The Complete Damage Formula for Black & White

1. Introduction
2. Main concepts
   1. General flow of damage calculation
   2. How to apply a modifier
   3. How to chain modifiers
   4. The multi-target modifier
   5. The weather modifier
   6. Critical hits
   7. The random factor
   8. STAB
   9. Type effectiveness
   10. Effect of a burn
   11. Final modifier
3. The base power
   1. Triggers for variable base power
   2. Modifiers for the base power
4. User attack stat
   1. Base value
   2. Boost level
   3. Attack modifiers
5. Target defense stat
   1. Base value
   2. Boost level
   3. Sandstorm modifier
   4. Defense modifiers
6. Special cases

Introduction

In Generation IV, the damage formula was derived empirically by X-Act from running it countless times, an approach that is both tedious and prone to errors. The good understanding of the ARM code for Black & White allows us to document the damage formula based on the actual source code of the game. It doesn't guarantee that we didn't make any mistake (interpreting assembly language is in itself a tricky task) but having the documented source along with the formula backs up our claims and allows anyone who spots any error to fix it by themselves.

Main concepts

General flow of damage calculation

Roughly speaking, the damage formula in Pokémon is a big multiplication, each factor representing the user's level and attack stat, the foe's defense stat, and a bunch of factors for STAB, held items, abilities and other field effects. In a perfect world where ARM CPUs could work on real numbers, it would be possible to multiply each factor in any order and get the same result, but in practice the game will round some multiplications and truncate others, meaning that in order to get accurate damage results, it is of utmost importance to perform the multiplication in the same order as the game and using the same rounding methods. Even though rounding errors might not sound like a big problem, they will be amplified at each step, and a few factors such as Reflect and Life Orb in a double battle can cause a significant difference between an unrounded and a properly rounded calculation.

There are three main parameters for damage calculation: the user's attack stat, the target's defense stat and the move's base power. To compute these stats, the game starts from a base value and apply a modifier to reflect the various effects that can alter the base value. This modifier is obtained by running through a list of short functions called triggers that are called based on the current active effects on field. Different triggers can modify the same modifier before it is applied, this operation is called chaining and is explained below.

Once the main parameters are set, the general steps of the calculation are as follows:

BaseDamage = ((((2 × Level) ÷ 5 + 2) * BasePower * [Sp]Atk) ÷ [Sp]Def) ÷ 50 + 2

1. Apply the multi-target modifier
2. Apply the weather modifier
3. In case of a critical hit, double the value
4. Alter with a random factor
5. Apply STAB modifier
6. Alter with type effectiveness
7. Alter with user's burn
8. Make sure damage is at least 1
9. Apply the final modifier

In this article, ÷ always denotes the in-game unsigned divmod function, i.e. the unrounded/truncated integer division. By contrast, "apply a modifier" is a rounded operation explained in the next subsection.

There are some exceptions to the formula above that correspond to the set of triggers at the very top of the damage function; they are detailed in a separate section.

How to apply a modifier

A modifier is a 16 bit fixed point factor, i.e. a fraction whose divisor is always 0x1000 (4096). For instance, 0x14cc is the modifier for Life Orb (0x14cc/0x1000 is about 1.3). Applying the modifier M to the damage value D means multiplying D by M and dividing the result by 0x1000; then if the decimal part is ≤0.5, round the result down, otherwise round it up. Simply put: D' = round(D * M / 0x1000)

How to chain modifiers

Recall that modifiers for a given parameters are computed by the triggers for that parameter. This means that when multiple triggers apply, you have to chain the modifier for the parameter, starting from 0x1000. If the current modifier is M and you want to chain with another modifier M', the resulting modifier would be: M'' = ((M * M') + 0x800) >> 12

The multi-target modifier

This modifier doesn't have any trigger and is set to 0xC00 if the move has more than one target and 0x1000 otherwise. Being a target is independent of all accuracy and effectiveness checks, but a fainted Pokémon on the field will not count as a target.

The weather modifier

Even though the weather modifier has its own set of triggers listed below, they never affect the actual value of the modifier: a water move used during rain or a fire move used during intense sunlight will use 0x1800 as modifier, while a fire move used during rain or a water move during intense sunlight will use 0x800.

Trigger address	Trigger description
21d9850	Cancel weather if any Pokémon on field has Air Lock or Cloud Nine.
21d9084	Internal.

Critical hits

Trigger address	Trigger description
21d9be8	Super Luck: increase user's critical hit level by 1.
21d9bc4	Battle Armor / Shell Armor: if the target has either of these abilities, bypass critical hit checks.
21dae18	Internal.
21de5fc	Stick: if user is Farfetch'd and holds Stick, increase critical hit level by 2.
21de5b8	Lucky Punch: if user is Chansey and holds Lucky Punch, increase critical hit level by 2.
21de584	Razor Claw: increase holder's critical hit level by 1.
21e53b4	Internal.
6899210	Lucky Chant: if the user's party is protected by Lucky Chant, bypass critical hit checks.

The random factor

Provided the battle isn't rigged to always use minimum damage, the current damage value D is altered using a random number 0 ≤ R ≤ 15:

D' = (D * (100-R)) ÷ 100

STAB

If the type of the move match one of its users', the STAB modifier is set to 0x1800. The only trigger for this modifier is listed below.

Trigger address	Trigger description
21D8C2D	Adaptability: if the user has this ability and move matches one of the user's types, the initial value for the final modifier is set to 0x2000.

Type effectiveness

Type effectiveness doesn't use a modifier but a simple left (respectively right) shift of one for a simple and two for a double weakness (respectively resistance), in other words an unrounded division or multiplication by 2 or 4.

Effect of a burn

The effect of a burn is directly taken into account in the damage formula. First, the game checks if the attack is physical, then if the user is burned, and finally if its ability is different than Guts. If all conditions are satisfied, the current damage is divided by 2 with no rounding.

Final modifier

The final modifier is decided by calling the appropriate triggers, which are listed below. Be sure to chain the modifiers in the order they are listed in.

Trigger address	Modifier	Trigger description
6898E29	Variable	If the target's side is affected by Reflect, the move used was physical, the user's ability isn't Infiltrator and the critical hit flag isn't set. The value of the modificator is 0xA8F if there is more than one Pokémon per side of the field and 0x800 otherwise.
6898E45	Variable	Same as above with Light Screen and special moves.
21DC125	0x800	If the target's ability is Multiscale and the target is at full health.
21D8B3D	0x2000	If the user's ability is Tinted Lens and the move wasn't very effective.
21DC15D	0xC00	If one of the target's allies' ability is Friend Guard.
21D8BA5	0x1800	If user has ability Sniper and move was a critical hit.
21D8B71	0xC00	If the target's ability is Solid Rock or Filter and the move was super effective.
21DBA95		Internal.
21DEC91	Variable	If the user is holding the item Metronome. If n is the number of time the current move was used successfully and successively, the value of the modifier is 0x1000+n*0x333 if n≤4 and 0x2000 otherwise.
21DEBD5	0x1333	If the user is holding an expert belt and the move was super effective.
21DEC65	0x14CC	If the user is holding a Life Orb.
21DDB85	0x800	If the target is holding a damage lowering berry of the attack's type. There is one trigger for each type of berry, the others are at: 21DDC05, 21DDAE5, 21DDB05, 21DDB25, 21DDB45, 21DDB65, 21DDBA5, 21DDBC5, 21DDBE5, 21DDC25, 21DDC45, 21DDC65, 21DDC85, 21DDCA5, 21DDCC5 and 21DDCE5.
21E3A25	0x2000	If move is Stomp and target has used Minimize.
21E316D	0x2000	If move is Earthquake and target is in the charging turn of Dig.
21E39E1	0x2000	If move is Surf and target is in the charging turn of Dive.
21E1455	0x2000	If move is Steamroller and target has used Minimize.

The base power

There are two separate sets of triggers for the base power of moves. The first is mainly used for moves with a variable base power, while the second contains the various modifiers for base power.

Triggers for variable base power

Trigger address	Summary of BP formula	Move and remarks.
21d88cc		Internal.
21e2aec	((255 - Happiness) * 10) ÷ 25	Frustration: if result is 0 add 1.
21e2968	50, 100	Payback: BP is doubled to 100 if target has moved this turn, 50 otherwise.
21e2aa0	(Happiness * 10) ÷ 25	Return: if result is 0 add 1.
21e7184	150, 120, 80, 60, 40	Electro Ball: Let S = UserModSpeed ÷ TargetModSpeed. BP = {150: S ≥ 4, 120: 3 ≤ S < 4, 80: 2 ≤ S < 3, 60: 1 ≤ S < 2, 40: otherwise};
21e283c	60, 120	Avalanche: BP is doubled to 120 if the target has inflicted non-effect damage to the user this turn.
21e27d0	min(150, 25 * TargetSpd ÷ UserSpd)	Gyro Ball.
21e29a8	(150 * CurrentHP) ÷ MaxHP	Eruption, Water Spout: if result is 0 set BP to 1.
21e2de0	min(120, 60 + 20 * statup_total)	Punishment: statup_total is the sum of the target's stat levels that are ≥ 0, including accuracy and evasion.
21e2e48	20 * 2^(use_counter)	Fury Cutter: use_counter counts successive and successful previous uses up to a maximum of 3.
21e2ef4	20, 40, 60, 80, 100, 120	Low Kick, Grass Knot: let W be the final weight after modifiers. If W ≥ 200, BP is 120, else if W ≥ 100, BP is 100, else if W ≥ 50, BP is 80, else if W ≥ 25, BP is 60, else if W ≥ 10, BP is 40, else BP is 20.
21e7204	40, 80, 120, 160, 200	Echoed Voice: BP increases in the listed order every turn this move is used successively on the user's side of the field.
21e702c	50, 100	Hex: BP is doubled to 100 if target has a status problem.
21e2a08	round(120 * TargetHP%) ÷ 100	Wring Out, Crush Grip: TargetHP% is computed by a fixed point division using 0x1000 as the scaling factor.
21e2eb0	50, 100	Assurance: BP is doubled to 100 if target has already been inflicted non-effect damage this turn.
21e7104	120, 100, 80, 60, 40	Heavy Slam, Heat Crash: let W = UserModWeight ÷ TargetModWeight. BP = {120: W ≥ 5, 100: 4 ≤ W < 5, 80: 3 ≤ W < 4, 60: 2 ≤ W < 3, 40: W < 2}.
21e70a0	20 + 20 * statups	Stored Power: statups is the sum of all positive stat increases, including accuracy and evasion.
21e706c	55, 110	Acrobatics: BP is doubled to 110 if user has no held item.
21e28b8	P = (48 * CurrentHP) ÷ MaxHP	Flail, Reversal: 200 if P ≤ 1, 150 if 2 ≤ P ≤ 4, 100 if 5 ≤ P ≤ 9, 80 if 10 ≤ P ≤ 16, 40 if 17 ≤ P ≤ 32, 20 otherwise.
21e2d7c	40, 50, 60, 80, 200	Trump Card: listed BP correspond to decreasing PP (if PP is ≥ 5 or this move was called by another move BP is 40).
21e7dd0	60, 120	Round: BP is doubled to 120 if used in direct succession of an ally.
21e2788	10, 20, 30	Triple Kick: BP is listed for the successive hits.
21e2b38	60, 120	Wake-Up Slap: BP is doubled to 120 if target is asleep.
21e2bd4	60, 120	SmellingSalt: BP is doubled to 120 is target is paralyzed.
21e2fd0	50, 100	Weather Ball: BP is doubled to 100 in any non-default weather.
21e302c	40, 80	Gust, Twister: BP is doubled to 80 is target is in the charging turn of Bounce, Fly or Sky Drop.
21e6074	CurrentPartyMemberAttack ÷ 10 + 5	Beat Up: this move attacks once for every non fainted member in the user's party, including the user.
21e3318	30 + (40 * sum(((IV[i]>>1)&1)<<i)) ÷ 63	Hidden Power: IV are indexed from 0 and listed as HP, At, Df, Sp, SA, SD.
21e17d0	100 * stockpile	Spit Up: stockpile is the stockpile counter ranging from 0 to 3.
21e1dbc	40, 80	Pursuit: BP is doubled to 80 if target is switching out.
21e2d40	40, 80 or 120	Present: let 0 ≤ r < 80 be a random number. If r < 40, BP is 40, else if r < 70, BP is 80, otherwise BP is 120.
21e33dc	Variable	Natural Gift: base power and type depend on held berry. See 2021030 and 20210E4 for corresponding tables.
21e398c	10 + 20 * factor	Magnitude: let R = rand(100), factor = {0: R < 5, 1: 5 ≤ R < 15, 2: 15 ≤ R < 35, 3: 35 ≤ R < 65, 4: 65 ≤ R < 85, 5: 85 ≤ R < 95, 7: R ≥ 95}.
21e2720	30 * 2 ^ (use_counter + defense_curl)	Rollout: use_counter counts successive and successful previous uses up to a maximum of 5, defense_curl is 1 if user used Defense Curl previously on field, 0 otherwise.
21e5d44	Variable	Fling: base power depends on the held item. See 21D807C for table of items.
21e84b8	150	Grass/Fire/Water Pledge: if a slower ally used a different Pledge move this turn, it will skip its turn and this move's base power will be set to 150.

Modifiers for the base power

Trigger address	Modifier	Trigger description
21d9108	0x1800	If user has ability Technician and move's base power is ≤60.
21dc27c	0x1800	If user has ability Flare Boost, is burned and uses a special move.
21dc6c0	0x14CD	If user has ability Analytic, move isn't Future Sight or Doom Desire and target has already moved this turn.
21d9174	0x1333	If user has ability Reckless and move has recoil or is either Jump Kick or Hi Jump Kick.
21d9138	0x1333	If the user has ability Iron Fist and move has the "Punching move" (0x7) flag set.
21dc238	0x1800	If user has ability Toxic Boost, is poisoned and move is physical.
21d9090	Variable	If user has ability Rivalry. The value of the modifier is 0x1000 if either the user or target is genderless, 0x1400 if the user and target are of the same gender and 0xC00 otherwise.
21dc718	0x14CD	If user has ability Sand Force and move is Rock, Ground or Steel type.
21da864	0x800	If target has ability Heatproof and move is Fire type.
21daa90	0x1400	If target has ability Dry Skin and move is Fire type.
21dbf48	0x14CD	If the user has ability Sheer Force and move has a flag (0xA) set.
21d9dc4		Internal.
Multiple	0x1333	Type boosting items, plates, incenses. All are wrappers for the 21DF95C trigger. List of locations: 21df7a8, 21df878, 21df760, 21df748, 21df778, 21df7c0, 21df860, 21df890, 21df730, 21df908, 21df950, 21df790, 21df7d8, 21df7f0, 21df808, 21df718, 21df8c0, 21df938, 21df920, 21df8d8, 21df8a8.
21de6ec	0x1199	If user holds a Muscle Band and move is physical.
21df994	0x1333	If user is Palkia, holds the Lustrous Orb and move is Water or Dragon type.
21de72c	0x1199	If user holds Wise Glasses and move is special.
21df458	0x1333	If user is Giratina, holds the Griseous Orb and move is Dragon or Ghost type.
21df8f0	0x1333	If user holds Odd Incense and move is Psychic type.
21df9e8	0x1333	If user is Dialga, holds the Adamant Orb and move is Steel or Dragon type.
21e01e4	0x1800	If user holds a Normal Gem and move is normal type. Similar triggers for the other types are at: 21DFF14, 21DFF40, 21DFF6C, 21DFF98, 21DFFC4, 21DFFF0, 21E001C, 21E0048, 21E0074, 21E00A0, 21E00CC, 21E00F8, 21E0124, 21E0150, 21E017C, 21E01A8
21e2928	0x2000	If move is Facade and user is either paralyzed, poisoned or burned.
21e2a58	0x2000	If move is Brine and target's HP is ≤ 50%.
21e6fe8	0x2000	If move is Venoshock and target is poisoned.
21e729c	0x2000	If move is Retaliate and a Pokémon from the target's party fainted on the previous turn.
21e8330	0x2000	If move is either Fusion Bolt or Fusion Flare and the previously used move was respectively Fusion Flare or Fusion Bolt.
21e6f34	0x1800	If move was called using Me First.
21e64a0	0x800	If move is SolarBeam in non-sunny, non-default weather.
21e1f38	0x2000	If user used Charge the previous turn and move is Electric type.
21e5ff0	0x1800	If user has been the target of Helping Hand this turn.
6898158	0x548	If Water Sport was used by any Pokémon still on the field and move is Fire type.
6898110	0x548	If Mud Sport was used by any Pokémon still on the field and move is Electric type.

User attack stat

Base value

The first step of computing the attack stat is to decide whether the attack or special attack stat should be used, and on which Pokémon. By default, the user's attack is used if the move is physical and the special attack otherwise but this behavior can be altered by the following triggers:

Trigger address	Trigger description
21da828	Unaware: if target has ability Unaware do not apply any attack level boosts.
21d8db0	Internal.
21e7320	Foul Play: use the target's base attack stat instead of the user's.
21e39b0	Internal.

Boost level

Once the base stat is decided, the stat boost level is applied:

1. If a trigger decided to skip stat boosts, use the base stat.
2. If the hit was critical and the boost level is negative, use the base stat.
3. Otherwise, apply the factor corresponding to the boost level according to the table below (multiply stat by the dividend first then use unrounded division on divisor).

Stat boost level	Multiplier	Decimal Approximate
-6	2/8	0.25
-5	2/7	0.2857
-4	2/6	0.3333
-3	2/5	0.4
-2	2/4	0.5
-1	2/3	0.6667
0	2/2	1
+1	3/2	1.5
+2	4/2	2
+3	5/2	2.5
+4	6/2	3
+5	7/2	3.5
+6	8/2	4

Attack modifiers

The final attack stat is altered using the following modifiers:

Trigger address	Modifier	Trigger description
21d871c	0x800	If target has ability Thick Fat and move is Ice or Fire type.
21d8c78	0x1800	If user has ability Torrent, has MaxHP ÷ 3 or less HP and move is water type.
21d8d14	0x1800	If user has ability Guts, has a status problem and move is physical.
21d8cb0	0x1800	If user has ability Swarm, has MaxHP ÷ 3 or less HP and move is bug type.
21d8c94	0x1800	If user has ability Overgrow, has MaxHP ÷ 3 or less HP and move is grass type.
21d8d60	0x1800	If user has ability Plus or Minus and an ally has ability Plus or Minus and move is special.
21d8c5c	0x1800	If user has ability Blaze, has MaxHP ÷ 3 or less HP and move is fire type.
21dc0dc	0x800	If user has ability Defeatist and CurrentHP ≤ MaxHP ÷ 2.
21d8754	0x2000	If user has ability Pure Power or Huge Power and move is physical.
21d9954	0x1800	If user has ability Solar Power and weather is intense sunlight and move is special.
21d8894	0x1800	If user has ability Hustle and move is physical. This is a special trigger in the sense that instead of chaining it will directly apply the 0x1800 on the current attack stat instead of being chained with others.
21daf04	0x1800	If user has ability Flash Fire activated and move is Fire type.
21d892c	0x800	If user has ability Slow Start, has been on field for less than 5 turns and move is physical.
21d8fec	0x1800	If ally is Cherrim and has ability Flower Gift, weather is intense sunlight and move is physical.
21db424		Internal.
21de91c	0x2000	If user is Cubone or Marowak, holds a Thick Club and move is physical.
21de76c	0x2000	If user is Clamperl, holds a DeepSeaTooth and move is special.
21df53c	0x2000	If user is Pikachu and holds a Light Ball.
21de898	0x1800	If user is Latios or Latias, holds a Soul Dew and move is special.
21de968	0x1800	If user is holding Choice Band and move is physical.
21de9a0	0x1800	If user is holding Choice Specs and move is special.
21e310c		Internal.

Target defense stat

Base value

Just like for the attack stat, the first step is to decide which defense stat to use and whether to apply the active boost level. This is done by the following triggers:

Trigger address	Trigger description
21da840	Unaware: if foe has ability Unaware do not apply any Defense level boosts.
21d8db0	Internal.
21e7944	This triggers is used for special moves that deal physical damage. It replaces the identifier of the base special defense stat with the one for defense.
21e797c	Chip Away: ignore defense level boosts if foe has it.
68981a0	Wonder Room: has the same effect as 21e7944 but for all Pokémon on field. Will also cancel the effect of 21e7944.

Boost level

This works like attack boosts except the base defense stat is used on critical hits if the boost level is positive.

Sandstorm modifier

At this point, if the current weather (after triggers) is Sandstorm, the user is Rock type and the base stat was special attack, apply a 0x1800 modifier to the current defense stat. This is done regardless of critical hits and before any other modifier.

Defense modifiers

The final defense stat is altered using the following modifiers:

Trigger address	Modifier	Trigger description
21d91bc	0x1800	If target has ability Marvel Scale, has a status problem and move is physical.
21d903c	0x1800	If ally is Cherrim and has ability Flower Gift, weather is intense sunlight and move is special.
21db8f0		Internal.
21de7bc	0x1800	Is target is Clamperl, holds a DeepSeaScale and move is special.
21de804	0x2000	Is target is (untransformed) Ditto, holds Metal Powder and move is physical.
21dfaa8	0x1800	If target is holding Eviolite and is not fully evolved.
21de8d4	0x1800	If target is Latios or Latias holding a Soul Dew and move is special.

Special cases

The following moves do not depend on the user's attack or the target's defense and are handled by specific triggers:

Trigger address	Trigger description
21e1608	Psywave: damage is always max(1, ((rand(101) + 50) * UserLevel) ÷ 100)
21e15d0	Night Shade: damage is always UserLevel.
21e1504	SonicBoom: damage is always 20.
21e1498	Super Fang: damage is always max(1, TargetHP ÷ 2).
21e14e0	Dragon Rage: damage is always 40.
21e1578	Endeavor: damage is always max(0, TargetHP-UserHP).
21e7c98	Final Gambit: damage is always UserHP.
21e0838	Brick Break: cancels the effect of Reflect / Light Screen.
21e1978	Counter: if last Pokémon to hit the user was a foe using a physical move, use double the set damage.
21e19bc	Mirror Coat: same as Counter for special moves.
21e1a00	Metal Burst: if the user was hit by an attack earlier this turn, use 1.5 times the set damage.
21e3e50	Bide: store energy for 2 turns, then set damage to twice the total damage dealt to user during the charging turns.

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