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[on site] The Complete Damage Formula for Diamond & Pearl

Discussion in 'Archives' started by X-Act, Jul 18, 2007.

  1. X-Act

    X-Act np: Biffy Clyro - Shock Shock
    is a Site Staff Alumnusis a Programmer Alumnusis a CAP Contributor Alumnusis a Researcher Alumnusis a Tiering Contributor Alumnusis a Contributor Alumnusis an Administrator Alumnus

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    THIS IS ON SITE; THIS VERSION IS PROBABLY OUTDATED. CHECK THE SITE: http://www.smogon.com/dp/articles/damage_formula


    Introduction


    The Damage Formula is one of the two most important calculations in a Pokémon game (the other one being the Stats Formula). Here, we provide the damage formula for Diamond and Pearl (DP). Note that this formula is not the same as that for the games preceding DP, so don't use it to calculate damage for other games.

    I need to immediately thank Peterko for all the testing data he has provided for me. This guide wouldn’t have seen the light of day without all his efforts. He literally triggered the damage formula thousands of times (not an exaggeration) during the game so that I could come up with such a detailed description of it. I cannot thank him enough for his efforts. Thank you Peterko... you are one of the best testers I’ve ever seen!



    Section 1 - The Damage Formula and How to Use It

    Here is the damage formula for DP:

    Damage Formula = (((((((Level × 2 ÷ 5) + 2) × BasePower × [Sp]Atk ÷ 50) ÷ [Sp]Def) × Mod1) + 2) × CH × Mod2 × R ÷ 100) × STAB × Type1 × Type2 × Mod3

    where:

    Level is the user's current level.

    BasePower is the move's base Power (after performing all necessary modifiers to it... see Section 2).

    [Sp]Atk is the user's Attack or Special Attack stat (after performing all necessary modifiers to it... see Section 3). If the move used is physical, the Attack stat is utilized; otherwise, the Special Attack stat is used.

    [Sp]Def is the foe's Defense or Special Defense stat (after performing all necessary modifiers to it... see Section 4). If the move used is physical, the Defense stat is utilized; otherwise, the Special Defense stat is used.

    Mod1 is the first modifier to the damage formula. See Section 5 for more details.

    CH is 3 if the move is a Critical Hit and the user has the Sniper ability, 2 if the move is a Critical Hit and the user's ability is not Sniper, and 1 otherwise.

    Mod2 is the second modifier to the damage formula. See Section 6 for more details.

    R is (Rand × 100) ÷ 255, rounded down, where Rand is a random whole number between 217 and 255 inclusive with uniform probability. This produces a whole number between 85 and 100 inclusive, but not with uniform probability. See Section 8 for more details.

    STAB is 2 if the move is of the same type as that of the user and the user has the Adaptability ability, 1.5 if the move is of the same type as that of the user and the user's ability is not Adaptability, and 1 otherwise. This is known as Same Type Attack Bonus (hence STAB).

    Type1 is 2 if the move is super effective against the first type of the foe, 0.5 if the move is not very effective against the first type of the foe, 0 if the move type does not affect the first type of the foe, and 1 otherwise.

    Type2 is 2 if the move is super effective against the second type of the foe, 0.5 if the move is not very effective against the second type of the foe, 0 if the move type does not affect the type of the foe, and 1 otherwise (or if the foe has only one type).

    Mod3 is the third modifier to the damage formula. See Section 7 for more details.


    It should be immediately mentioned that after successfully performing an operator (an operator being +, -, × or ÷), you need to "round down" the number to the nearest whole number before performing the next one. In simple terms, this means to remove all the numbers to the right of the decimal point every time the answer is a decimal before proceeding with the next arithmetic operation.

    If the damage formula's damage is 0 and the foe is not immune to the move used, the damage dealt will be 1 instead. This will happen if, say, a Level 2 Bidoof uses Tackle against a Level 100 Aggron. To paraphrase, unless the move does not affect the foe, the minimum amount of damage done is 1.

    The way the formula is written above is such that you can actually ignore all the brackets and proceed from left to right (ignoring the BODMAS rules, so to speak) and still come up with the correct answer.

    Let's provide an example here. For the sake of simplicity, we shall assume that Mod1, Mod2 and Mod3 are all 1 in this example.

    Say we want to calculate the minimum and maximum damage that a Level 47 Staraptor with 140 Attack stat will deal with the move Aerial Ace against a Roserade with 77 Defense stat.

    1) We start with the Level of Staraptor, 47, and multiply it by 2, getting 94.
    2) Next, we divide 94 by 5, getting 18.8, which is rounded down to 18.
    3) Next, we add 2 to 18, getting 20.
    4) Next, we multiply 20 by 60 (the move power of Aerial Ace), getting 1200.
    5) Next, we multiply 1200 by 140 (the Attack stat of Staraptor), getting 168000.
    6) Next, we divide 168000 by 50, getting 3360.
    7) Next, we divide 3360 by 77 (the Defense stat of Roserade), getting 43.636363..., which is rounded down to 43.
    8) Next, we multiply 43 by 1 (Mod1 is 1 here), getting 43.***
    9) Next, we add 2 to 43, getting 45.
    10) Next, we multiply 45 by 1 (assuming that we didn't get a Critical Hit here), getting 45.***
    11) Next, we multiply 45 by 1 (Mod2 is 1 here), getting 45.***
    12) Next, we multiply 45 by 85 (the minimum number that the random number can be), getting 3825.
    13) Next, we divide 3825 by 100, getting 38.25, which is rounded down to 38.
    14) Next, we multiply 38 by 1.5 (since Aerial Ace is Flying-type, like one of Staraptor's types is), getting 57.
    15) Next, we multiply 57 by 2 (since Aerial Ace is Flying-type, which is super effective against Roserade's first type, Grass), getting 114.
    16) Next, we multiply 114 by 1 (since Aerial Ace is Flying-type, which is neutral against Roserade's second type, Poison), getting 114.***
    17) Finally, we multiply 114 by 1 (Mod3 is 1 here), getting 114.***

    So Staraptor's minimum damage would be 114.

    For the maximum damage, we do exactly the same steps, except that we multiply by 100 instead of by 85 in Step 12. We get 134 as the maximum damage if we do that. Try it out. (If you do not get 134, make sure that you have actually rounded down your answer at EVERY step in the calculation.)

    Note: The steps marked *** can be omitted, since multiplying by 1 does not change the answer.



    Section 2 - The Base Power and Its Modifiers

    The base power of the move might be considered to be simple, but in fact it can change by many things during the battle that can affect it.

    So many, in fact, that it can be summarised by the following formula:

    BasePower = HH × BP × IT × CHG × MS × WS × UA × FA

    where

    HH is 1.5 if the move has been boosted by the move Helping Hand by the partner, and 1 otherwise.

    BP is the base power of the move. This is usually found easily, like 80 for Energy Ball, 60 for Aerial Ace, etc. Some moves have a variable BP, a list of which is given in Section 2A.

    IT is the item multiplier. The list of items that affect Base Power, together with their effects, is given in Section 2B.

    CHG is 2 if the Pokémon's last move was Charge and this move's type is Electric and 1 otherwise.

    MS is 0.5 if one of the Pokémon in play used the move Mud Sport and this move's type is Electric, and 1 otherwise.

    WS is 0.5 if one of the Pokémon in play used the move Water Sport and this move's type is Fire, and 1 otherwise.

    UA is the user ability multiplier. A list of user abilities that affect Base Power, together with their effects, is given in Section 2C.

    FA is the foe ability multiplier. A list of foe abilities that affect Base Power, together with their effects, is given in Section 2D.

    The Base power is calculated from left to right, and is rounded down before the next multiplication is performed. The order of the multiplications is as written in the formula above... changing the order might result in the incorrect base power.


    Section 2A - Moves having a Variable Base Power

    Here is a list of moves having variable base power. This base power is equal to BP in the Base Power formula.

    Assurance - BP = 100 if the foe was hurt that turn, BP = 50 otherwise.

    Avalanche - BP = 120 if the targeted Pokémon did damage to the user, BP = 60 otherwise.

    Brine - BP = 130 if the targeted Pokémon’s current HP is less than or equal to half of its maximum HP, rounded down, BP = 65 otherwise.

    Crush Grip*** - BP = 1 + (120 × Foe’s Current HP ÷ Foe’s Max HP), rounded down.

    Eruption*** - BP = 150 × User’s Current HP ÷ User’s Max HP, rounded down.

    Facade - BP = 140 if the user is Paralyzed, Poisoned, or Burned, BP = 70 otherwise.

    Flail - BP = 200 if CP is between 0 and 1, BP = 150 if CP is between 2 and 5, BP = 100 if CP is between 6 and 12, BP = 80 if CP is between 13 and 21, BP = 40 if CP is between 22 and 42, and BP = 20 if CP is between 43 and 64, where CP = User's Current HP × 64 ÷ User's Total HP, rounded down.

    Fling*** - http://www.smogon.com/forums/showpost.php?p=379940&postcount=1016

    Frustration - BP = 102 - (User's Happiness × 2 ÷ 5), rounded down. If BP is 0, it becomes 1.

    Fury Cutter - BP = 10 if Fury Cutter was not already used or it missed when it was last used, otherwise, BP is double the BP of the last used Fury Cutter. If BP is greater than 160, it becomes 160.

    Grass Knot - BP = 20 if W is between 0 and 10, BP = 40 if W is between 10.1 and 25, BP = 60 if W is between 25.1 and 50, BP = 80 if W is between 50.1 and 100, BP = 100 if W is between 100.1 and 200, and BP = 120 otherwise, where W is the weight of the foe in kilograms.

    Gyro Ball - BP = 1 + (25 × Foe’s Speed ÷ User’s Speed), rounded down. If BP is greater than 150, it becomes 150.

    Ice Ball - If Defense Curl was used by the user in any of the previous turns, then BP = 60 for the first turn that Ice Ball is used, followed by BP = 120, 240, 480 and 960 for the second, third, fourth and fifth turns respectively. If Defense Curl was not used by the user in any of the previous turns, then BP = 30 for the first turn that Ice Ball is used, then BP = 60, 120, 240, and 480 for the second, third, fourth and fifth turns respectively. If Ice Ball fails, BP restarts from 60 or 30 in its next usage.

    Hidden Power - http://www.smogon.com/forums/showthread.php?t=20649

    Low Kick - BP = 20 if W is between 0 and 10, BP = 40 if W is between 10.1 and 25, BP = 60 if W is between 25.1 and 50, BP = 80 if W is between 50.1 and 100, BP = 100 if W is between 100.1 and 200, and BP = 120 otherwise, where W is the weight of the foe in kilograms.

    Magnitude - BP = 10 if R is between 0 and 4 (Magnitude 4), BP = 30 if R is between 5 and 14 (Magnitude 5), BP = 50 if R is between 15 and 34 (Magnitude 6), BP = 70 if R is between 35 and 64 (Magnitude 7), BP = 90 if R is between 65 and 84 (Magnitude 8), BP = 110 if R is between 85 and 94 (Magnitude 9), and BP = 150 if R is between 95 and 99 (Magnitude 10), where R is a random whole number between 0 and 99 with uniform probability.

    Natural Gift - http://www.smogon.com/forums/showpost.php?p=322687&postcount=406

    Nature Power - Becomes Earthquake if the location is on a road or in the desert, Tri Attack if the location is inside a building (this is the default choice in battles), Seed Bomb if the location is on grass or tall grass, Rock Slide if the location is in a cave or on a mountain, Blizzard if the location is on snow, and Hydro Pump if the location is on a pond or in the sea.

    Payback - BP = 100 if the targeted Pokémon moves before the user, BP = 50 otherwise.

    Present*** - BP = 40 if R is between 0 and 102, BP = 80 if R is between 103 and 179, BP = 120 if R is between 179 and 204, and BP = 0 and the foe is healed by 80 HP otherwise, where R is a random whole number between 0 and 255 inclusive, with uniform probability.

    Punishment - BP = 60 + (20 × Sum of positive stat modifiers of the foe). If BP is greater than 200, it becomes 200.

    Pursuit - BP = 80 if the foe switches out during that turn, BP = 40 otherwise.

    Return - BP = User's Happiness × 2 ÷ 5, rounded down. If BP is 0, it becomes 1.

    Revenge - BP = 120 if the targeted Pokémon did damage to the user, BP = 60 otherwise.

    Reversal - BP = 200 if CP is between 0 and 1, BP = 150 if CP is between 2 and 5, BP = 100 if CP is between 6 and 12, BP = 80 if CP is between 13 and 21, BP = 40 if CP is between 22 and 42, and BP = 20 if CP is between 43 and 64, where CP = User's Current HP × 64 ÷ User's Total HP, rounded down.

    Rollout - If Defense Curl was used by the user in any of the previous turns, then BP = 60 for the first turn that Rollout is used, followed by BP = 120, 240, 480 and 960 for the second, third, fourth and fifth turns respectively. If Defense Curl was not used by the user in any of the previous turns, then BP = 30 for the first turn that Rollout is used, then BP = 60, 120, 240, and 480 for the second, third, fourth and fifth turns respectively. If Rollout fails, BP restarts from 60 or 30 in its next usage.

    Smellingsalt - BP = 120 if the foe is paralyzed (and is healed from paralysis afterwards), BP = 60 otherwise.

    Spit Up - BP = 100 if one Stockpile was used, BP = 200 if two Stockpiles were used, BP = 300 if three Stockpiles were used, BP = 0 otherwise.

    Stomp - BP = 130 if the foe used the move Minimize, BP = 65 otherwise.

    Triple Kick - BP = 10 in the first kick, BP = 20 in the second kick, BP = 30 in the third kick.

    Trump Card - BP = 40 if P is at least 4, BP = 50 if P is 3, BP = 60 if P is 2, BP = 80 if P is 1, and BP = 200 if P is 0, where P is the PP of Trump Card after being used.

    Wake-up Slap - BP = 120 if the foe is asleep (and is healed from sleep afterwards), BP = 60 otherwise.

    Water Spout*** - BP = 150 × User’s Current HP ÷ User’s Max HP, rounded down.

    Weather Ball - BP = 100 if the weather is Sunny Day, Rain Dance, Sandstorm, Hail or Fog, BP = 50 otherwise.

    Wring Out - BP = 1 + (120 × Foe’s Current HP ÷ Foe’s Max HP), rounded down.


    *** - Exact BP not confirmed.


    Section 2B - Items that affect Base Power

    The following items equipped to the user provide the following boost to the IT multiplier:

    Muscle Band - IT = 1.1 if the move used is physical, IT = 1 otherwise.
    Wise Glasses - IT = 1.1 if the move used is special, IT = 1 otherwise.
    Type-boosting items, plates and incenses - IT = 1.2 if the move used is of the same type as the type that the item, plate or incense boosts, IT = 1 otherwise.
    Adamant Orb - IT = 1.2 if the user is Dialga and the move used is Steel or Dragon type, IT = 1 otherwise.
    Lustrous Orb - IT = 1.2 if the user is Palkia and the move used is Water or Dragon type, IT = 1 otherwise.
    Any other item - IT = 1.


    Section 2C - User Abilities that affect Base Power

    The following abilities provide the following numbers to the UA multiplier if the user has one of them:

    Rivalry - UA = 1.25 if the user is of the same gender as the targeted Pokémon, UA = 0.75 if the user is of the opposite gender of the targeted Pokémon, UA = 1 otherwise.
    Reckless - UA = 1.2 if the user uses a recoil move, UA = 1 otherwise.
    Iron Fist - UA = 1.2 if the user uses a punching move, UA = 1 otherwise.
    Blaze - UA = 1.5 if the user uses a Fire move and its current HP is less than 1/3 of its maximum HP (rounded down), UA = 1 otherwise.
    Overgrow - UA = 1.5 if the user uses a Grass move and its current HP is less than 1/3 of its maximum HP (rounded down), UA = 1 otherwise.
    Torrent - UA = 1.5 if the user uses a Water move and its current HP is less than 1/3 of its maximum HP (rounded down), UA = 1 otherwise.
    Swarm - UA = 1.5 if the user uses a Bug move and its current HP is less than 1/3 of its maximum HP (rounded down), UA = 1 otherwise.
    Technician - UA = 1.5 if the user uses a move with BP at most 60, UA = 1 otherwise.
    All other user abilities - UA = 1.


    Section 2D - Foe Abilities that affect Base Power

    The following abilities provide the following numbers to the FA multiplier if the foe has one of them:

    Thick Fat - FA = 0.5 if the user is using an Ice or Fire move, FA = 1 otherwise.
    Heatproof - FA = 0.5 if the user is using a Fire move, FA = 1 otherwise.
    Dry Skin - FA = 1.25 if the user is using a Fire move, FA = 1 otherwise.
    All other foe abilities - FA = 1.



    Section 3 - The Attack and Special Attack stats and their Modifiers

    The Attack and Special Attack stats can also be changed throughout the match by various things.

    [Sp]Atk = Stat × SM × AM × IM

    where:

    Stat is the normal Attack or Special Attack stat.

    SM is the stat modifier multiplier. See Section 3A for more information.

    AM is the ability modifier. See Section 3B for a list of abilities that change the attacking stats.

    IM is the item modifier. See Section 3C for a list of items that change the attacking stats.

    As we said for the calculation of the base power, the above multiplication is also performed from left to right, rounding down before performing the next one.


    Section 3A - The Stat Modifier Multipliers

    Each stat (excluding HP) has a stat modifier which is a whole number between -6 and 6 inclusive. This stat modifier starts from 0 and is changed by various moves like Swords Dance and Defense Curl. Some attacks can also change either the user’s stat modifier or that of the foe as a secondary effect, like Overheat and Shadow Ball.

    The effect of SM is the following:

    Stat Modifier is -6: SM = 2/8 (0.25)
    Stat Modifier is -5: SM = 2/7 (0.2857)
    Stat Modifier is -4: SM = 2/6 (0.3333)
    Stat Modifier is -3: SM = 2/5 (0.4)
    Stat Modifier is -2: SM = 2/4 (0.5)
    Stat Modifier is -1: SM = 2/3 (0.6667)
    Stat Modifier is 0: SM = 2/2 (1)
    Stat Modifier is 1: SM = 3/2 (1.5)
    Stat Modifier is 2: SM = 4/2 (2)
    Stat Modifier is 3: SM = 5/2 (2.5)
    Stat Modifier is 4: SM = 6/2 (3)
    Stat Modifier is 5: SM = 7/2 (3.5)
    Stat Modifier is 6: SM = 8/2 (4)

    A few points:

    1) Critical Hits: If the Stat Modifier for Attack or Special Attack is less than zero, SM is made equal to 1 if the attack hits for a Critical Hit. Also, if the Stat Modifier for Defense or Special Defense is greater than zero, SM is made equal to 1 if the attack hits for a Critical Hit.

    2) Unaware: If the user has the ability Unaware, SM for Defense or Special Defense of the foe is made equal to 1. If the foe has the ability Unaware, SM for Attack or Special Attack of the user is made equal to 1.

    3) Simple: If any Pokemon has the ability Simple, SM conforms to a different chart:

    Stat Modifier is between -3 and -6: SM = 2/8 (0.25)
    Stat Modifier is -2: SM = 2/6 (0.3333)
    Stat Modifier is -1: SM = 2/4 (0.5)
    Stat Modifier is 0: SM = 2/2 (1)
    Stat Modifier is 1: SM = 4/2 (2)
    Stat Modifier is 2: SM = 6/2 (3)
    Stat Modifier is between 3 and 6: SM = 8/2 (4)


    Section 3B - Abilities that change the Attack or Special Attack stat

    Here is a list of abilities that modify the Attack or Special Attack stat of the user, which affect the AM multiplier:

    Abilities that affect the Attack stat:

    Pure Power: AM = 2.
    Huge Power: AM = 2.
    Flower Gift: AM = 1.5 if Sunny Day is in effect, AM = 1 otherwise.
    Guts: AM = 1.5 if the user is Paralyzed, Poisoned, Burned, or Asleep, AM = 1 otherwise.
    Hustle: AM = 1.5 (and physical moves have 80% accuracy).
    Slow Start: AM = 0.5 if the user has been in the battlefield for less than 5 turns, AM = 1 otherwise.
    Other abilities: AM = 1.

    Abilities that affect the Special Attack stat:

    Plus: AM = 1.5 if the partner has ability Minus, AM = 1 otherwise.
    Minus: AM = 1.5 if the partner has ability Plus, AM = 1 otherwise.
    Solar Power: AM = 1.5 if Sunny Day is in effect (and loses 1/8 of HP per turn), AM = 1 otherwise.
    Other abilities: AM = 1.


    Section 3C - Items that change the Attack or Special Attack stat

    Here is a list of items that modify the Attack or Special Attack stat of the user, which affect the IM multiplier:

    Items that affect the Attack stat:

    Choice Band: IM = 1.5 (the user can't use any other move).
    Light Ball: IM = 2 if the user is Pikachu, IM = 1 otherwise.
    Thick Club: IM = 2 if the user is Cubone or Marowak, IM = 1 otherwise.
    Other items: IM = 1.

    Items that affect the Special Attack stat:

    Choice Specs: IM = 1.5 (the user can't use any other move).
    Light Ball: IM = 2 if the user is Pikachu, IM = 1 otherwise.
    Soul Dew: IM = 1.5 if the user is Latios or Latias, IM = 1 otherwise.
    Deepseatooth: IM = 2 if the user is Clamperl, IM = 1 otherwise.
    Other items: IM = 1.



    Section 4 - The Defense and Special Defense stats and their Modifiers

    Various changes can also be performed to the Defense and Special Defense stats of the foe during a match.

    In this case, there aren't many things that can change the Defense or Special Defense stats:

    [Sp]Def = Stat × SM × Mod × SX

    where:

    Stat is the normal Defense or Special Defense stat.

    SM is the stat modifier multiplier. See Section 3A for more information.

    Mod is a modifier depending on a few factors. These are:

    Defense modifiers:

    Metal Powder: Mod = 1.5 if the foe is Ditto, is holding the item Metal Powder and has not used the move Transform.
    Marvel Scale: Mod = 1.5 if the foe has the ability Marvel Scale and is Paralysed, Poisoned, Burned, Asleep or Frozen.

    Special Defense modifiers:

    Sandstorm: Mod = 1.5 if Sandstorm is in effect and the foe is of Rock type.
    Soul Dew: Mod = 1.5 if the foe is Latios or Latias and is holding the item Soul Dew.
    Metal Powder: Mod = 1.5 if the foe is Ditto, is holding the item Metal Powder and has not used the move Transform.
    Deepseascale: Mod = 2 if the foe is Clamperl and is holding the item Deepseascale.
    Flower Gift: Mod = 1.5 if one of the foes has the ability Flower Gift and Sunny Day is in effect.

    Otherwise, Mod = 1.

    SX is 0.5 if the move used by the user is Selfdestruct or Explosion, otherwise it is 1.

    Again, remember to multiply from left to right and round down after each multiplication.

    If there are two simultaneous boosts in Mod, first apply the ability boost, and then the item boost.

    If the Defense or Special Defense stat is equal to zero after all these modifiers, it becomes 1 instead.



    Section 5 - The First Modifier to the Damage Formula

    This section will explain the function of Mod1, the first modifier to the damage formula.

    Mod1 = BRN × RL × TVT × SR × FF

    where

    BRN is the Burn modifier;

    RL is the Reflect/Light Screen modifier;

    TVT is the 2vs2 modifier;

    SR is the Sunny Day/Rain Dance modifier;

    FF is the Flash Fire modifier.

    BRN is 0.5 if the move performed is physical, the user is affected by the Burn special condition and the user's ability is not Guts, and 1 otherwise.

    RL is:
    0.5 if the move performed is physical, the foe has setup a Reflect and the game is 1vs1,
    0.5 if the move performed is special, the foe has setup a Light Screen and the game is 1vs1,
    2/3 if the move performed is physical, the foe has setup a Reflect and the game is 2vs2,
    2/3 if the move performed is special, the foe has setup a Light Screen and the game is 2vs2,
    1 otherwise.
    Also, if the move is a Critical Hit, RL is made equal to 1 no matter what.

    TVT is 0.75 if the game is 2vs2 and the move used hits more than one Pokemon, and 1 otherwise. Note: These moves don't always hit for 75% damage. Research on what conditions trigger the 75% damage are being carried out.

    SR is:
    1.5 if Sunny Day is in effect and the move is of Fire type,
    1.5 if Rain Dance is in effect and the move is of Water type,
    0.5 if Sunny Day is in effect and the move is of Water type,
    0.5 if Rain Dance is in effect and the move is of Fire type,
    1 otherwise.

    FF is 1.5 if the user has the ability Flash Fire, was previously attacked by a move that is of Fire type, and is using a Fire move, 1 otherwise.

    Yet again, it must be emphasized that the order of the multiplication must be as written above.



    Section 6 - The Second Modifier to the Damage Formula

    This section explains what affects Mod2, the second modifier of the damage formula.

    Mod2 = ITM × TT × MF

    where

    ITM is:
    1.3 if the user is holding the item Life Orb,
    1, 1.1, 1.2, 1.3, ..., 2 if the user is holding the item Metronome and has used the same move once, twice, three times, four times, ... etc. consecutively,
    1 otherwise.

    TT is 2 if the user's ability is Tinted Lens and the move used is not very effective against the foe, 1 otherwise.

    MF is 1.5 if the user is attacking with the move Me First, 1 otherwise.

    The order for the multiplication of Mod2 is not completely clear. What's sure is that the item multiplier is done first. Whether Tinted Lens is activated second and Me First last, or the other way round, is still unclear. Please help us to test this.



    Section 7 - The Third Modifier to the Damage Formula

    Finally, we come to the third and final modifier to the damage formula, Mod3.

    Mod3 is:
    1.2 if the user is holding the item Expert Belt and the move used is super effective against the foe,
    0.5 if the foe is holding one of the type resisting berries and the move used is
    super effective and of the same type as the type that the berry knocks down.
    0.5 if the foe is holding Chilan Berry and the move used is Normal type,
    0.75 if the foe's ability is Solid Rock or Filter and the move used is super effective against it,
    1 otherwise.

    In the case where the foe's ability is Solid Rock or Filter and there's also an item boost (Expert Belt or a type resist berry), the Solid Rock/Filter multiplier (x0.75) is performed first, followed by the other multipliers as needed.



    Section 8 - The Random Value In The Formula

    As was already stated in the first section, R is the random number in the formula, which is a number between 85 and 100, but not with uniform probability. This section clarifies which numbers are chosen with which probability:

    85, 87, 89, 90, 92, 94, 96 and 98 each have a 7.69% chance of being chosen.
    86, 88, 91, 93, 95, 97 and 99 each have a 5.13% chance of being chosen.
    100 has only a 2.56% chance of being chosen.

    That means that the most improbable damage that you are able to deal is the maximum possible damage.



    Section 9 - Exceptional Cases


    The ninth and final section will concern moves that do not follow the damage formula to the rule.

    1) Doom Desire and Future Sight use a slightly different variation of the damage formula for the calculation of the damage dealt two turns after they are used. They use the Special Defense stat of the foe that was targeted when the move was used. Type1 and Type2 are also both equal to 1 irrespective of the type of the Pokémon that is being dealt damage.

    2) When Spit Up is used, the variable R in the damage formula (i.e. the random number between 85 and 100) is always taken to be 100.

    3) There are certain moves that do not use the usual damage formula to determine the damage done to the foe. Here is a list of them, and how to determine the damage dealt by each:

    Bide - Damage is equal to twice the damage received during the last two turns to the last Pokémon attacking the user.
    Counter - Damage is equal to twice the damage received from the last Pokémon attacking the user during that turn, if the move used was physical.
    Dragon Rage - Damage is always 40.
    Endeavor - Damage is equal to the foe's remaining HP minus the user's remaining HP. It fails if this number is not positive.
    Fissure, Guillotine, Horn Drill and Sheer Cold - Damage is equal to the foe's maximum HP (even if the foe is behind a substitute, in which case this amount of damage is dealt to the substitute instead).
    Metal Burst - Damage is equal to 1.5 times the damage received from the last Pokémon attacking the user during that turn. Fails if that Pokémon is your partner.
    Mirror Coat - Damage is equal to twice the damage received from the last Pokémon attacking the user during that turn, if the move used was special.
    Night Shade - Damage is equal to the user's Level.
    Psywave - Damage is equal to (R + 5) × Level ÷ 10, rounded down, where R is a random whole number between 0 and 10 inclusive with uniform probability, and Level is the user's Level.
    Seismic Toss - Damage is equal to the user's Level.
    Sonicboom - Damage is always 20.
    Super Fang - Damage is equal to half the foe's remaining HP, rounded down. (If this damage is 0, it becomes 1 instead.)

    4) Pain Split does not even do damage. The user's remaining HP and that of the foe are averaged and rounded down, and then both are set to this value.
  2. Peterko

    Peterko Never give up!
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    good job, as always :D

    smogon users, this took 20 days to test, so you better be thankful

    I´d like to thank X-Act for taking a lot of work of my shoulders with figuring out the positions of the modifiers with his incredibly speedy damage calculations, eliminating positions that wouldn´t work etc., you´re the man ;)

    And thank you my awesome pkmn which helped me get the needed damages

    enjoy
  3. Arseus

    Arseus
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    Wow, this looks great! Fantastic work by X-Act and Peterko as usual. I'm going to be sure to print this off at some point ... I can actually understand the formula and everything! The way you included all the moves that can vary is great! Just one thing though :
    Correct me if I'm mistaken (which I very well could be), but isn't Doom Desire a Special move in D/P? Or is that just an error in the SerebiiDex?

    EDIT : Acutally, Section 2A may be a little hard on the eyes. Just my opinion though, I think perhaps a new line after each move would help.
  4. Mekkah

    Mekkah
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    Splendid work. I suppose the next step is writing the most accurate damage calculator ever...which I can do in mIRC if I find motivation but I'm sure someone will beat me to it.

    EDIT:

    Nitpick - technically I believe Marvel Scale works on any Pokemon and not just Milotic, with for example Trace, Skill Swap, Role Play, etc. It's also been confirmed that Ditto doesn't keep his Metalpowder boost if he Transforms, so it should probably say "untransformed Ditto" or something.
  5. daksunt

    daksunt

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    Remarkable, totally perfect. Everything is explained very clearly. Thanks for the hard work and now I don't have to search for a damage calculator lol
  6. AJC

    AJC

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    your wrong about pluck its just a flying typed Bug Bite it does not double in BP if user is holding a berry it has the exact same effect has bug bite it steals the foes berry and gains its effect if possable
  7. Footnote

    Footnote

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    It's true. Pluck's power doesn't double when the target has a berry.

    Superb work overall, though. Thanks for taking the time.
  8. Peterko

    Peterko Never give up!
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    thnx for the corrections

    some of the variable move power moves were added just for the sake of completion, there was a "refer to other sources for these" sentence before...but I told X-Act to add the ones that we personally tested, hmm he added all he could find - I think the list of those moves was compiled from serebii attackdex, where pluck is wrong, sorry for that, I had no clue about pluck personally, so I didn´t see it as a mistake when checking the text

    what I´ve tested out of those were moves like Assurance, Avalanche, Revenge, Wring Out, Facade, Payback, Rollout, Wake-up Slap...

    I´m currently testing reversal/flail HP % when the base power changes, I can tell you now that they´re a bit different from what is written above (and also the D/P analysis move index), but not by much...

    footnote you didn´t have to repeat what AJC wrote, we can read you know...X-Act will change the things that are wrong when he´ll be online the next time
  9. Misty

    Misty oh
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    I really want to thank you guys for all this... I'd give you badges but you both already have the relevant badges :[ so you'll just have to accept the thanks of Smogon. I'm not a cheapskate, really!!
  10. Synre

    Synre
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    misty is a cheapskate



    But yeah, thanks for writing this, you guys have been rather amazing lately
  11. Team Rocket Elite

    Team Rocket Elite Data Integration Thought Entity
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    Awesome work. Just a few things that need to be cleared up:

    Attack drop from Burn and damage reduction from attacks that hit multiple targets in Double Battles. Burn probably does just cut your Attack in half, but I'm not sure where the other one would go.

    Section 2A -
    IIRC Fury Cutter has a max power. I think it was 160 before, I'm not sure if it still is.

    Section 4 -
    It really only matters if Deepseascale is involved but what order is Mod calculated in?

    What happens if the Defense cut from Explosion/Selfdestruct drops Defense to 0? Does it get set to 1?

    Section 7 -
    Expert Belt mod is before or after Type Resist Berry mod?
    Tinted Lens before or after Chilan Berry?

    Section 8 -
    Future Sight ignores the damage boost from Life Orb. Any idea if it ignores anything else?
  12. david stone

    david stone Fast-moving, smart, sexy and alarming.
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    TRE just said most of what I was about to say, so this is going to be a rather short post.

    Did you test specifically if Defense Curl needs to be used immediately prior to using Rollout, or can you use Defense Curl, then Tackle, then Rollout and still get the boost?

    I was under the impression that Triple Kick's third kick has 40 power, not 30 (10, 20, 40), but, as usual, I haven't tested this myself, so did you guys test that?

    Also I can affirm that Peterko is a great tester. :toast:
  13. Peterko

    Peterko Never give up!
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    thnx for your posts TRE, also Obi


    burn, ok, not hard to test

    double battles multiple target moves...well all my tests were vs seeker 2vs2 battles, for example it´s impossible to test pursuit this way, as it doesn´t work on your partner...and it is impossible to test moves like razor leaf in 2vs2 for me as I can only test stuff ingame (can´t get the damage from foe trainer´s pkmn) , don´t have a usb connector yet and also no friend for a "linked" battle

    fury cutter wasn´t tested by me as I was told that it was already tested and the base dmg doubles each turn, I can check if it has a max pwr

    I don´t know what you mean with deepseascale, there is no way that two of those modifiers could collide...or am I misunderstanding what you said?

    hmm are we talking about lv.1 - def nature target with - 6 defense mods that is being exploded on? ehm, now I´m not sure if the halving def is a normal stat boost or not...leaving this fun to X-Act

    expert belt + type resist berry, I think we tested this but not sure...X-Act has the notes

    doom desire/future sight were added from a source I´m not sure of, I think from previous smogon tests??? you´re better of in the research topic, but good try :)

    rollout and def curl was only tested to prove what was known, to see how the base power changes, I haven´t thought of curl-move-rollout, although I did this kind of tests with charge out of curiosity...I mean we can´t do everything ourselves, right? :D

    triple kick, another one of those variable move power moves added from "reliable" sources, lol X-Act sorry for pushing you into posting their descriptions, I want the "refer to other sources for these" sentence back :D

    this kinda proves to myself what I think anyway, be sceptical about other sources other than my own tests (unless they have enough proof), as almost everything that´s been asked so far wasn´t tested by me...


    needs more D/P research topic work, right guys?
  14. X-Act

    X-Act np: Biffy Clyro - Shock Shock
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    Thanks a lot to everyone for spotting mistakes. I fixed the ones I know were wrong. As we say in Maltese, "four eyes are better than two" (translated), meaning that having more people to look at your work is better than just looking at it yourself.

    Also, of course, we need to thank whoever posted information about certain moves, because we didn't test each and every move.

    Nitpick - technically I believe Marvel Scale works on any Pokemon and not just Milotic.

    You're right. Edited.

    It's also been confirmed that Ditto doesn't keep his Metalpowder boost if he Transforms, so it should probably say "untransformed Ditto" or something.

    I'll try to word that better. Lol.

    your wrong about pluck its just a flying typed Bug Bite it does not double in BP if user is holding a berry it has the exact same effect has bug bite it steals the foes berry and gains its effect if possable

    Pluck's power doesn't double when the target has a berry.

    I can reduce my guide by a sentence thanks to you two!

    Attack drop from Burn and damage reduction from attacks that hit multiple targets in Double Battles. Burn probably does just cut your Attack in half, but I'm not sure where the other one would go.

    Attack drop from burn is admittedly something we didn't think of (lol we thought of Mud Sport but not of this!) We'll need to test this, but as you say, it's probably the attack stat that's halved. I bet that damage reduction from attacks that hit multiple targets just change the move power though, not that stat. As you say, we'll need to see where the burn modifier goes especially.

    IIRC Fury Cutter has a max power. I think it was 160 before, I'm not sure if it still is.

    I don't know, we relied on other Fury Cutter testers for its information.

    It really only matters if Deepseascale is involved but what order is Mod calculated in?

    Good catch. We had shown that as regards to stats, the ability modifier is multiplied first, and then the item modifier. So if for example there's Flower Gift + Deepseascale, first you do the x1.5 and then the x2 to the SpDef of Clamperl.

    What happens if the Defense cut from Explosion/Selfdestruct drops Defense to 0? Does it get set to 1?

    Can it ever be 0? Hmm, let's see... even a Level 1 Pokemon has 4 defense stat at least. This could be lowered to 1 by a -6 modifier though, so in that case... well, I think the Defense stat can never be less than 1 as well. But we may try it out. Maybe, who knows, we might find a bug in the game as the damage formula tries to divide by a 0 Defense!

    Expert Belt mod is before or after Type Resist Berry mod?

    The order doesn't matter in this case. Any number x1.2 and then x0.5 is equal to the same number x0.5 and then x1.2 (rounding down in each step.) I proved this mathematically.

    Tinted Lens before or after Chilan Berry?

    I never thought of this, lol. Well spotted. We need to test this, yeah. I had forgotten all about Tinted Lens actually, and I put it there recently, and I forgot to test this. (I hope Peterko has a Chilan Berry, lol.)

    Future Sight ignores the damage boost from Life Orb. Any idea if it ignores anything else?

    Again, we relied on information found by someone else for the Future Sight and Doom Desire text.

    Did you test specifically if Defense Curl needs to be used immediately prior to using Rollout, or can you use Defense Curl, then Tackle, then Rollout and still get the boost?

    I don't know if Peterko had tested this case. I'll ask him.

    I was under the impression that Triple Kick's third kick has 40 power, not 30 (10, 20, 40), but, as usual, I haven't tested this myself, so did you guys test that?

    We didn't test that. I found the 10, 20, 30 power from another source. It might be wrong, though.
  15. X-Act

    X-Act np: Biffy Clyro - Shock Shock
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    The damage formula is actually not 100% finished... it's maybe 95% finished, but definitely not 100%.

    I have a recommendation for Peterko to take a break from testing now... lol.

    I'm going to do just that, btw. I won't be online between next Friday and Sunday. So if you have any quibbles, I'll try to look at them tomorrow (Thursday), and then I won't see anything else until next Monday.
  16. Arseus

    Arseus
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    Okay, you guys both deserve a break from all the work you've been doing for us since day 1 of D/P. Thanks for fixing up 2A, it's much easier to read now :P
  17. chaos

    chaos
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    You guys are amazing. Thanks for being such a great part of Smogon.
  18. Hipmonlee

    Hipmonlee Have a rice day
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    This is impressive..

    I mean.. Wow..

    Have a nice day.
  19. Krul

    Krul

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    Hipno basically said what I was thinking.

    Wow.

    Absolutely spectacular work. The things you have done for the Smogon community has just been...I can't think of a word to describe it. Thank you guys so much for your work.
  20. Layell

    Layell Alas poor Yorick, I knew him, Peter Gabriel too!
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    I'm making an excel damage calculator for this, just finishing up defence modifiers then I am done. I'll post it up for everyone.

    EDIT: Ok I put my calculator through the example X-Act had with Staraptor. It worked perfectly.

    See here for the calculator!
  21. -FL-

    -FL-

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    FLawless work here guys, You're amazing and this is a great analysis.
  22. peach

    peach

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    Thanks. But why is everything on the right side password-protected? I can't change any of the values.

    @X-Act and Peterko: Awesome work.
  23. X-Act

    X-Act np: Biffy Clyro - Shock Shock
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    Edited the guide a bit with new data from Peterko's testing, since he seems like he didn't heed my advice... lol.
  24. Layell

    Layell Alas poor Yorick, I knew him, Peter Gabriel too!
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  25. timw06

    timw06

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    Here's another damage calculator for those of us without Excel. It has got almost everything in it.

    http://files.filefront.com/damagecalc6rb CURRENT VERSION/;8135164;;/fileinfo.html

    It's programmed in Ruby so if you have Ruby installed on your computer (if you haven't get it here www.ruby-lang.org ) all you have to do to run it is...

    1. Start > Run > cmd.exe
    2. type cd [the directory where you saved the file]
    3. type damagecalc6.rb
    4. Follow the instructions.

    edit: now has its own thread http://www.smogon.com/forums/showthread.php?t=25590

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