[GMS] MapleStory Formula Compilation

[Russt]

Originally posted by Technolink on SW:

Well I noticed that we have quite a lot of maplestory's formulas cracked, the problem is between sleepy, lolbasil, mapletip, hidden-street, etc, its very hard to find a formula. I've even seen two people from different sites working on the same formula.

I hope to eventually put this thread on all sites so maplestory knowledge can be spread and easily accessed from everywhere.

Unsolved formulas will be detonated in red so perhaps we could get to work on those next!

Please point out any errors that I have made, or equations you know of that aren't here. I will update this periodically with any new information.

Equations/expressions/values in blue have not been verified and may be outdated
Equations/expressions/values in red are incomplete, unconfirmed, or experimental

General Damage Calculation

In general, damage is calculated this way:

{((BaseDamage * A) - (Defense * rand(0.5, 0.6))) * (Skill * B + Critical) * C} * D

where:
- BaseDamage is a random number selected from a base damage range (see Base Damage Equations),
- A, B, C, and D are modifiers (see Modifiers),
- Defense is PDDamage for physical attacks and MDDamage for magic attacks; also see Level Disadvantage under Modifiers > A which has a defense-like effect,
- Skill and Critical are expressed as decimals, such that a 260% damage skill is 2.6 (see Critical),
- Skill is equal to 1 if no skill or a magic skill is used, and
- {X} restricts the value of X to the range [1, 199999] and removes its fractional part.

There are certain exceptions to the general formula, outlined below:

No critical: Blizzard, Shadow Meso, Assassinate first 3 hits
Ignores defense (but not dLevel modifier): Assaulter, Sacrifice, Demolition, Phoenix/Frostprey/Octopus/Gaviota

Base Damage Equations

Weapon Damage:
Max = (Primary + Secondary) * WeaponAttack / 100
Min = (Primary * Mastery * 0.9 + Secondary) * WeaponAttack / 100
where:
Primary and Secondary vary depending on the weapon (see Weapon Modifiers below),
Mastery is weapon mastery as a decimal, such that 60% mastery is 0.54, and
WeaponAttack is the sum of all equips, and includes projectiles if and only if they are consumed during the attack.

For the rest of this post I will use the notation: rand(min, max). Using this convention the general Weapon Damage equation can be expressed in one line:
(Primary * rand(Mastery * 0.9, 1) + Secondary) * WeaponAttack / 100

Weapon Modifiers:

Weapon	Primary	Secondary
One Handed Sword	STR * 4.0	DEX
One Handed Axe/BW/Wand/Staff (Swinging)	STR * 4.4	DEX
One Handed Axe/BW/Wand/Staff (Stabbing)	STR * 3.2	DEX
Two Handed Sword	STR * 4.6	DEX
Two Handed Axe/BW (Swinging)	STR * 4.8	DEX
Two Handed Axe/BW (Stabbing)	STR * 3.4	DEX
Spear (Swinging)	STR * 3.0	DEX
Spear (Stabbing)	STR * 5.0	DEX
Polearm (Swinging)	STR * 5.0	DEX
Polearm (Stabbing)	STR * 3.0	DEX
Dagger (Non-Thieves)	STR * 4.0	DEX
Dagger/Throwing Stars (Thieves)	LUK * 3.6	STR + DEX
Bow	DEX * 3.4	STR
Crossbow	DEX * 3.6	STR
Knuckle	STR * 4.8	DEX
Gun	DEX * 3.6	STR

Magic:
((Magic * 0.058)^2 + Magic * 3.3 * rand(Mastery * 0.9, 1) + INT * 0.5) * SpellAttack / 100

Heal Damage:
(INT * rand(0.3, 1.2) + LUK) * Magic / 200 * TargetMultiplier
The % listed in the skill description (300% at max) acts as the Skill value (see General Damage Calculation above)

Heal Target Multiplier: 0.3 + 1/NumTargets (including yourself)
1: 1.3
2: 0.8
3: 0.633
4: 0.55
5: 0.5
6: 0.467

Dragon Roar:
(STR * 4.0 * rand(Mastery * 0.9, 1) + DEX) * WeaponAttack / 100

Lucky Seven/Triple Throw:
(LUK * rand(2.5, 5.0)) * WeaponAttack / 100

Bow (Swinging) / Power Knock Back:
(DEX * 3.4 * rand(0.09, 1) + STR) * WeaponAttack / 150

Claw (Punching):
(LUK * rand(0.09, 1) + STR + DEX) * WeaponAttack / 150

Gun (Punching):
(DEX * rand(0.09, 1) + STR) * WeaponAttack / 200

Bare Hands:
(STR * J * rand(0.09, 1) + DEX) * WeaponAttack / 100
WeaponAttack equals floor((2*level+31)/3) and is capped at 31.
J equals 3.0 for Pirates and 4.2 for all 2nd+ job Pirates.

Phoenix/Frostprey/Octopus/Gaviota:
(DEX * 2.5 * rand(0.7, 1) + STR) * AttackRate / 100

Damage Modifiers

A

A = LevelDisadvantage * ElementAttribute * Charges * ArrowBomb

Level Disadvantage:
For physical attacks, LevelDisadvantage = 1 - 0.01 * dLevel,
where dLevel = MobLevel - CharLevel if MobLevel > CharLevel and 0 otherwise.

For magic attacks, LevelDisadvantage = 1.

Element Modifier:
ElementAttribute = 1 + X_i * E_i
where for each element i:
X_i = portion of the skill used that has that element, and
E_i = 0.5 if weak, 1 if neutral, -0.5 if resistant to that element.

Element examples:
Fire Arrow has X = 1 for Fire only
I/L Composition has X = 0.5 for both Ice and Lightning
Level 1 Holy Charge has X = 0.43 for Holy (see Skill Tables)

Charges:
Dual charging?

Arrow Bomb:
ArrowBomb = 0.5 for impact hits and SkillDamage% for splash hits. "Skill" for Arrow Bomb is always 1.
(As an aside, this causes critical to act as multiplicative on Arrow Bomb rather than additive.)

B

B = ComboModifier * FinisherModifier * Barrage

Combo Attack and Finishers:
ComboModifier 1-5 orbs = ComboAttack% + [(Orbs - 1) * (ComboLevel / 6)]%
ComboModifier 6-10 orbs = ComboAttack% + 20% + [(Orbs - 5) * 4]%
where:
ComboLevel refers to the Crusader skill, and
[X] denotes X rounded down to the nearest integer.

FinisherModifier is applied for Panic and Coma only, as follows:
1 orb = 1.0
2 orbs = 1.2
3 orbs = 1.54
4 orbs = 2.0
5 - 10 orbs = 2.5

Barrage:
Barrage = 1 for 1st-4th hit, 2 for 5th hit, 4 for 6th hit

C

C = KeyDown modifier for Big Bang/Pierce/Screw Punch

C = 10% + 90% * KeyDownTime / FullChargeTime

D

D = chain lightning effect

'OrderHit' refers to, e.g., 1 for the first hit, 2 for the second, etc. 'NumHits' refers to the number of hits in total.

Slash Blast FA:
D = 2 * (1/3) ^ (OrderHit - 1)
Cumulative damage = 3 * (1 - (1/3) ^ NumHits)

Iron Arrow:
D = 0.9 ^ (OrderHit - 1)
Cumulative damage = 10 * (1 - 0.9 ^ NumHits)

Pierce:
D = 1.2 ^ (OrderHit - 1)
Cumulative damage = 5 * (-1 + 1.2 ^ NumHits)

Chain Lightning:
D = 0.7 ^ (OrderHit - 1)
Cumulative damage = 3.333 * (1 - 0.7 ^ NumHits)

Energy Orb:
D = (2/3) ^ (OrderHit - 1)
Cumulative damage = 3 * (1 - (2/3) ^ NumHits)

Critical

Critical is normally additive to the skill percentage. For the canonical example, Double Shot is 130% with no critical, and 230% with +100% critical.

Sharp Eyes adds an additional 100%, for +140% to base critical when maxed. When combined with Stun Mastery, a further 100%, totalling to Stun Mastery + Sharp Eyes + 200%, or +300% when both are maxed.

Corsair's Elemental Boost also acts as "critical" in that it is additive to the skill percentage, so it is +200% when maxed.

Other Damage Equations (damage per tick, healing, etc)

Venom:
Damage per second tick = (rand(8.0, 18.5) * [STR + LUK] + DEX * 2) / 100 * BasicAttack

Ninja Ambush:
Damage per second tick = (STR + LUK) * (1.5 + (SkillLevel * 0.05))

Shadow Web:
Damage per 3-second tick = MonsterHP / (50 - SkillLevel)

Flamethrower:
Damage per second tick = InitialHitDamage * (5% + AmpBulletDamage%)

Shadow Meso:
Damage = 10 * Mesos * SpecialCritical (in skill description; ignores regular critical)

Meso Explosion:
if Mesos <= 1000, then Damage per bag = (50 * Mastery) * rand(0.5, 1) * ((Mesos * 820 + 28000) / 5300)
if Mesos >= 1000, then Damage per bag = (50 * Mastery) * rand(0.5, 1) * ((Mesos * 50000) / (Mesos + 5250))

note: Mastery = X/1000, where X is the internal skill variable.

Chakra Recovery:
Base = (LUK * 6.6 * 0.5 + DEX) * (SkillRecovery + 1) / 5

Heal Recovery:
Recovery = something * Magic * HealLevel * TargetMultiplier

Heal Target Multiplier: 0.3 + 1/NumTargets (including yourself)
1 - 1.3
2 - 0.8
3 - 0.633
4 - 0.55
5 - 0.5
6 - 0.467

Nekonecat's old equation:
Max = (1.132682429*10^-7*luk^2 + 3.368846366*10^-6*luk + 1.97124794*10^-3) * magic * int * healSkillLevel * multiplier
Min = MAX*0.8

Poison Brace/Poison Mist/Fire Demon/Ice Demon:
Damage per second tick = MonsterHP / (70 - SkillLevel)

Mob Damage

Weapon Damage:
PADamage^2 * rand(0.0085) - WDEF*A - (WDEF-StandardPDD)*B

where:

A = C + 0.28

if WDEF >= StandardPDD, then B = (C*28/45 + (CharacterLevel)*7/13000 + 0.196)
if WDEF < StandardPDD, then B = D * (C + (CharacterLevel)/550 + 0.28)

C (warriors) = STR/2800 + DEX/3200 + INT/7200 + LUK/3200
C (everyone else) = STR/2000 + DEX/2800 + INT/7200 + LUK/3200

if Character Level >= Mob Level, then D = 13/(13 + CharacterLevel - MobLevel)
if Character Level < Mob Level, then D = 1.3

StandardPDD values can be found here.

Magic Damage:
MADamage^2 * rand(0.0075, 0.008) - (MDEF/4 + STR/28 + DEX/24 + LUK/20) * K
where K = 1.2 for magicians and 1 otherwise.

Accuracy

Physical Accuracy:

HitRate = (13 - Avoid / Accuracy * (dLevel + 25.5)) / 6
FullAccuracy = Avoid * (dLevel + 25.5) / 7
MinAccuracy = Avoid * (dLevel + 25.5) / 13
where dLevel = MobLevel - CharLevel, and 0 if negative

Magical Accuracy:

HitRate = (12 - Avoid / Accuracy * (dLevel + 25.5)) / 7
FullAccuracy = Avoid * (dLevel + 25.5) / 5
MinAccuracy = Avoid * (dLevel + 25.5) / 12
where
Accuracy = (floor(INT/10) + floor(LUK/10)) * 5, and
dLevel = MobLevel - CharLevel, and 0 if negative

EXP Splitting

Leech conditions: At least one of the following must be met in order to share a cut of party EXP
1. Deal at least 1 damage to the monster.
2. Be within 5 levels of the monster.
3. Be within 5 levels of a party member that fulfills 1 or 2.

EXP received when partied = Monster EXP * (0.4 * Player level / Total party level + 0.6 * Damage dealt / Monster HP) * Party bonus
(Total party level = sum of the levels of all players that satisfy leech conditions. When not partied, you count as your own party, i.e. you get all the EXP.)
(In order words, 60% is split proportional to damage dealt and 40% is split proportional to character level.)

EXP recieved when not partied = Monster EXP * (Damage dealt / Monster HP)
(In order words, all EXP is split proportional to damage dealt.)

If your party is not the only one who dealt damage:
EXP received when partied = Monster EXP * (Damage your party dealt / Monster HP) * (0.4 * Player level / Total party level + 0.6 * Damage dealt / Damage your party dealt) * Party bonus
(It's the same as treating each party as a separate unpartied individual and then splitting within each party.)

EXP Required

Character
1: 15
2: 34
3: 57
4: 92
5: 135

6 ≤ level ≤ 50:
if level%3 = 0, exptnl(level) = (level^4 + 57*level^2)/9
otherwise, exptnl(level) = (level^4 + 55*level^2 - 56)/9

51 ≤ level:
exptnl(level) = floor(1.0548*exptnl(level-1))

Monster Book (credit to Chris from Kryptodev)
numCardsNeeded = (5 * MBLevel) * (MBLevel + 1)

Stat Related Stuff

Everything relating to HP/MP:
See LazyBui's Guide to HP and MP, no need to have info twice.

Base Accuracy:
Warriors/Magicians/Beginners = DEX * 0.8 + LUK * 0.5
Brawlers = DEX * 0.9 + LUK * 0.3
Bowmen/Thieves/Pirates/Gunslingers = DEX * 0.6 + LUK * 0.3

Base Avoid:
Warriors[/Magicians/Bowmen/Thieves/Beginners] = DEX * 0.25 + LUK * 0.5
Pirates = DEX * 0.25 + LUK * 0.5
Brawlers = DEX * 1.5 + LUK * 0.5
Gunslingers = DEX * 0.125 + LUK * 0.5

Hands = DEX + INT + LUK (used for Maker skill in KMS, thanks GW2000 for pointing that out)

Misc/Constants

Caps: (most of these are trivially common knowledge, but they're here for reference anyway)
Level: 200
HP/MP: 30000
STR/DEX/INT/LUK: 999
Weapon/magic attack/defense: 1999
Accuracy/avoid: 999
Meso: 2147483647 (or 2^31-1, the maximum value of a signed int)
Damage in one hit (normally): 199999

All of the above also apply to mobs, if the stat applies.

(non-thieves)
Min Miss Rate: 2%
Max Miss Rate: 80%
(thieves)
Min Miss Rate: 5%
Max Miss Rate: 95%

Cast times can be found in LazyBui's Attack Speed Reference

Base HP Recovery: 10 / 10 seconds while inactive
Base MP Recovery: 3 / 10 seconds

Mages' Improving MP Recovery skill: Character level * MP Recovery level / 10

EXP lost on death:
Warriors/Mages/Pirates' = (5 + 20 / Base LUK)%
Bowmen/Thieves' = (5 + 8 / Base LUK)%

Battleship Durability: Battleship level * 5000 + (Character level - 120) * 3000
Each point of durability is equivalent to 1 HP.

Energy Charge:
10000 units = 1 fully charged meter
Charge rate: Skill % * 100 units per monster per hit. In other words, at maximum level, it charges 192 units per monster per hit.
Energy Charge decay: 200 units / 10 seconds while inactive

Contributors

AGF
blitzkrieg
Devil's Sunrise
Fiel
GameMX
Hidden-Street
JoeTang
KaidaTan
Kortestanov
LazyBui
RFSurg
Stereo
Sybaris
Truemark
ZakumSlaYers
50504724

Thank you!

Not dealt with

This is for my own reference.

http://pastebin.com/UGt7uE66

[Devil's Sunrise]

Holy charge:
[120% + (1.5% *(lvl)] - advantage
[80% - (1.5% * lvl)] - disadvantage


Slash blast FA:
[FA multiplier]*(1+(1/3)^6-(1/3)^monsters) - Damage multiplier for Slash blast FA. Total damage on monsters (switch with amount of monsters).
FA multiplier * 2 * (1/3)^monster# - Per monster. Monster# is the number of the monster hit. (1 = 1st, 2 = 2nd, etc...)

[RFSurg]

Combo Attack
Combo Multiplier = (115% + Advanced Combo % + 5% * number of orbs)

Combo, if you have Max Combo Attack, would be 120% + AC percent + (5% * orbs 2-5) + (4% * orbs 6 - 10)

The 120% would be the 1st orb wih just max Combo Attack and it grows with the AC percent
-

Finishers = Skill Description % * Combo Multiplier * number of orbs / 2

This formula only works with max combo attack and a maxed finisher and stop working with AC orbs.

From what I've seen This post is right

Combo Effect % * Finsiher % * Orbs Multiplier

The orb multipliers are:

1 orb = 100%
2 orbs = 120%
3 orbs = 154%
4 orbs = 200%
5 - 10 orbs = 250%

[GW2000]

Hands is used for the Maker alchemy skill. It's only released in kMS so far though.

[Technolink]

Sap, might wanna keep Peirce at 1.18 for now, we have done 0 testing with 1.10, so it seems silly to think its soley a reversed IA.

[Kevvl]

Wait, there's an avoid formula? I've seriously been wondering about that for like a year XD

[Devil's Sunrise]

also, just fyi:

weapon damage:
(Base Damage*Elemental Charge * Elemental (dis)Advantage - Defense Reduction) * (Attack Percent + Critical Bonus) * Effect Multiplier

[LazyBui]

Might want to fuse 1H Axe and 1H Blunt Weapon as well as 2H Axe and 2H Blunt Weapon. They're calculated in the same way and that's just less text for the limit.

Uhh.

Shadow Partner does exactly 50% of whatever damage you inflict with skills, but exactly 80% of single star damage at max level. The damage is displayed well enough in the skill description, there's really not much of a need to add that.

Shadow Meso damage is 10 * number of mesos thrown. When it does crit, it does 150% damage. It has its own critical system.

Shadow Web does a weird HP percentage thing depending on its level, might want to look more into that, I know I've seen a table before.

Oh, Elemental Amplification does not apply to 4th job summons for Mages.

I think the 55.2 accuracy formula is more correct than the 55.0 accuracy formula, you'd have to get some second opinions on that though.

I'm pretty sure Arrow Bomb has two classifications of splash damage. It's one of two attacks that can break the damage barrier in a single hit (as in, the numbers can reach over 99,999 - the other being Piercing Arrow). But that's another formula, another day. I'm more interested in a concrete representation of charge skills and Meso Explosion. Or multi-target Heal.

Regardless, keeping tabs on every formula in Maple is no simple task. Good luck.

[RFSurg]

Since all Weapon Damage formulas follow the same base with just different primary stats, secondary stats(str + dex for thieves), and multipliers, wouldn't it be cleaner and easier to just post the base formula and the different stats/multipliers for different weapons?

[Russt]

That is true.

Updating thread.

also, just fyi:

weapon damage:
(Base Damage*Elemental Charge * Elemental (dis)Advantage - Defense Reduction) * (Attack Percent + Critical Bonus) * Effect Multiplier

Those are included in Effect Multiplier (which is everything in the 'Effect Multiplier' spoiler tag except actual attack skills). As for whether they come before the defense reduction and everything else, I'd doubt it. As far as I know, all multipliers come after defense, and everything other than the actual attack skill's damage comes after critical as well.

[JoeTang]

Combo Attack:
If Orbs = 0

100%

Else

Level 1:
95% + Orbs * 5%
1 < Level < 10
97% + Orbs * 5% + Level
10 <= Level < 21
102% + Orbs * 5% + (Level - 1) / 2
Level > 20
105% + Orbs * 5% + (Level / 3);

Advanced Combo Attack:
Orbs < 6
115% + Orbs * 5% + Level
Orbs > 5
120% + Orbs * 4% + Level

[Devil's Sunrise]

That is true.

Updating thread.


Those are included in Effect Multiplier (which is everything in the 'Effect Multiplier' spoiler tag except actual attack skills). As for whether they come before the defense reduction and everything else, I'd doubt it. As far as I know, all multipliers come after defense, and everything other than the actual attack skill's damage comes after critical as well.

Elemental charge + Elemental advantage has always been added in before weapon reduction for white knights and paladins, at least.

accuracy To 100% = (55.2 + (2.15 * lvlDifference)) * mavoid / 15;

if lvlDifference is less than 0, put it 0 instead.

chance to hit:
2 * (accuracy - (accuracyTo100% / 2)) / accuracyTo100% ;

[Stereo]

Dragon Roar ~ no slash/stab, uses spear/PA though
Primary: 4*STR
Secondary: DEX

I've been working on the monster damage formula but it's a lot more complicated than I initially expected.

A decent approximation is
base max: (atk^2)/120 + atk/15*classmod
base min: 0.945 * max
max = base max - 0.5*def
min = base min - 0.4*def
* classmod = 1 for warriors, 0.8 for thief, 0.7 for bowman, 0.4 for mages, 0.01 for beginners - may change by level, I haven't done extensive testing on low level characters because they die too fast on anything strong enough for the effect to be measurable.
The actual formula has 5 factors that I can find:
(monster)
[M]ATK
(player)
STR
[M]DEF
CLASS
LEVEL

The trouble is figuring out how these play off each other - what I do know is that there's a "baseline" defense/str, where a class takes normal reduction (0.5*def), and a "baseline" class specific increase to damage, which may or may not directly be affected by level (I've seen a chart that was in the wz that listed specifics for each class at certain levels but I can't confirm whether it's used).
STR and Defense are somehow working together, so that the ideal situation is to have as much as possible of both (higher STR = higher damage reduction per defense point). The extent of this is not currently known to me except for some vague formula which may or may not be accurate: 0.5*DEF+STR/2000*(DEF-K)
K is some value that seems to depend on class & level, I suspect it's in the range of 500 defense for high level warriors but other than that I can't say.

[Technolink]

Would you mind passing your data onto us? Perhaps we could help ya out.

I actually remember there being an addition to the wz files for armours, something that made it more advantagous to wear armour of your level (it gives less defence if it isn't your level bracket).

Perhaps you should work on naked tests first.

[EndlessAxis]

Ohhh Thanks , Very usefull was lookin for this

[Stereo]

Would you mind passing your data onto us? Perhaps we could help ya out.

3 sections; the 0 stats ones are where I reached the 94.5% figure for minimum damage based on max.
1) Bains. 425 atk, 0 stat damage is to a level 200 character with 0 wdef, 0 luk, 0 dex, 0 int. STR varied as shown, all STR figures are with 1 wdef.
Bain obs max obs min str
Beginner
1535 1453 0
1537 1454 5000
WK
1566 1485 0
1604 1519 2000
1658 1569 5000
Mage
1553 1464 0
1620 1532 5000

2) Jr. Cerebes. 132 atk, same character, same order of observations.
jr cerebes obs max obs min
148 140
149 141
172 163
197 189
237 229
161 152
208 200

3) Horntail's Tail (1750 atk). Level 200 WK, 20000 STR, 0 dex/luk/int. All numbers are maximum hit recorded, to within about 20.
0 wdef: 26500
500 wdef: 22000
1000 wdef: 16000
1500 wdef: 10000
1999 wdef[max wdef]: 4000



Oh and one final thing - most of my testing was done dually with level 0 and level 120 gear having identical stats - there was no observed difference in damage taken, the idea of gear level mattering is a myth.

[Technolink]

lvl 120 gear with the stats of lvl 0 gear O-o

This is actual observed right? I assume tespia?

[JoeTang]

Consider:
(Base Damage * Elemental Advantage * Multipliers - Defense Reduction) * (Skill% + Critical% + Sharp Eyes%)
If Elemental Advantage and Multipliers are calculated before Defense Reduction for White Knights and Paladins. Of course, the only attacks that have Multipliers are Charges, Combo, Berserk, and Shadow Partner (I think).

[butterfλi]

Magic Damage Formula found by Kyran

Max Power = (.005979 x Magic)² + (.0359 x Magic)
Min Power = (.005979 x Magic)² + (.0359 x Magic x Spell Mastery)

There are others since the magic formula is quadratic but this is awfully close.


A magic damage calculator made by Crovie that uses the formula.

http://img263.imageshack.us/img263/3589/magicwo3.swf

----

I found this to be more close than the one on HS.

[Russt]

Consider:
(Base Damage * Elemental Advantage * Multipliers - Defense Reduction) * (Skill% + Critical% + Sharp Eyes%)
If Elemental Advantage and Multipliers are calculated before Defense Reduction for White Knights and Paladins. Of course, the only attacks that have Multipliers are Charges, Combo, Berserk, and Shadow Partner (I think).

I lump IA multipliers and such in with the others, since it just logically makes more sense to me if every single multiplier that has any effect on damage is put in the same place.
So that includes IA and Pierce, as well as SBFA, Heal, Amp, and everything else of that sort.
On a semi-related note, Shadow Partner damage is most definitely calculated after defense. Then again, since SP just copies the numbers, it doesn't actually follow the order of operations. It just takes the damage number from below it and multiplies by the thing in the skill description.