Level Correction Function and pDIF
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The Level Correction function
The Level Correction function modifies your (ranged) attack / monster defense ratio before it is used in the pDIF function.
Let's say you have 400 attack / ranged attack and the monster has 400 defense. Your (r)atk/def ratio would then be 1.
If the monster has a higher level than you, then a level corrected ratio is needed before calculating the pDIF.
Otherwise, when fighting EM monsters or lower, your atk/def ratio will not be modified when used in the pDIF function. In other words, there is no level correction.
For this example, assume you are fighting a level 81 monster and your own character is level 75.
Let Ratio be the value of your (r)atk divided by monster defense.
Ratio = your (r)atk/monster defense
Melee cRatio = Ratio - 0.050 x level difference
Ranged cRatio = Ratio - 0.025 x level difference
So after the level correction, your melee attack ratio is 0.7 and your Ranged Attack ratio is 0.85.
The min and max value of pDIF is the lower bound and upper bound of damage fluctuation.
pDIF
The pDIF calculation takes your (level corrected) Attack and Defense ratio and outputs a random number in certain value range.
pDIF always has a positive value.
- Melee and Ranged pDIF have different formulas:
Melee Attack
Note: The following equations are no longer correct. Research is currently being done to determine the new equations.
- max pDIF has the following formulas:
Ratio Range Function Value 0 ≤ cRatio < 0.5 fMax(cRatio) = 0.4 + 1.2 x cRatio 0.5 ≤ cRatio ≤ 5/6 fMax(cRatio) = 1 5/6 < cRatio ≤ 2 fMax(cRatio) = 1.2 x cRatio
- and Min pDIF has the following formulas:
Ratio Range Function Value 0 ≤ cRatio < 1.25 fMin(cRatio) = -0.5 + 1.2 x cRatio
if fMin < 0 → fMin = 01.25 ≤ cRatio ≤ 1.5 fMin(cRatio) = 1 1.5 < cRatio ≤ 2 fMin(cRatio) = -0.8 + 1.2 x cRatio
- When cRatio exceeds 2.0, cRatio is 2.0 (capped for melee)
- Rules for melee Critical Hit
- When critical hit occurs, your pDIF will be raised by 1 and the max pDIF cap is 3.0 instead of 2.4.
- Examples:
- When your pDIF is 0.4 and you score a critical hit, your pDIF is raised to 1.4 (add 1.0 to current pDIF value)
- When your pDIF is 2.3 and you score a critical hit, your pDIF is raised to 3.0 (3.3 → 3.0, since 3.0 is the cap)
- When your pDIF is -0.4 and you score a critical hit, your pDIF is raised to 0.6, but your normal attack will have pDIF = 0 (pDIF lower bound is 0)
Melee pDIF characteristic
When you have pDIF_min≤1.0 AND pDIF_max ≥1.0, the mode of pDIF lies on 1.0 about 33%±7% 
of the time.
Ranged Attack
Ratio Range Function Value 0 ≤ cRatio < 0.9 fMax(cRatio) = 10/9 x cRatio 0.9 ≤ cRatio ≤ 1.1 fMax(cRatio) = 1 1.1 < cRatio ≤ 3.0 fMax(cRatio) = cRatio
Ratio Range Function Value 0 ≤ cRatio < 0.9 fMin(cRatio) = cRatio 0.9 ≤ cRatio ≤ 1.1 fMin(cRatio) = 1 1.1 < cRatio ≤ 3.0 fMin(cRatio) = -3/19 + 20/19 x cRatio
- When cRatio exceeds 3.0, cRatio is 3.0 (capped for ranged)
- Rules for ranged Critical Hit
- Ranged critical hit always multiplies your pDIF by 1.25
- Example:
- When your pDIF is 3.0 and you score a critical hit, your pDIF will be 3.75
Notes
It seems that ratio, cRatio, and pDIF values are truncated to 3 digits.
