Calculating Magic Damage

Actual Damage

Actual Damage is calculated by multiplying the following factors in order and flooring after each step.
1) D
2) Multiple-Target Damage Reduction
3) Resistance
4) Staff Bonus
5) Day | Weather Bonus
6) Magic Burst Bonus
6a) Magic Burst Bonus Gear #1
6b) Magic Burst Bonus Gear #2
7) MAB / MDB
8) Target Magic Damage Adjustment

There is reason to believe that the magic burst portion is calculated prior to MAB. Further testing would be necessary to confirm the order of the other parts with respect to magic bursts.

Explanation of Factors

Calculation of D

Each magic tier has an inherent mutliplier value M.
Each magic spell has a base value V.
Let dINT be (Caster's INT - Target's INT).
(Banishes and Holy, substitute MND for INT).

For dINT < 0: D = V + dINT (when dINT is a penalty, the tier mult. is always 1)
For dINT > 0, but less than some inflection point: D = V + (dINT * M)
For dINT > 0, but after some inflection point: D = V + (const + (dINT-const) * M / 2))
(above some critical value, adding INT/MND becomes half as effective)
For dINT > 0, but after some cap: D = cap

Elemental Magic:

M = 1.0 for all Helix spells.
M = 1.0 for all Ichi and Ni Ninjutsu spells.
M = 1.0 for all tier I/II single-target spells.
M = 1.0 for all -ga spells up to Blizzaga II.
M = 1.0 for all -ra spells up to Aerora II.
M = 1.5 for all San Ninjutsu spells.
M = 1.5 for all tier III single-target spells.
M = 1.5 for all -ga spells Thundaga II and beyond.
M = 1.5 for all -ra spells Fira II and beyond.
M = 2.0 for all tier IV and Ancient Magic spells.
M = ~2.299 for all tier V single-target spells.
M = 2.3 for Comet and all -ja spells. [except Aeroja and Impact, which is 2.3 repeating, see tests]

Divine Magic:

M = 1.0 for Banish and Banish II.
M = 1.0 for Banishga and Banishga II.
M = 1.0 for Holy.
M = 1.5 for Banish III.

V values by spell:

Spell	Earth	Water	Wind	Fire	Ice	Thunder	Dark	Light
I	10	16	25	35	46	60	N/A	14
II	78	95	113	133	155	178	N/A	85
III	210	236	265	295	320	345	N/A	198
IV	381	410	440	472	506	541	N/A	N/A
V	626	680	738	785	828	874	963	N/A
VI	Template:Information	Template:Information	Template:Information	Template:Information	Template:Information	Template:Information	N/A	N/A
I-ga	56	74	93	120	145	172	N/A	50
II-ga	201	232	266	312	350	392	N/A	180
III-ga	434	480	527	589	642	697	N/A	N/A
-ja	719	782	844	902	953	1004	N/A	N/A
I-ra	128	153	179	216	247	282	N/A	N/A
II-ra	317	356	396	450	496	544	N/A	N/A
AM I	577	630	552	657	526	603	939	125
AM II	710	710	710	710	710	710	N/A	N/A
Helix	25	25	25	25	25	25	25	25
Ichi	10	10	10	10	10	10	N/A	N/A
Ni	78	78	78	78	78	78	N/A	N/A
San	105	105	105	105	105	105	N/A	N/A

Any equipment with "Magic Damage +" statistic as well as the bonus from Cascade has this value added to D at this point.

Multiple-Target Damage Reduction

single-target spells = 1.0
-ga spells on a single target = 1.0
-ga spells on 2 to 9 targets = 0.9 - 0.05T where T = number of targets
-ga spells on 10+ targets = 0.4
(Also applies to -ja spells)

Note: Magical Blue Magic spells and all AoE magical Blood Pacts are not subject to the multi-target damage penalty. It is unknown if Manifestation Drain is affected by this penalty.

Resist

resist = 1, 1/2, 1/4, 1/8, or 1/16

Staff Bonus

See Magic Affinity.

Day of the Week | Weather Bonus

Day | Weather Bonus is calculated as:

• 1.0
  
• +0.05 for Twilight Cape when magic matches the current day or weather.
  
• +0.05 for Sorcerer's Tonban when magic matches the current day.
  
• +0.03 for Zodiac Ring when magic matches the current day.
  

plus approximately a 1/3 chance for one of the following:

• +0.1 for magic of the day
  
• -0.1 for magic weak to the current day
  

plus approximately a 1/3 chance for one of the following:

• +0.1 for magic matching single weather
  
• -0.1 for magic weak to single weather
  
• +0.25 for magic matching double weather
  
• -0.25 for magic weak to double weather
  

The day and weather components are guaranteed to take effect when wearing an obi matching that day or weather.
Helix spells calculate day and weather bonuses at 100% at all times regardless of equipment. Weather spells do stack with natural weather and day but not beyond the natural cap of 20 for double weather and 10 for day. Also of note is this effect can work against you as weather and day of the opposing element will negatively impact your helix damage even with weather of the supporting element active in the spell form.
While DWB can only naturally reach 1.35, Zodiac Ring and Twilight Cape can raise it to 1.43 if equipped together on matching day with double weather.

Magic Burst Bonus

MB bonus is 1.0 for no MB and 1.3 for a 2-WS renkei, gaining 5% per extra WS in the renkei series (i.e. 1.35, 1.4 etc)
Sorcerer's Gloves multiply the magic burst bonus by 1.05.
Static Earring multiplies the magic burst bonus by 1.05.
ex. floor(floor(floor(floor(... * MB) * Sorc.Gloves) * St.Earring) * ...) -> floor(floor(floor(floor(... * 1.3) * 1.05) * 1.05) * ...)

Magic Attack Bonus / Magic Defense Bonus

MAB is divided by MDB.

MAB is as we know it (i.e. MAB I = 1.2, MAB II = 1.24 etc). Items with the description "Magic Atk. Bonus"+X means to add X/100 to the current MAB. For example, Moldavite Earring which states "Magic Atk. Bonus"+5 means to add 0.05. Correct element potency merits are +2 MAB per merit, which adds 0.02.

MDB is 1.0 if not present and depends on the target of the magic.

After calculating the ratio of MAB to MDB, this term is truncated to two decimal places.

Target Magic Damage Adjustment

Target Magic Damage Adjustment means exactly what it sounds like. Certain targets are designed to take more or less % damage. Values for this portion of the equation appear to use the 256 number system. The base value is 1 (256/256) and is adjusted according to the fractional values in the charts below. The values are added together in the presence of more than one adjustment.
ex. Ahriman have a TMDA value of (1 - 64/256) = 192/256
ex. An Evil Weapon with Shell has a TMDA value of (1 - 32/256 - 24/256) = 200/256
Note: For player targets, this value is capped at 128/256 (50%).

Monster	Base Adjustment (%)	Adjustment (256ths)
Ahriman	75%	-64/256
Flans	125%	+64/256
Cardians	75%	-64/256
Corse	75%	-64/256
Demons	75%	-64/256
Evil Weapons	87.5%	-32/256
Ghrahs	87.5%	-32/256
Magic Pots	50%	-128/256
Lamiae	87.5%	-32/256
Effect	Base Adjustment (%)	Adjustment (256ths)
Shell	90.6%	-24/256
Shell II	85.9%	-36/256
Shell III	81.2%	-48/256
Shell IV	78.1%	-56/256
Shell V (1 merit)	75.8%	-62/256
Shell V (2 merits)	75%	-64/256
Shell V (3 merits)	74.2%	-66/256
Shell V (4 merits)	73.4%	-68/256
Shell V (5 merits)	72.6%	-70/256
Bubble Curtain	50%	-128/256
Shining Ruby	96%	-10/256
Player Equipment	varies	varies

Helixes

Follow the same rule as above but the initial Damage dealt is repeated a number of times in 10 second intervals. Weather seems to have little to no effect on duration.