# Character Attack Formulas

(Difference between revisions)
 Revision as of 20:56, 1 October 2009 (edit) (clarification)← Previous diff Revision as of 04:00, 2 October 2009 (edit) (undo) (huge expansion w/analysis, some corrections, restructure)Next diff → Line 1: Line 1: + == Damage Formula == + The formula has been well tested and seems to be extremely close, barring possible issues with different rounding algorithms.
The formula has been well tested and seems to be extremely close, barring possible issues with different rounding algorithms.

Line 32: Line 34: Defense bug lurks though, so it's just:
Defense bug lurks though, so it's just:
Final Damage = Base + Rnd[1 to Atk/8]
Final Damage = Base + Rnd[1 to Atk/8]
-
+ + == Chance to Hit Formula == + Chance to Hit Formula in percent, range [1 to 97]
Chance to Hit Formula in percent, range [1 to 97]
if Atk = 0 and Def = 0: 50
if Atk = 0 and Def = 0: 50
Line 38: Line 42: if Atk < Def: 0.5 - 0.5 * (Def - Atk) / Def
if Atk < Def: 0.5 - 0.5 * (Def - Atk) / Def
Since Monster Defense passed to this formula is 0, you should always have 97% chance to hit.
Since Monster Defense passed to this formula is 0, you should always have 97% chance to hit.
+ + == Critical/Backstab Formula == + + Chance of scoring a critical hit or backstab: + + ;Crit: + ((((LN((GLvl / 999) + 1) * 100) * LN(CritMod + 1)) / 3) - (LN((MonLvl / 999) + 1)) * 100))/2 + Ln(ItemDropLevel+1) * Ln(10) + + Minimum 1% (if the character has any critical hit ability) or whatever the weapon's crit % is (see below) + Maximum 50% (although 33.1% is the highest that can be achieved in-game) + + ;Backstab: + ((((LN((GLvl / 999) + 1) * 100) * LN(BSMod + 1)) / 3) - (LN((MonLvl / 999) + 1)) * 100))/2 + Ln(ItemDropLevel+1) * Ln(100) + + Minimum 2% (if the character has any backstab ability) or whatever the weapon's backstab % is (see below) + Maximum 75% (39.4% is the maximum that can be achieved in-game) +

- Chance of scoring a critical hit or backstab:
- Crit: ((((LN((GLvl / 999) + 1) * 100) * LN(CritMod + 1)) / 3) - (LN((MonLvl / 999) + 1)) * 100))/3 + Ln(ItemDropLevel+1) * Ln(10), maximum 50%
- Backstab: ((((LN((GLvl / 999) + 1) * 100) * LN(BSMod + 1)) / 3) - (LN((MonLvl / 999) + 1)) * 100))/2 + Ln(ItemDropLevel+1) * Ln(100), maximum 75%

CritMod = Value found in Help File, i.e., Warrior = 9, Seeker = 3
CritMod = Value found in Help File, i.e., Warrior = 9, Seeker = 3
BSMod = Value found in Help File, i.e, Thief = 9, Ninja = 2
BSMod = Value found in Help File, i.e, Thief = 9, Ninja = 2
+ + === An analysis === + + A simplified way of looking at the formula is: + + LN(1 + (GLvl / 999)) * 38.38 (assuming Warrior or Thief)
+ - LN(1 + (MonLvl / 999)) * 50
+ + LN(ItemLevelDrop + 1) * [2.30 if crit or 4.61 if backstab]
+ + ==== Portion from guild ability ==== + + The contribution from guild ability alone is: + + * +26.6% for warrior/thief 999 for crit/backstab, respectively + * +15.6% for warrior/thief 500 + * +8.6% for warrior/thief 250 + * +4.4% for warrior/thief 120 + * +2.2% for warrior/thief 60 + + For other guilds, the 38.38 figure above should be replaced by LN(CritMod + 1 or BSMod + 1) * 16.667. For instance, for a guild ability of 5 (Scavenger's backstab or Ninja's crit), the figures would be: + + * +20.7% for level 999 + * +12.1% level 500 + * +6.7% level 250 + * +3.4% level 120 + * +1.7% level 60 + + ==== Portion subtracted by monster ability ==== + + The amount subtracted by various monsters is: + + * -34.7% for level 999 (you-know-who) + * -15.0% for level 350 (the highest you'll see for most other monster types) + * -9.1% for level 200 (semi-common for level 15 monsters) + * -4.8% for level 100 (pretty common for levels 10-15) + * -2.4% for level 50 + + ==== Portion from weapon ability ==== + + The amount added by various weapons is: + + ;Critical Hit: + * +2.5% for a [[Katana]] (from level 2) + * +6.5% for a [[Sword of Flames]] (from level 16) + + ;Backstab: + * +5.1% for a [[Thief Sword]] (from level 2) + * +12.8% for a [[Dagger of Swiftness]] (from level 15) + + The percentage chance of a crit or backstab will never be lower than the chance given by the weapon alone, regardless of the level of the monster faced. In most cases, this means any guild ability you have will be completely overshadowed if your weapon has crit/backstab ability, unless your guild level is very high. This is further compounded when you factor in the effect of monster "defense". [http://mordor.uni.cc/forum/index.php?showtopic=1207 Discuss this topic in the forum] [http://mordor.uni.cc/forum/index.php?showtopic=1207 Discuss this topic in the forum]

## Damage Formula

The formula has been well tested and seems to be extremely close, barring possible issues with different rounding algorithms.

GLvl = Guild Level with best fighting ability, should be the same as the one in "Guild" Tab
FightingMod = Value found in Help File / 10, i.e., Warrior = 1.2, Nomad = 0.7
Size = Range [0 to 5] or Very Small, Small, Normal, Big, Very Big, Huge
Ln stands for natural logarithm.
Rnd is a number ranging from 0 to 0.999.. (not 1, this is important because it produces different top values).

This is the Damage Modifier, a bit more complex than I expected really
1: DamMod = 0.6 + (((Ln(100 + GLvl) / 1.75) - 2.3) * FightingMod^2 / 2)
2: * WeaponModifier
3: + 5 if Critical Hit, Chance see below
4: + 2 if Backstab, Chance see below
5: / 2 if Monster is invisible and character can't see invisible
6: +0.1/-0.1 per size bigger/smaller than monster
7: if DamMod is > 1, then DamMod = DamMod - ln(DamMod)^2
Value 0.1 to 7ish (Lv 999 Human Warrior with a Mod 2.6 Weapon, severing a Tiny monster)

Let's get the Strength Modifier, it's actually 2 parts, and requires a new Strength Value (called BSV here)
BSV = Int(Strength - (LN(Strength) * ((LN(Strength) - 2,4) * 2,25))) + 1
StrMod1 = Int((Rnd * ((BSV + 10) / 2)) + ((BSV + 10) / 4)) / 10
StrMod2 = BSV/30
Str 1 to 40 -> Value [0.3-0.8 * 0.06667] to [1-2.9 * 1] Note, this value is the 2 StrMods combined

And last part of formula, Level Modifier.
LvlMod = (Ln(GLvl + 5) + 1) / Ln(1.2)
Lvl 1 to 999 -> Value 15.31228 to 43.39447

Base Damage = LvlMod * StrMod1 * StrMod2 * DamMod
Final Damage = Base - Rnd[1 to (Def-Atk)/8] or very close to this
Defense bug lurks though, so it's just:
Final Damage = Base + Rnd[1 to Atk/8]

## Chance to Hit Formula

Chance to Hit Formula in percent, range [1 to 97]
if Atk = 0 and Def = 0: 50
if Atk > Def: 0.5 + 0.5 * (Atk - Def) / Atk
if Atk < Def: 0.5 - 0.5 * (Def - Atk) / Def
Since Monster Defense passed to this formula is 0, you should always have 97% chance to hit.

## Critical/Backstab Formula

Chance of scoring a critical hit or backstab:

Crit

((((LN((GLvl / 999) + 1) * 100) * LN(CritMod + 1)) / 3) - (LN((MonLvl / 999) + 1)) * 100))/2 + Ln(ItemDropLevel+1) * Ln(10)

Minimum 1% (if the character has any critical hit ability) or whatever the weapon's crit % is (see below) Maximum 50% (although 33.1% is the highest that can be achieved in-game)

Backstab

((((LN((GLvl / 999) + 1) * 100) * LN(BSMod + 1)) / 3) - (LN((MonLvl / 999) + 1)) * 100))/2 + Ln(ItemDropLevel+1) * Ln(100)

Minimum 2% (if the character has any backstab ability) or whatever the weapon's backstab % is (see below) Maximum 75% (39.4% is the maximum that can be achieved in-game)

CritMod = Value found in Help File, i.e., Warrior = 9, Seeker = 3
BSMod = Value found in Help File, i.e, Thief = 9, Ninja = 2

### An analysis

A simplified way of looking at the formula is:

LN(1 + (GLvl / 999)) * 38.38 (assuming Warrior or Thief)
- LN(1 + (MonLvl / 999)) * 50
+ LN(ItemLevelDrop + 1) * [2.30 if crit or 4.61 if backstab]

#### Portion from guild ability

The contribution from guild ability alone is:

• +26.6% for warrior/thief 999 for crit/backstab, respectively
• +15.6% for warrior/thief 500
• +8.6% for warrior/thief 250
• +4.4% for warrior/thief 120
• +2.2% for warrior/thief 60

For other guilds, the 38.38 figure above should be replaced by LN(CritMod + 1 or BSMod + 1) * 16.667. For instance, for a guild ability of 5 (Scavenger's backstab or Ninja's crit), the figures would be:

• +20.7% for level 999
• +12.1% level 500
• +6.7% level 250
• +3.4% level 120
• +1.7% level 60

#### Portion subtracted by monster ability

The amount subtracted by various monsters is:

• -34.7% for level 999 (you-know-who)
• -15.0% for level 350 (the highest you'll see for most other monster types)
• -9.1% for level 200 (semi-common for level 15 monsters)
• -4.8% for level 100 (pretty common for levels 10-15)
• -2.4% for level 50

#### Portion from weapon ability

The amount added by various weapons is:

Critical Hit
Backstab

The percentage chance of a crit or backstab will never be lower than the chance given by the weapon alone, regardless of the level of the monster faced. In most cases, this means any guild ability you have will be completely overshadowed if your weapon has crit/backstab ability, unless your guild level is very high. This is further compounded when you factor in the effect of monster "defense".