# PDIF

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 Physical Difference or "pDIF" is a series of functions that consider the ratio of player attack vs. monster defense and determine how much melee damage is dealt every time your character swings its weapon or gets swung at. There are at least three different kinds of pDIF equations. The formulas below mostly refer to melee pDIF, with a nod here and there to ranged pDIF. They completely ignore pet/monster/avatar pDIF, which is thought to follow different equations or have different caps.
Pre-Randomizer pDIF Caps by Weapon Type
Weapon Type Non-crit Crit
1-Handed 3.25 4.25
H2H & Great Katana 3.5 4.5
2-Handed 3.75 4.75
Archery & Throwing 3.25 3.25*1.25
Marksmanship 3.5 3.5*1.25
Pre-Randomizer pDIF Caps by Weapon Type and Lv99 Jobs with Damage Limit+ Trait
Job:            Weapon Type Non-Crit Crit Non-Crit Crit Non-Crit Crit Non-Crit Crit
1-Handed 3.75 4.75 3.55 4.55 3.45 4.45 3.35 4.35
H2H & Great Katana 4.0 5.0 3.8 4.8 3.7 4.7 3.6 4.6
2-Handed 4.25 5.25 4.05 5.05 3.95 4.95 3.85 4.85
Archery & Throwing 3.75 3.75*1.25 3.55 3.55*1.25 3.45 3.45*1.25 3.35 3.35*1.25
Marksmanship 4.0 4.0*1.25 3.8 3.8*1.25 3.7 3.7*1.25 3.6 3.6*1.25

## Attack/Defense Ratio

• Ratio = Attacker's Attack/ Target's Defense
• 1H melee weapons have an effective ratio cap of 3.625
• H2H and GKT melee weapons have an effective ratio cap of 3.875
• 2H melee weapons have an effective ratio cap of 4.125
• Archery and Throwing have an unknown ratio cap (perhaps approximately 3.2375)
• Marksmanship also has an unknown ratio cap (perhaps approximately 3.475)
Example: 1H Player Earthworm Jim has 1000 Attack and is fighting a monster that has 500 Defense. His Ratio is 1000/500, or 2.00.
• Additional Factors during this stage
• Estimating Ratio via /check command
• If your Ratio is less than 1, the monster will check "High Defense."
• If it is higher than 1.25, the monster will check "Low Defense."

## Level Correction Function (cRatio)

Level correction function imposes a penalty to attack/defense ratio if the target's level is higher than attacker's level (or item level). After the Attack/Defense Ratio has been corrected, it is referred to as "cRatio" or "corrected Ratio." This correction does not apply in all zones (not in Adoulin zones, Legion, or zones in Escha/Reisenjima). Monsters are also affected by level correction when they attack players, but their formulas give a bonus to ratio when they are over the player's level. It is unclear whether this mechanic applies in the aforementioned zones, but it probably does not.

• Melee attacks have 0.05/level ratio penalty
cRatio = Ratio - (target's level - attacker's level) × 0.05
• Ranged attacks have 0.025/level ratio penalty
cRatio = Ratio - (target's level - attacker's level) × 0.025

These equations are one of the reasons that Rangers are preferred for fighting targets many levels above you.

Example: 1H Player Earthworm Jim has 2.00 Ratio, but the enemy he's fighting is level 124 and he's item level 119. The 5 level difference loses him .25 (=5×.05) Ratio, dropping him to 1.75 cRatio.

## After Ratio and Level Correction (Melee)

Beyond this point, there are several competing models that explain how cRatio translates into damage. The below description of melee pDIF is from Motenten's model, extended due to the 2/2016 pDIF changes. For a review of model differences, please see the talk page. Ranged damage is better understood (or at least our understanding of it is challenged less frequently), so it will be handled separately at the bottom. Motenten has expressed that this model is complete in an algorithmic manner, but explicitly incomplete.

### 1. wRatio

• 1. Calculate wRatio using your cRatio
• If you critical hit: wRatio = (cRatio + 1)
• If you do not critical hit: wRatio = (cRatio + 0)
Example 1: 1H Player Earthworm Jim has 2.0 cRatio. If he crits, he will have 3.0 wRatio. If he doesn't crit, he will have 2.0 wRatio.
Example 2: 1H Player Earthworm Jim has 3.0 cRatio. If he crits, he will have 4.0 wRatio. If he doesn't crit, he will have 3.0 wRatio.
• Optional: You can represent this mathematically write this using a logical expression, which will be 1 when true and 0 when false. Rand represents a random number from 0 to 1.
wRatio = cRatio + ( Rand < CritRate% )
ex: If your critical hit rate is 25% (0.25) and Rand (A random number between 0-1) is 0.1, the equation becomes wRatio = cRatio + 1

### 2. qRatio

• 1. Determine the Upper and Lesser Limit
• Upper Limit (See UL Equations)
• Lesser Limit (See LL Equations)
• Min/Max is only there for testing convenience; do not bother with them if they are confusing
• It is currently unknown if the cap per weapon type is applied to the UL and the LL. Doing so would only be noticeable when the UL is above the cap but the LL is not, resulting in a lower average result on the following step of qRatio.
wRatio UL Equation Min Max
0 ≤ wRatio < 0.5 wRatio + 0.5 0.5 < 1
0.5 ≤ wRatio < 0.7 1 1 1
0.7 ≤ wRatio < 1.2 wRatio + .3 1 < 1.5
1.2 ≤ wRatio < 1.5 (wRatio × 0.25) + wRatio 1.5 < 1.875
1.5 ≤ wRatio wRatio + 0.375 1.875 (varies)
wRatio LL Equation Min Max
0 ≤ wRatio < 0.38 0 0.5 < 1
0.38 ≤ wRatio < 1.25 (wRatio) × (1176/1024) - (448/1024) 0 < 4083/4096
1.25 ≤ wRatio < 1.51 1 1 1
1.51 ≤ wRatio < 2.44 (wRatio) × (1176/1024) - (755/1024) 0.9968359375 2.064882813
2.44 ≤ wRatio wRatio - 0.375 2.065 (varies)
• 2. Randomly select a value between LL and UL
• If the value is less than zero, set to zero
• If the value is greater than the cap shown for your weapon type in the list below, set to the cap value.
• 1H qRatio caps at 3.25 for non-crits and 4.25 for crits
• H2H qRatio caps at 3.5 for non-crits and 4.5 for crits
• 2H qRatio caps at 3.75 for non-crits and 4.75 for crits

### 3. Multiply the final

Multiply the final value by a random number between 1 and 1.05

• For example, if the final qRatio is 3, you'll end up with 3, 3.15, or a value between 3 and 3.15
• (3 ・ 1) = 3
• (3 ・ 1.05) = 3.15

## After Ratio and Level Correction (Ranged )

Ranged damage uses cRatio, which is calculated as described above. Then it picks a random value between the below damage limits. It is notable that there is no secondary random multiplier for ranged damage, but qRatio is capped differently for different weapon types:

• Archery and Throwing qRatio is capped at 3.25
• Marksmanship qRatio is capped at 3.50
cRatio UL Equation Min Max
0 ≤ cRatio < 0.9 cRatio × (10/9) 0 1
0.9 ≤ cRatio < 1.1 1 1 1
1.1 ≤ cRatio cRatio 1.1 3.5
cRatio LL Equation
0 ≤ cRatio < 0.9 cRatio 0 0.9
0.9 ≤ cRatio < 1.1 1 1 1
1.1 ≤ cRatio cRatio×(20/19) - (3/19) 1.1 3.5

### Ranged Critical Hit Damage

Unlike melee hits (which have additive damage from critical hits), Ranged critical hits are implemented as a +25% multiplier that bypasses the cap.

• Critical ranged pDIF = Normal Ranged pDIF × 1.25

### Distance Correction

Also unlike melee hits, ranged attacks have Distance Correction and utilize True Shot, which uniquely affects damage multipliers for Ranged Attacks and also is not capped.

Ex: Master RNG with 4% True Shot gear 7% from traits and 8% from gifts would have 19% True Shot. The multiplier for archery would then become 3.25 * 1.19 = 3.8675 and the multiplier for marksmanship would become 3.5 * 1.19 = 4.165 if fired from proper distance ranges.