? -> get his -enemy res to 120 to 135 of his main element. (After some testing I will add some item suggestions in Merc section)
Edited by mortimer_85 5 months.
Pub
Core Lord
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Short and sweet, detailed where it matters. Great guide!
Soulfighter
Destroyer
7 | 1
This the most amazing thread I've found on the forums, it's so detailed I absolutely love it. I started playing median a couple of weeks ago and I was a bit sad at the lack of specific, precise infos like that. Thanks a bunch man!