Magic Damage

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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, 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 Light-WHM-Icon.gif 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 ~ 299
    • dINT = 300 ~ 399
    • dINT = 400 ~ 499
    • dINT = 500 ~ 599
    • dINT > 600
  • 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. On tier 2 single target nukes, the damage increase from INT caps when dINT is 200, Tier 3 at dINT 300 etc... Up to Tier 6 theoretically capping out at 600 dINT. A moment of silence for the Wild Rabbits (INT = 6) in Ronfaure used to test these numbers...
  • 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 ΔINT200-299 ΔINT300-399 ΔINT400-499 ΔINT500-599 ΔINT600+ ΔINTCap
V0 M V50 M V100 M V200 M V300 M V400 M V500 M V600+ VCap
Stone 10 2 110 1 160 0 160
Water 25 1.8 115 1 165 0 165
Aero 40 1.6 120 1 170 0 170
Fire 55 1.4 125 1 175 0 175
Blizzard 70 1.2 130 1 180 0 180
Thunder 85 1 135 1 185 0 185
Stone II 100 3 250 2 350 1 450 0 450
Water II 120 2.8 260 1.9 355 1 455 0 455
Aero II 140 2.6 270 1.8 360 1 460 0 460
Fire II 160 2.4 280 1.7 365 1 465 0 465
Blizzard II 180 2.2 290 1.6 370 1 470 0 470
Thunder II 200 2 300 1.5 375 1 475 0 475
Stone III 200 4 400 3 550 2 750 1 850 0 850
Water III 230 3.7 415 2.9 560 1.95 755 1 855 0 855
Aero III 260 3.4 430 2.8 570 1.9 760 1 860 0 860
Fire III 290 3.1 445 2.7 580 1.85 765 1 865 0 865
Blizzard III 320 2.8 460 2.6 590 1.8 770 1 870 0 870
Thunder III 350 2.5 475 2.5 600 1.75 775 1 875 0 875
Spell ΔINT0-49 ΔINT50-99 ΔINT100-199 ΔINT200-299 ΔINT300-399 ΔINT400-499 ΔINT500-599 ΔINT600+ ΔINTCap
V0 M V50 M V100 M V200 M V300 M V400 M V500 M V600+ VCap
Stone IV 400 5 650 4 850 3 1150 2 1350 1 1450 0 1450
Water IV 440 4.7 675 3.9 870 2.95 1165 1.99 1364 1 1464 0 1464
Aero IV 480 4.4 700 3.8 890 2.9 1180 1.98 1378 1 1478 0 1478
Fire IV 520 4.2 730 3.7 915 2.85 1195 1.97 1397 1 1497 0 1497
Blizzard IV 560 3.9 755 3.6 935 2.8 1210 1.96 1411 1 1511 0 1511
Thunder IV 600 3.6 780 3.5 955 2.75 1225 1.95 1425 1 1525 0 1525
Stone V 650 6 950 5 1200 4 1600 3 1900 2 2100 1 2200 0 2200
Water V 700 5.6 980 4.74 1217 3.95 1612 2.99 1911 1.99 2110 1 2210 0 2210
Aero V 750 5.2 1010 4.5 1235 3.9 1625 2.98 1923 1.98 2121 1 2221 0 2221
Fire V 800 4.8 1040 4.24 1252 3.85 1637 2.97 1934 1.97 2131 1 2231 0 2231
Blizzard V 850 4.4 1070 4 1270 3.8 1650 2.96 1946 1.96 2142 1 2242 0 2242
Thunder V 900 4 1100 3.74 1287 3.75 1662 2.95 1957 1.95 2152 1 2252 0 2252
Stone VI 950 7 1300 6 1600 5 2100 4 2500 3 2800 2 3000 1 3100 3100
Water VI 1010 6.5 1335 5.9 1630 4.9 2120 3.9 2510 2.95 2805 1.99 3004 1 3104 3104
Aero VI 1070 6 1370 5.8 1660 4.8 2140 3.8 2520 2.9 2810 1.98 3008 1 3108 3108
Fire VI 1130 5.5 1405 5.7 1690 4.7 2160 3.7 2530 2.85 2815 1.97 3012 1 3112 3112
Blizzard VI 1190 5 1440 5.6 1720 4.6 2180 3.6 2540 2.8 2820 1.96 3016 1 3116 3116
Thunder VI 1250 4.5 1475 5.5 1750 4.5 2200 3.5 2550 2.75 2825 1.95 3020 1 3120 3120
Spell ΔINT0-49 ΔINT50-99 ΔINT100-199 ΔINT200-299 ΔINT300-399 ΔINT400-499 ΔINT500-599 ΔINT600+ ΔINTCap
V0 M V50 M V100 M V200 M V300 M V400 M V500 M V600+ VCap
Stonega 60 3 210 2 310 1 410 0 410
Waterga 80 2.8 220 1.9 315 1 415 0 415
Aeroga 100 2.6 230 1.8 320 1 420 0 420
Firaga 120 2.4 240 1.7 325 1 425 0 425
Blizzaga 160 2.2 270 1.6 350 1 450 0 450
Thundaga 200 2 300 1.5 375 1 475 0 475
Stonega II 250 4 450 3 600 2 800 1 900 0 900
Waterga II 280 3.7 465 2.9 610 1.95 805 1 905 0 905
Aeroga II 310 3.4 480 2.8 620 1.9 810 1 910 0 910
Firaga II 340 3.1 495 2.7 630 1.85 815 1 915 0 915
Blizzaga II 370 2.8 510 2.6 640 1.8 820 1 920 0 920
Thundaga II 400 2.5 525 2.5 650 1.75 825 1 925 0 925
Stonega III 500 5 750 4 950 3 1250 2 1450 1 1550 0 1550
Waterga III 540 4.7 775 3.9 970 2.95 1265 1.99 1464 1 1564 0 1564
Aeroga III 580 4.4 800 3.8 990 2.9 1280 1.98 1478 1 1578 0 1578
Firaga III 620 4.2 830 3.7 1015 2.85 1295 1.97 1497 1 1597 0 1597
Blizzaga III 660 3.9 855 3.6 1035 2.8 1310 1.96 1511 1 1611 0 1611
Thundaga III 700 3.6 880 3.5 1055 2.75 1325 1.95 1525 1 1625 0 1625
Spell ΔINT0-49 ΔINT50-99 ΔINT100-199 ΔINT200-299 ΔINT300-399 ΔINT400-499 ΔINT500-599 ΔINT600+ ΔINTCap
V0 M V50 M V100 M V200 M V300 M V400 M V500 M V600+ VCap
Stoneja 750 6 1050 5 1300 4 1700 3 2000 2 2200 1 2300 0 2300
Waterja 800 5.6 1080 4.75 1317 3.95 1712 2.98 2010 2 2210 1 2310 0 2310
Aeroja 850 5.2 1110 4.5 1335 3.9 1725 2.96 2021 2 2221 1 2321 0 2321
Firaja 900 4.8 1140 4.25 1352 3.85 1737 2.94 2031 2 2231 1 2331 0 2331
Blizzaja 950 4.4 1170 4 1370 3.8 1750 2.92 2042 2 2242 1 2342 0 2342
Thundaja 1000 4 1200 3.75 1387 3.75 1762 2.9 2052 2 2252 1 2352 0 2352
Stonera 150 3 300 2 400 1 Verification Needed
Watera 180 2.8 320 1.9 415 1 Verification Needed
Aerora 210 2.6 340 1.8 430 1 Verification Needed
Fira 240 2.4 360 1.7 445 1 Verification Needed
Blizzara 270 2.2 380 1.6 460 1 Verification Needed
Thundara 300 2 400 1.5 475 1 Verification Needed
Stonera II 350 4 550 3 700 2 Verification Needed
Watera II 390 3.7 575 2.9 720 1.95 Verification Needed
Aerora II 430 3.4 600 2.8 740 1.9 Verification Needed
Fira II 470 3.1 625 2.7 760 1.85 Verification Needed
Blizzara II 510 2.8 650 2.6 780 1.8 Verification Needed
Thundara II 550 2.5 675 2.5 800 1.75 Verification Needed
Stonera III Verification Needed
Watera III Verification Needed
Aerora III Verification Needed
Fira III Verification Needed
Blizzara III Verification Needed
Thundara III Verification Needed
Spell ΔINT0-49 ΔINT50-99 ΔINT100-199 ΔINT200-299 ΔINT300-399 ΔINT400-499 ΔINT500-599 ΔINT600+ ΔINTCap
V0 M V50 M V100 M V200 M V300 M V400 M V500 M V600+ VCap
Ancient Magic 700 2 800 2 900 2 1100 2 1300 2 1500 2 1700 2 1900 Verification Needed 1900
Ancient Magic II 800 2 900 2 1000 2 1200 2 1400 2 1600 2 1800 2 2000 Verification Needed 2000
Comet 1000 4 1200 3.75 1387 3.5 1737 3 2037 2 2237 1 2337 0 2337
Helix II Spells 75 2 175 1 225 0Verification Needed
ΔINT0-77 ΔINT78-234 ΔINT235+
Helix I Spells 25 1Verification Needed 103Verification Needed 0.5Verification Needed 181Verification Needed 0Verification Needed
  • Table Updated 1/13/2022
  • Still need Geo and Helix Spell values.

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, also referred to as "Elemental Magic Attack Bonus", adds damage in a separate multiplier term from all standard forms of Magic Attack Bonus.

The base value for this term when no Affinity gear is present = 1.0.

Affinity has three primary sources:

  • Elemental staves created through Trial of the Magians (generally labeled "Affinity");
  • Certain Atma and Atmacite;
  • Several newer pieces of equipment, all added in the item level era (generally labeled 'Elemental "Magic Atk. Bonus"').

For Magian Staves:

  • 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.

Elemental Magic Attack Bonus from gear is additive with this term. This statistic is found on gear such as Pixie Hairpin +1 and Weatherspoon Ring.

Equipment that provides Elemental Magic Attack Bonus include:

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.

Consecutive Elemental Damage Penalty

Also known as the "Nuke Wall", there is a penalty applied to any elemental magic [1] cast on a monster for 5 seconds after that first instance.

  • The 2nd nuke within 5 seconds deals -20% damage. While further nukes within 5 seconds deal -40~50% damage, varying with the target. [2] [3]
    • More testing is required to understand this variance. Information Needed
    • The full damage reduction penalty is not reached until ~2,500 damage has been dealt. It scales linearly until reaching said value. [4] Verification Needed
  • Rayke with a corresponding elemental rune will reduce this penalty to 20% for all affiliated nukes, regardless of number of runes expended.
  • This wall only applies to Notorious Monsters.
  • The elemental damage from Skillchains is excluded from this.

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
  • 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
    • Iridal Staff/Chatoyant Staff with matching weather, and weather proc: +0.05/+0.1 (respectively)
    • Ascendant/opposed single weather and spell proc: -0.1
    • Ascendant/opposed double weather and spell proc: -0.25
    • Iridal Staff/Chatoyant Staff with ascendant/opposed weather, and weather proc: -0.05/-0.1 (with respect to staff)
  • Twilight Cape and matching weather proc or matching day proc (will never apply twice): +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 1.25 for a two-stage Skillchain, with an additional 0.1 for every additional stage.

  • Magic Burst:
    • No Magic Burst: MB = 1.0
    • 2-stage Skillchain: MB = 1.35
    • 3-stage Skillchain: MB = 1.45
    • X-stage Skillchain:

MB = 1.25 + (0.1 × X)

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

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

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