How Spell Damage is calculated [MXL 2017, Sigma] [WIP]

[mortimer_85]

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I really appreciate the presence of the skill calculator but unfortunately it is outdated.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:


TD: Total Damage of Spell per cast/projectile/missile/arbitrary time-unit
BD: Base Damage that depends on base and soft 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:



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

The Damage taken by a monster from a hit of a spell is TD*min[1-(res-pierce)/100%,2].
where res is the monster resistance to the corresponding element in % and pierce the total amount of -enemy res of the corresponding damage type in %.

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 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

Twin Fang Strike: dex + ene
Pestilence: str + dex
Poison Flash: str
Wildfire: str
... tbc

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
Required Level: 115
Keep in Inventory to Gain Bonus
+1 to All Skills
+1 to Necromancer Skill Levels
+(21 to 25) Spell Focus
Weapon Physical Damage +0.1875% (Based on Character Level)

,

Silver Seal of Ureh

Silver Seal of Ureh
Required Level: 120
Keep in Inventory to Gain Bonus
+1 to All Skills
+(21 to 30) Spell Focus
+(11 to 13)% 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
By Richard Knaak

Required Level: 110
Keep in Inventory to Gain Bonus
+(21 to 25) Spell Focus
+1 to Jitan's Gate
Half Freeze Duration

,

The Sleep

The Sleep
Required Level: 125
Cube After Completing a Trophy Challenge to Awaken
Disenchant to open a portal to the World Nexus
Keep in Inventory to Gain Bonus
Maximum Fire Resist +(0 to 1)%
Maximum Lightning Resist +(0 to 1)%
Maximum Cold Resist +(0 to 1)%
Maximum Poison Resist +(0 to 1)%

with CoL trophy,

Nexus Crystal

Nexus Crystal
(Sorceress Challenge Item)

(Sorceress Only)
Required Level: 90
Keep in Inventory to Gain Bonus
Unlocks your Ennead Skill
+2 to Sorceress Skill Levels
+15% Bonus to Spell Focus
+15% to Spell Damage

)
Items with the modifier xx% Bonus to Energy Factor (

Wake of Destruction

Wake of Destruction
Greaves (4)
Defense: (90 - 102) to (135 - 152)
Required Level: 9
Required Strength: 17
Item Level: 19
+(4 to 6)% Bonus to Spell Focus
(10 to 40)% Movement Speed
+(11 to 13)% to Physical/Magic Spell Damage
+(6 to 8)% to Fire Spell Damage
+(6 to 8)% to Poison Spell Damage
+(24 to 40)% Enhanced Defense
+(21 to 25) to Energy
Requirements -20%
Socketed (1)
Defense: (333 - 369) to (462 - 512)
Required Level: 27
Required Strength: 33
Item Level: 36
+(7 to 9)% Bonus to Spell Focus
(10 to 40)% Movement Speed
+(15 to 17)% to Physical/Magic Spell Damage
+(10 to 12)% to Fire Spell Damage
+(10 to 12)% to Poison Spell Damage
+(58 to 75)% Enhanced Defense
+(26 to 30) to Energy
Requirements -25%
Socketed (2)
Defense: (854 - 930) to (1152 - 1254)
Required Level: 44
Required Strength: 158
Item Level: 59
+(10 to 12)% Bonus to Spell Focus
(10 to 40)% Movement Speed
+(19 to 21)% to Physical/Magic Spell Damage
+(14 to 16)% to Fire Spell Damage
+(14 to 16)% to Poison Spell Damage
+(92 to 109)% Enhanced Defense
+(31 to 35) to Energy
Requirements -30%
Socketed (3)
Defense: (1274 - 1378) to (1713 - 1853)
Required Level: 52
Required Strength: 272
Item Level: 85
+(13 to 15)% Bonus to Spell Focus
(10 to 40)% Movement Speed
+(23 to 25)% to Physical/Magic Spell Damage
+(18 to 20)% to Fire Spell Damage
+(18 to 20)% to Poison 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)
Defense: (6692 - 7471) to (8202 - 9156)
Required Level: 100
Required Strength: 469
Item Level: 105
+(11 to 20)% Bonus to Spell Focus
25% Cast Speed
+(21 to 30)% to Spell Damage
+(115 to 140)% Enhanced Defense
+100 to Strength
+100 to Energy
Elemental Resists +20%
+250 Life after each Demon Kill
50% Bonus to Defense
Requirements -33%
Socketed (6)

,

Auriel's Focus

Auriel's Focus
Mystic Orb

Right-Click to Apply
+2% Bonus to Spell Focus
+25% Enhanced Defense
+15 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

Right-Click to Apply
+15 Spell Focus
+30% Damage to Demons
+3% to Spell Damage
+10 Required Level

,

Lone Wolf's Path

Lone Wolf's Path
(Druid Seer Set)

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

Set Bonus with 2 or more set items:
+150 Spell Focus
+14 to Firedance

Set Bonus with 3 or more set items:
+50% to Poison Spell Damage
Poison Resist +50%

Set Bonus with complete set:
+1 Hunting Banshee/Ember Spirit 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

.
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 10% 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

smax Bacha and with less than 1000 Energy you will have a total Synergy Bonus of 500 % without even looking at Factor Synergies. As long as your corresponding Spell Damage is much lower than that, you should increase it before bothering with EF and such

Assassin:


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

lvl SF
1 150
2 246
3 318
4 382
5 430
6 470
7 502
8 526
9 558
10 574
11 598
12 614
13 630
14 646
15 654
16 670
17 678
18 686
19 694
20 702
21 710
22 718
23 726
24 734
25 734
26 742
27 750
28 750
29 758
30 758
31 766
32 766
33 774
34 774
35 774
36 782
37 782
38 790
39 790
40 790
41 790
42 798
43 798
44 798
45 806
46 806
47 806
48 806
49 814

Necromancer:

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

Paladin:


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 complete this list, when the BBcode for new items is working

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)
One-Hand Damage: 53 to 54
(Paladin Only)
Required Level: 100
Required Strength: 574
Item Level: 120
Strength Damage Bonus: (0.14 per Strength)%
Holy: Holy Fire Deals 4.5% of Strength as More Total Damage (max 250%)
Unholy: Blood Thorns: +40% Damage Multiplier
Nephalem: +25% Total Vessel Damage Bonus from Passives
+1 to Paladin Skill Levels
Adds 175-325 Fire Damage
Adds 1-600 Lightning Damage
Adds 200-250 Cold Damage
+800 Poison Damage over 1 seconds
-(15 to 25)% to Enemy Elemental Resistances
Socketed (3)

• adds 30% Total Bonus to Blood Thorns if you go Unholy.
  
• Adds 200% to SD Percentage for Vessels if you go neutral.

How to Gear my A3 merc?

► Show Spoiler

in progress

All mercs have the ability Heroic Strength, that grants 1/6 EF per Str. The A3 Mercs additionally get an Energy and EF Boost
E=200+20 per level
EF=250+5 per level
This way they have a relatively high Synergy Bonus already without equipping any item.
The following graph shows progression of Synergy Percentage with the level (assuming str progression is equal on all A3 mercs)

To maximize damage output it is again better to balance Synergy and Spell Damage. On a naked lvl 120 merc his Synergy is at 390% already.
So adding SD is much better until some point when socketing a P Topaz gives more TD.

Blood Mage

Necrolyte

For high Single Target put a nice Hailstorm amulet on him.

Abjurer

The gearing of the Abjurer is quite different to the other two because of his ability to cast Superbeast. The minimum fpc is 5 (@195fcr) in Superbeast morph and it adds Spell Damage.
So besides fcr, pierce and all skills increased buff duration is much more important than Lightning Spell Damage.

---

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)

[nofurylion]

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.

The ef docs have different formula and caps(900).
Why put SF and EF in same equation block? Is the docs outdated?

[mortimer_85]

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.

The ef docs have different formula and caps(900).
Why put SF and EF in same equation block? Is the docs outdated?

The docs are not outdated, but not entirely accurate. If you take a look at the current formula you will notice that the Energy Factor Part has a hard cap at 200%. Idk where you got the number 900 from.
I put both Factor parts in one equation because I tested a lot and can tell for sure that the sum of both is capped. So regardless of how much EF, ene, SF and str you have, the synergy from Factors will not go above 200 %

[nofurylion]

The graph on ef docs here put 450 as the highest value. So, 450 from SF + 450 from EF make 900.

[mortimer_85]

The graph on ef docs here put 450 as the highest value. So, 450 from SF + 450 from EF make 900.

The graph shows the total bonus of the Energy part and the Energy Factor Part. Theoretically this sum can go up to 459 % - 200% from the EF part and 259 % from the Energy Part (@energy=61250). The range of Energy and EF in this graph only show values that may be reachable in practice, what is totally fine.

[nofurylion]

The graph shows the total bonus of the Energy part and the Energy Factor Part. Yes, thats my 450% based on.
450% from NRG + NRG_factor plus 450% from STR + STR_factor = 900% spell dmg.

Theoretically this sum can go up to 459 % - 200% from the EF part and 259 % from the Energy Part (@energy=61250). The range of Energy and EF in this graph only show values that may be reachable in practice, what is totally fine.

So why you say the caps is 200% ?
4000 NRG and 1k+ NRG_factor can be achieved with shrinecraft and charms. Its not only theory, its doable.

[mortimer_85]

I think you got something wrong here.
You only gain one Synergy from a stat that has diminishing returns and one Synergy bonus from the sum of Both Factors. If you get an item with SF on it does not mean that you gain an additional bonus of [260*(str+10)/(str+250)][/c] you only gainstr*SF/15000 but only if (str*SF+ene*EF)/15000 is below 200%.

Test it yourself if you not believe me!

[nofurylion]

Ok now I got it. Your point is that 260 blabla is bonus for nrg/str and the min(blabla) is bonus for nrg/str factor. Correct?