Magic damage

### Magic Damage Equation

Damage Dealt = D × MTDR × Staff × Affinity × Resist × Resistance Rank Reduction × MB × MBB × Day & Weather × MAB/MDB × TMDA × Potency Multipliers

Damage Dealt is calculated by multiplying the following terms in order (see above). After each multiplication step, the product is floored to the next lowest integer before continuing to the next multiplier. Each term after D starts with a base of 1.0 and is increased or decreased by caster and target stats and attributes as well as other effects.

1. **D**: INT-adjusted base spell damage
2. **MTDR**: Multiple-Target Damage Reduction (for area of effect spells)
3. **Staff**: Elemental staff hidden damage bonus multiplier
4. **Affinity**: Elemental affinity damage bonus multiplier (from Magian Staves, Atma, Atmacite, and Elemental "Magic Atk. Bonus")
5. **Resist**: Reduction of spell damage due to resist states
6. **Resistance Rank Reduction**: Reduction of spell damage due to resistance rank
7. **MB**: Magic Burst
8. **MBB**: Magic Burst Bonus
9. **Day & Weather**: Day and Weather multipliers, including Iridescence and equipment modifiers
10. **MAB / MDB**: Caster Magic Attack Bonus factor divided by target's Magic Defense Bonus factor
11. **TMDA**: Target Magic Damage Adjustment (Magic Damage Taken reduction)
12. **Potency Multipliers**: e.g. Ebullience, Klimaform Bonus, etc.

## 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.

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:

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.

### Resist

There are four possible Resist states for spells which deal magical damage. The likelihood of increasing resist states is dependent on the caster's Magic Accuracy and the target's Magic Evasion (the combined influence of the two determines the caster's Magic Hit Rate).

* Unresisted: Resist = 1.0
* 1/2 Resist: Resist = 0.5
* 3/4 Resist: Resist = 0.25
* 7/8 Resist: Resist = 0.125

Note that for spells with multiple targets, the resist value for each target is determined independently.

### Resistance Rank Reduction

When a monster's resistance rank to an element is 50% or lower, an additional forced resist of 1/2 = 50% is added onto the previous resist, calculated multiplicatively.

### Staff

* For Chatoyant Staff or HQ Staff matching element (e.g. Vulcan's Staff and a fire-elemental spell), Staff = 1.15
* For Iridal Staff or NQ Staff matching element (e.g. Fire Staff and a fire-elemental spell), Staff = 1.1
* For NQ Staff of the ascendant or opposed element (e.g. Earth Staff and a lightning-elemental spell) Staff = 0.9
* For HQ Staff of the ascendant or opposed element (e.g. Terra's Staff and a lightning-elemental spell), Staff = 0.85
* For all other weapons, Staff = 1.0

### Day of the Week | Weather Bonus

Day | Weather Bonus is calculated as:

* 1.0
* +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%).

## 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.