Damage Formula

A player's damage output, shown directly above monsters when attacking, is calculated by multiplying specific factors.

All numbers in this page are decimals instead of percents.

Calculation

Paraphrased from https://strategywiki.org/wiki/MapleStory/Formulas, approximate average output is the product of these unofficially named factors:

• 0.01
• Current Applied Weapon Constant
• Stat Multiplier
• Attack Power/Magic ATT
• Damage Multiplier
• Final Damage Multiplier

Multiplying only the factors above, while subtracting Boss Damage or Normal Enemy Damage from Damage Multiplier, outputs Default Damage Range

• Critical Damage Multiplier
• Ignore Defense Multiplier
• Ignore Elemental Resistance Multiplier
• Level Multiplier
• Map Multiplier
• Skill Multiplier
• Mastery Multiplier

Stat Multiplier

For jobs except Demon Avenger:

4 (Main Stat 1 + Main Stat 2 + Main Stat 3) + Secondary Stat 1 + Secondary Stat 2; inapplicable Stats are 0

A Stat is floor(Base Value (1 + % Value)) + % Value Not Applied

All Stats increase STR, DEX, INT, and LUK; nothing else.

Basic Base Main Stat for jobs except Demon Avenger and Xenon:

5 (Level - 10) + 4 + 54 + 5 + 5 = 5 (Level) + 18

Attack Power/Magic ATT

floor(Base Value (1 + % Value)) + % Value Not Applied

For jobs except Kanna:

floor(Base Value (1 + % Value))

This factor is approximately equal to Base Value (1 + % Value), which can be separated into two independent factors.

Magicians use Magic ATT; other jobs use Attack Power.

Damage Multiplier

1 + % Damage + % Boss Damage for bosses

or

1 + % Damage + % Normal Enemy Damage for mobs

If a source isn't always applied for all skills, it will not appear on the Character Info UI. Some sources will only appear on the UI under specific circumstances when mobbing or bossing.

Conditional % Damage: Hyper "Reinforce" passives, Ark/Illium/Mo Xuan/Hoyoung/Explorer Magician/Explorer Thief/Cadena/Angelic Buster/Kain/Adele Link Skills, Wild Hunter/Sia Astelle Legion effect, Inner Ability: Additional Status Damage, etc

Conditional % Boss Damage: Hyper "Boss Rush" passives

Conditional % Normal Enemy Damage: Lara Link Skill

Final Damage Multiplier

1 + % Final Damage

Adding a source:

(1 + % Final Damage without Source) (1 + Source)

Maxed 5th Job Boost Nodes on a skill:

output (1 + 0.02 (60)) = output (2.2)

Critical Damage Multiplier

1.35 + % Critical Damage for critical hits

or

1 for non critical hits

Base % Critical Damage is a number between 1.2 and 1.5.

Ignore Defense Multiplier

1 - (% Enemy Defense (1 - % Ignore Defense))

If this multiplier is 0 or negative, output is 1 damage. Usually, mobs' % Defense is 0.1 and difficult bosses' Defense is 3.8.

% Ignore Defense = 1 - ((1 - Source 1) (1 - Source 2) (1 - Source 3) ...)

Adding a source:

1 - ((1 - % Ignore Defense without Source) (1 - Source))

Removing a source:

1 - ((1 - % Ignore Defense with Source) / (1 - Source))

Adding or removing a source using the whole multiplier:

1 - (% Enemy Defense (1 - % Ignore Defense) * or / (1 - Source))

Each line of potential is a separate source. 4th, Hyper, and 5th Job passives for one skill are separate sources. Hyper passives enhancing debuffs are simply added to the original value as percentage points.

Conditional % Ignore Defense: Hyper "Guardbreak" passives, Explorer Magician Link Skill

Ignore Elemental Resistance Multiplier

0.5 (1 + % Ignore Elemental Resistance) for almost all bosses

or

1 for almost all mobs

If Insight trait is maxed, this is usually 0.5 (1 + 0.05) = 0.525.

Level Multiplier

Player Level above Monster Level	Multiplier
5 or more	1.2
4	1.18
3	1.16
2	1.14
1	1.12
0	1.1
Player Level below Monster Level	Multiplier
1	1.0584
2	1.007
3	0.9672
4	0.918
5	0.88
6	0.85
7	0.83
8	0.8
9	0.78
10	0.75
11	0.73
12	0.7
13	0.68
14	0.65
15	0.63
16	0.6
17	0.58
18	0.55
19	0.53
20	0.5
21 (runes, chests, and elites stop spawning)	0.48
22	0.45
23	0.43
24	0.4
25	0.38
26	0.35
27	0.33
28	0.3
29	0.28
30	0.25
31	0.23
32	0.2
33	0.18
34	0.15
35	0.13
36	0.1
37	0.8
38	0.5
39	0.3
40 or more	0

If this multiplier is 0, output is 1 damage.

Map Multiplier

Depends on player's Sacred Power, Arcane Power, or Star Force compared to the map's recommendation. Includes event titles, event buffs, and guild passive skill.

50 Sacred Power over recommended: 1.25

Same Sacred Power: 1

1.5 times the recommended Arcane Power: 1.5

Same Arcane Power: 1

20 Star Force over recommended: 1.2

Same Star Force: 1

Skill Multiplier

+%p values are added to each hit of a skill's "Damage: damage%" as percentage points.

Mastery Multiplier

0.5 (1 + % Weapon Mastery)

Each hit of a skill is multiplied by a number between % Weapon Mastery and 1. After 5th Job, % Weapon Mastery varies between 0.86 and 0.99, depending on the job.

Stat Equivalence for Most Jobs

relative change = (new - old) / old

relative change + 1 = new / old

For most jobs:

Stat Multiplier = 4 (floor(Base Main Stat (1 + % Main Stat))) + 4 (% Main Stat Not Applied) + floor(Base Secondary Stat (1 + % Secondary Stat)) + % Secondary Stat Not Applied

= 4 (floor(a (b))) + 4 (c) + floor(d (e)) + f

≈ 4ab + 4c + de + f

Due to dropping the floor function, the formulas below are inexact.

For jobs except Demon Avenger, gaining 1 Flame score represents the same increase in output as gaining 1 Main Stat.

Currently, the best Flames are used to maximize burst damage during bossing. As a result, the factors below should be obtained during burst. While some factors are the same in both situations or easily seen from the Character Stat UI, others such as Damage Multiplier and Ignore Defense Multiplier are higher during burst and depend on conditions.

% All Stats Flame Score

1% All Stats = x Main Stat

$\frac{4(x+a)b+4c+de+f}{4ab+4c+de+f}=\frac{4a(b+0.01)+4c+d(e+0.01)+f}{4ab+4c+de+f}$

$4bx+4ab+4c+de+f=4ab+0.04a+4c+de+0.01d+f$

$4bx=0.04a+0.01d$

$x=\frac{0.01a+0.0025d}{b}$

Secondary Stat Flame Score

1 Secondary Stat = x Main Stat

$\frac{4(x+a)b+4c+de+f}{4ab+4c+de+f}=\frac{4ab+4c+(d+1)e+f}{4ab+4c+de+f}$

$4bx+4ab+4c+de+f=4ab+4c+de+e+f$

$4bx=e$

$x=\frac{e}{4b}$

Flame Score of Other Factors

$\frac{4(x+a)b+4c+de+f}{4ab+4c+de+f}=\frac{new}{old}$

$4b(x+a)+4c+de+f=\frac{new(4ab+4c+de+f)}{old}$

$4b(x+a)=\frac{new(4ab+4c+de+f)}{old}-4c-de-f$

$x+a=\frac{\frac{new(4ab+4c+de+f)}{old}-4c-de-f}{4b}$

$x=\frac{\frac{new(4ab+4c+de+f)}{old}-4c-de-f}{4b}-a$

new and old represent factors, Base Attack Power/Magic ATT, or 1 + % Attack Power/Magic ATT

Base Attack Power/Magic ATT Flame Score

1 Base Attack Power/Magic ATT = x Main Stat

For jobs except Kanna:

$x=\frac{\frac{(att+1)(4ab+4c+de+f)}{att}-4c-de-f}{4b}-a$

% Damage or % Boss Damage Flame (Weapons) Score

1% Damage or 1% Boss Damage = x Main Stat

$x=\frac{\frac{(1.01+\mathrm{\%}Damage+\mathrm{\%}BossDamage)(4ab+4c+de+f)}{1+\mathrm{\%}Damage+\mathrm{\%}BossDamage}-4c-de-f}{4b}-a$

Effectiveness of Hoyoung Link

Bravado's effectiveness against Fire Spirit monster

Bravado is not useful if the player will always one-shot without it or cannot reliably one-shot with it. If a lengthy mobbing session is possible, a Battle Analysis can show average output with and without Bravado. Otherwise, average output with Bravado is (average output without Bravado) (1 + % Damage + % Normal Enemy Damage + 0.19) / (1 + % Damage + % Normal Enemy Damage), including conditional sources. Even in a simple setup of Erda Fountain and Level 20+ Sol Janus: Dawn, mobbing output can change due to job skills. For example:

• Night Walker's Base Attack Power changes based on Vitality Siphon
• Hayato's % Attack Power changes based on Sword Energy
• Gauge level may affect some jobs' output

If average output without Bravado is approximately equal to monster HP, Bravado is worth using.