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Magic Damage

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Magic Damage Equation

Damage Dealt = D × MTDR × Staff × Affinity × SDT × Resist × 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 muliplier (from staff and/or atma/atmacite)
  5. SDT: Species Damage Taken
  6. Resist: Reduction of spell damage due to resist states.
  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, Goetia +2 Set Bonus, etc.

Factors

D: INT-adjusted Base Damage

Definition of Variables

  • V: Every individual damage-dealing magic spell has a base damage value denoted as V.
  • dINT: dINT represents the difference between caster and target INT: (Caster's INT - Target's INT).
  • M: Every individual damage-dealing magic spell has several INT multiplier values denoted as M for different dINT ranges.
    • Note: For offensive white magic, substitute dMND for dINT (Caster's MND - Target's MND)
  • mDMG: mDMG represents the "Magic Damage" statistic obtained from equipped weapons and armor.
  • D: INT and "Magic Damage" adjusted base spell damage calculated from the terms above.

Calculating D

D = mDMG + V + (dINT × M)

  • The calculation of D is a piecewise function with the multiplier M changing at the following INT levels:
    • dINT = 0 ~ 49
    • dINT = 50 ~ 99
    • dINT = 100 ~ 199
    • dINT > 200
  • When determining D, the appropriate V and M values must be applied depending on the INT difference. For example, with dINT = 134, V100 should be chosen for the base damage, and the M which corresponds to dINT = 100 ~ 199 should be chosen as the multiplier. When choosing a V value, reduce the dINT by the amount factored into the V value to come up with the correct result (for example, at 134 INT, when using V100 in the calculation, use dINT = 134-100 = 34)

dINT = 134: D = mDMG + V100 + (34 × M100-199)

Notes:

  • For dINT < 0, reduced M values apply. With a negative dINT, calculated value for D will be lower than V, potentially even 0.
  • On tier 1 single target nukes, the damage increase from INT caps when dINT is 100, so additional INT beyond this level will not add additional damage. There are likely higher tier dINT caps (200 or higher) on higher tier nukes, but these are difficult to achieve against high level foes so they are not normally relevant. The values in the table below are determined for dINT up to at least 250.
  • As shown by the multipliers below, the impact of INT on the adjusted base damage term is greatest for higher tier nukes, and for "lower level" elements (highest impact on Stone spells, then Water spells, etc.).
Elemental Magic
Spell ΔINT0-49 ΔINT50-99 ΔINT100-199 ΔINT200+
V0 M V50 M V100 M V200 M
Stone 10 2 110 1 160 0
Water 25 1.8 115 1 165 0
Aero 40 1.6 120 1 170 0
Fire 55 1.4 125 1 175 0
Blizzard 70 1.2 130 1 180 0
Thunder 85 1 135 1 185 0
Stone II 100 3 250 2 350 1 450 0
Water II 120 2.8 260 1.9 355 1 455 0
Aero II 140 2.6 270 1.8 360 1 460 0
Fire II 160 2.4 280 1.7 365 1 465 0
Blizzard II 180 2.2 290 1.6 370 1 470 0
Thunder II 200 2 300 1.5 375 1 475 0
Stone III 200 4 400 3 550 2 750 1
Water III 230 3.7 415 2.9 560 1.95 755 1
Aero III 260 3.4 430 2.8 570 1.9 760 1
Fire III 290 3.1 445 2.7 580 1.85 765 1
Blizzard III 320 2.8 460 2.6 590 1.8 770 1
Thunder III 350 2.5 475 2.5 600 1.75 775 1
Stone IV 400 5 650 4 850 3 1150 2
Water IV 440 4.7 675 3.9 870 2.95 1165 2
Aero IV 480 4.4 700 3.8 890 2.9 1180 2
Fire IV 520 4.2 730 3.7 915 2.85 1195 2
Blizzard IV 560 3.9 755 3.6 935 2.8 1210 2
Thunder IV 600 3.6 780 3.5 955 2.75 1225 2
Stone V 650 6 950 5 1200 4 1600 3
Water V 700 5.6 980 4.74 1217 3.95 1612 3
Aero V 750 5.2 1010 4.5 1235 3.9 1625 3
Fire V 800 4.8 1040 4.24 1252 3.85 1637 3
Blizzard V 850 4.4 1070 4 1270 3.8 1650 3
Thunder V 900 4 1100 3.74 1287 3.75 1662 3
Stonega 60 3 210 2 310 1 410 0
Waterga 80 2.8 220 1.9 315 1 415 0
Aeroga 100 2.6 230 1.8 320 1 420 0
Firaga 120 2.4 240 1.7 325 1 425 0
Blizzaga 160 2.2 270 1.6 350 1 450 0
Thundaga 200 2 300 1.5 375 1 475 0
Stonega II 250 4 450 3 600 2 800 1
Waterga II 280 3.7 465 2.9 610 1.95 805 1
Aeroga II 310 3.4 480 2.8 620 1.9 810 1
Firaga II 340 3.1 495 2.7 630 1.85 815 1
Blizzaga II 370 2.8 510 2.6 640 1.8 820 1
Thundaga II 400 2.5 525 2.5 650 1.75 825 1
Stonega III 500 5 750 4 950 3 1250 2
Waterga III 540 4.7 775 3.9 970 2.95 1265 2
Aeroga III 580 4.4 800 3.8 990 2.9 1280 2
Firaga III 620 4.2 830 3.7 1015 2.85 1295 2
Blizzaga III 660 3.9 855 3.6 1035 2.8 1310 2
Thundaga III 700 3.6 880 3.5 1055 2.75 1325 2
Stoneja 750 6 1050 5 1300 4 1700 3
Waterja 800 5.6 1080 4.75 1317 3.95 1712 3
Aeroja 850 5.2 1110 4.5 1335 3.9 1725 3
Firaja 900 4.8 1140 4.25 1352 3.85 1737 3
Blizzaja 950 4.4 1170 4 1370 3.8 1750 3
Thundaja 1000 4 1200 3.75 1387 3.75 1762 3
Stonera 150 3 300 2 400 1
Watera 180 2.8 320 1.9 415 1
Aerora 210 2.6 340 1.8 430 1
Fira 240 2.4 360 1.7 445 1
Blizzara 270 2.2 380 1.6 460 1
Thundara 300 2 400 1.5 475 1
Stonera II 350 4 550 3 700 2
Watera II 390 3.7 575 2.9 720 1.95
Aerora II 430 3.4 600 2.8 740 1.9
Fira II 470 3.1 625 2.7 760 1.85
Blizzara II 510 2.8 650 2.6 780 1.8
Thundara II 550 2.5 675 2.5 800 1.75
Ancient Magic 700 2 800 2 900 2 1100 2
Ancient Magic II 800 2 900 2 1000 2 1200 2
Comet 1000 4 1200 3.75 1387 3.5

MTDR: Multiple-Target Damage Reduction

  • For single-target spells, MTDR = 1.0
  • For Area of Effect spells with one target, MTDR = 1.0
  • For Area of Effect spells with T targets, 2 ≤ T ≤ 10,

MTDR = 0.9 - 0.05T

  • For Area of Effect spells with 10 or more targets. MTDR = 0.4
    • For their damage calculation, single target damaging spells made area of effect by Manifestation are affected by MTDR.

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

Affinity

Affinity adds damage in a separate multiplier term. When affinity is present, it starts at a base of 5% ("Affinity +0"), with 5% additional for each affinity level. Affinity from equipment can only be gained from elemental staves created through Trial of the Magians.

  • No affinity: Affinity = 1.0
  • Damage affinity +1: Affinity = 1.1
  • Damage affinity +2: Affinity = 1.15
  • Damage affinity +3: Affinity = 1.20
  • Damage affinity +4: Affinity = 1.25
  • Damage affinity +5: Affinity = 1.30
  • Damage affinity +6: Affinity = 1.35

Affinity in the form of element-specific attack power from Atma or Atmacite is additive with this term.

Species Damage Taken

Certain monster species will always take more or less damage from a particular element or elements. This is different than monsters being resistant or susceptible to an element which simply means they are more or less likely to resist. Reference individual monster or family pages (see Bestiary) for specific monster types. As an example, Sahagin have a SDT = 0.5 (128/256) for water elemental damage, meaning they take 50% less damage from water elemental spells prior to any resist reduction.

Note this is a different term than Target Magic Damage Adjustment, and applies only to certain elements.

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.

Day & Weather

Day & Weather is calculated with a base of 1.0 and additional values added or subtracted depending on the current day of the week, weather, or certain equipment pieces (E.g. Elemental Obis).
Note that in most cases, the day or weather effect must "proc" for the bonus to be received - this is a random occurrence when the day or weather matches the spell's element (bonus damage) or is ascendant/opposed to the spell's element (reduced damage). This proc may be forced via wearing an Elemental Obi.

  • Base value: 1.0
  • Day
    • Matching day and spell proc: +0.1
    • Ascendant/opposed day and spell proc: -0.1
    • Sorcerer's Tonban/+1 and matching day and spell: +0.05
    • Zodiac Ring and matching day and spell: +0.03
  • Weather
    • Matching single weather and spell proc: +0.1
    • Matching double weather and spell proc: +0.25
    • Matching double weather and day spell proc: +0.35
    • Ascendant/opposed single weather and spell proc: -0.1
    • Ascendant/opposed double weather and spell proc: -0.25
    • Iridescence proc: +0.1
  • Twilight Cape and matching weather or day and spell proc: +0.05

The Day & Weather factor cannot exceed 1.4.
Note: Elemental Obis and Helix spells force weather, day, and Iridescence procs.

MB: Magic Burst

The Magic Burst multiplier is dependent on the number weapon skills which resulted in the formation of the Skillchain which was magic bursted. This starts at a base of 1.3 for a two-stage Skillchain, with an additional 0.05 for every additional stage.

MB = 1.2 + (0.05 × X)

  • No Magic Burst: MB = 1.0

MBB: Magic Burst Bonus

Magic Burst Bonus is calculated as:

MBB = 1.0 + Gear + Atma/Atmacite + AMII Merits + Trait

  • Gear: See Magic Burst for a table of gear related bonuses.
  • Atma/Atmacite: See Atma or Atmacite for tables of atma/atmacite related bonuses.
  • AMII Merits: For Ancient Magic II, additional merits beyond the first yield a bonus on the MBB factor.
    • AMII Merits = 0.03 when a level 2 Ancient Magic II spell is used in a magic burst.
    • AMII Merits = 0.06 when a level 3 Ancient Magic II spell is used in a magic burst.
    • AMII Merits = 0.09 when a level 4 Ancient Magic II spell is used in a magic burst.
    • AMII Merits = 0.12 when a level 5 Ancient Magic II spell is used in a magic burst.
  • Trait: See Magic Burst Bonus for trait levels. This trait varies from 0.05 to 0.13 depending on the trait level.
    • Example: A level 90 black mage would have Magic Burst Bonus IV, Trait = 0.11
  • No Magic Burst: MBB = 1.0

The overall term caps at 1.4 prior to the addition of effects from the Magic Burst Bonus trait, for an absolute cap of 1.53 maximum at level 97 or higher BLM.

MAB/MDB: Magic Attack Bonus / Magic Defense Bonus

The MAB/MDB factor combines the effects of the caster's MAB and the target's MDB.

The caster MAB multiplier term is calculated as follows:

cMAB = 1 + (caster Magic Attack Bonus ÷ 100)

Example: A player with Magic Attack Bonus I trait (+20), and Moldavite Earring (+5) equipped, would have a MAB multiplier of 1 + 25/100 = 1.25

Note: BLM job-specific element potency merits add +2 MAB for the matching element per merit.

The target MDB divisor term is calculated as follows:

tMDB = 1 + (target Magic Defense Bonus ÷ 100)

Example: An enemy with 50 Magic Defense Bonus would have a MDB divisor of 1 + 50/100 = 1.5

The MAB/MDB term is simply the caster MAB value divided by the target MDB value:

MAB/MDB = cMAB ÷ tMDB

Example: For a player with 75 Magic Attack Bonus casting magic against a target with 25 Magic Defense Bonus, MAB/MDB = 1.75/1.25 = 1.4

TMDA: Target Magic Damage Adjustment

Certain specific enemies or families of monsters have traits which cause them to take more or less magical damage on a percentage basis, generally referred to as the "Magic Damage Taken" statistic. Values for Magic Damage Taken are determined as a fraction of 256.

The base value of TMDA is 1 (256/256) and this value is adjusted according to the fractional values for specific monster types or monster families, and other buffing effects the monster might have.

The effects of Shell Spells active on targets are included in the Magic Damage Taken term.

Several examples follow, reference individual monster or family pages within the Bestiary for monster-specific information:

  • Flan-type monsters take +64/256 (+25%) magic damage, TMDA = 1.25
  • Ghrah-type monsters take -32/256 (-12.5%) magic damage, TMDA = 0.875
  • An Ahriman-type monster (-64/256) with Shell III active (-48/256) takes -112/256 (-43.75%) magic damage, TMDA = 0.5625

Potency Multipliers

Other potency multipliers are applied individually to the overall equation, with flooring after each multiplication step. Example multipliers include:

Example Calculations

Example Calculation 1: Stone II

The following example is damage calculation for the spell Stone II.

Assumed caster statistics are:

  • Magic Attack Bonus +150
  • "Magic Damage" = 195 (e.g. Atinian Staff)
  • INT: 220

Assumed target statistics are:

  • Magic Defense Bonus +0
  • Magic Damage Taken -12.5%
  • INT: 100

dINT = 220-100 = 120

The terms in order (ignoring terms which are 1.0 for this calculation):

  1. D: 195 + 350 + (20 * 1) = 565
  2. MAB/MDB: 150 caster MAB, 0 target MDB = (100+150)/(100+0) = 2.5 multiplier | 565 * 2.5 = 1412 (floored)
  3. TMDA: 12.5% target MDT = 0.875 multiplier | 1412 * 0.875 = 1235 (floored)

Final damage: 1235 unresisted, with possible resisted damage of 617 (1/2), 308 (3/4), or 154 (7/8).

Example Calculation 2: Thundaja on multiple targets

The following example is damage calculation for the spell Thundaja cast on three targets.

Assumed caster statistics are:

  • Magic Attack Bonus +100
  • "Magic Damage" = 0
  • Lightning magic potency (BLM merits x5) = +10 MAB
  • INT: 180
  • Apamajas I (Lightning damage affinity +6)
  • Thunder weather (single) + Rairin Obi to guarantee proc

Assumed target statistics are:

  • Magic Defense Bonus +25
  • Magic Damage Taken -0%
  • INT: 100

dINT = 180-100 = 80

The terms in order (ignoring terms which are 1.0 for this calculation):

  1. D: 0 + 1200 + (30 * 3.75) = 1312 (floored)
  2. MTDR = 0.75 for three targets | 1312 * 0.75 = 984 per target (floored)
  3. Affinity: 1.35 for affinity +6 | 984 * 1.35 = 1328 per target (floored)
  4. Day/Weather: Weather bonus proc, 1.1 | 1328 * 1.1 = 1460 per target (floored)
  5. MAB/MDB: 110 caster MAB, 25 target MDB = (100+110)/(100+25) = 1.68 multiplier | 1460 * 1.68 = 2452 per target (floored)

Final damage: 2452 per target unresisted, with possible resisted damage of 1226 (1/2), 613 (3/4), or 306 (7/8).

Example Calculation 3: Freeze II magic burst

The following example is damage calculation for the spell Freeze II magic bursted on one target after a 2-step skillchain.

Assumed caster statistics are:

  • BLM Level 99 (Magic Burst Bonus +13% from job trait)
  • Magic Burst Bonus gear (+10%)
  • Magic Damage +191 (e.g. Atinian Staff)
  • Magic Attack Bonus +125
  • Ice magic potency (BLM merits x3) +6 MAB
  • Fully merited Freeze II (MB damage +12%)
  • INT: 210

Assumed target statistics are:

  • Magic Defense Bonus +25
  • Magic Damage Taken -12.5%
  • INT: 90

dINT = 210-90 = 120

The terms in order (ignoring terms which are 1.0 for this calculation):

  1. D: 191 + 900 + (20 * 2.0) = 1131
  2. Magic Burst: 1.3 for 2-stage SC | 1131 * 1.3 = 1470 (floored)
  3. Magic Burst Bonus: 1.35 (13% trait, 10% gear, 12% Freeze II merits) | 1470 * 1.35 = 1984
  4. MAB/MDB: 131 caster MAB, 25 target MDB = (100+131)/(100+25) = 1.848 multiplier | 1984 * 1.848 = 3666 (floored)
  5. TMDA (MDT): 12.5% damage reduction = 0.875 multiplier | 3666 * 0.875 = 3207 (floored)

Final damage: 3207 unresisted, with possible resisted damage of 1603, 801, or 400.

Sources

Broken Link (BG)
Magic Damage Formulae (Sloppysue, Alla)
Unsure, broken link
Magic Information Compilation (Yugl, BG)
How to calculate MDB/-MDT Quickly (Suiram, BG)



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