View source for PDIF

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|Intro Text='''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.<br />
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.
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<div style="display: flex; flex-wrap: wrap;">
{| class="BGBlue1 R-Highlight-WikiBlue altrowgrey" style="width: 100%; max-width: 350px;  text-align: center;"
|- style="border-bottom: 3px solid #FF8000;"
! colspan="3" |Pre-Randomizer pDIF Caps by Weapon Type
|- 
! Weapon Type
! Non-crit
!  Crit
|- 
| 1-Handed<br />[[File:Mandau icon.png|25px|link=Dagger]] [[File:Excalibur icon.png|25px|link=Sword]] [[File:Guttler icon.png|25px|link=Axe]] [[File:Kikoku icon.png|25px|link=Katana]] [[File:Mjollnir icon.png|25px|link=Club]]
| 3.25
| 4.25
|- 
| H2H & Great Katana<br />[[File:Spharai icon.png|25px|link=Hand-to-Hand]] [[File:Amanomurakumo icon.png|25px|link=Great Katana]]
| 3.5
| 4.5
|- 
| 2-Handed<br />[[File:Ragnarok icon.png|25px|link=Great Sword]] [[File:Bravura icon.png|25px|link=Great Axe]] [[File:Gungnir icon.png|25px|link=Polearm]] [[File:Claustrum icon.png|25px|link=Staff]]
| 3.75
| 4.75
|- 
| Scythe<br />[[File:Apocalypse icon.png|25px|link=Scythe]]
| 4
| 5
|- 
| Archery & Throwing<br />[[File:Yoichinoyumi icon.png|25px|link=Archery]] [[File:Wingedge  icon.png|25px|link=Throwing]]
| 3.25
| 3.25*1.25
|- 
| Marksmanship<br />[[File:Annihilator icon.png|25px|link=Marksmanship]]
| 3.5
| 3.5*1.25
|}
<div style="padding: 5px;"></div>
{| class="BGBlue1 C-Highlight-WikiBlue altrowgrey" style="max-width: 1300px; text-align: center;"
|- style="border-bottom: 3px solid #FF8000;"
!colspan="9" |Pre-Randomizer pDIF Caps by Weapon Type and Lv99 Jobs with [[Damage Limit+|<span style="color: #C9E8FD;">Damage Limit+ Trait</span>]]
|- style="background: #C9E8FD;"
!style="width: 25%;"|Job:
|colspan="2" style="border-right: 1px solid #4696CF;" |{{DRK}}
|colspan="2" style="border-right: 1px solid #4696CF;" |{{MNK}} {{RNG}} {{DRG}}
|colspan="2" style="border-right: 1px solid #4696CF;" |{{WAR}} {{SAM}} {{BST}} {{PUP}} {{DNC}}
|colspan="2" style="border-right: 1px solid #4696CF;" |{{THF}} {{NIN}} {{RDM}}
|- style="color: #FFFFFF; background: #4696CF;"
! Weapon Type
! style="width: 9%;"| Non-Crit
! style="width: 9%;"| Crit
! style="width: 9%;"| Non-Crit
! style="width: 9%;"| Crit
! style="width: 9%;"| Non-Crit
! style="width: 9%;"| Crit
! style="width: 9%;"| Non-Crit
! style="width: 9%;"| 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
|-
| Scythe
| 4.5
| 5.5
| 4.3
| 5.3
| 4.2
| 5.2
| 4.1
| 5.1
|- 
| 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
|}
</div>
== 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
** Great Sword, Staff, Great Axe, and Polearm have an effective ratio cap of 4.125
** Scythe has an effective Ratio of 4.375
** Archery and Throwing have an unknown ratio cap (perhaps approximately 3.2375)
** Marksmanship also has an unknown ratio cap (perhaps approximately 3.475) 
:NOTE: The effective ratio cap is the point where pDIFmin becomes equal to the pre-randomized pDIFmax value. 

'''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'''
** Attack Bonuses (ex: [[Tachi: Gekko]])
** Ignore Defense Traits (ex: [[Quietus]])
* '''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 generally doesn't apply to zones with content added after 2013 including [[:Category:East Ulbuka Territory|Adoulin]], [[:Category:Ambuscade|Ambuscade]], and [[:Category:Escha|Escha]]/[[Reisenjima]]: refer to [[Level_Difference_Penalty#Zones_Without_Level_Difference_Penalty|Level Difference Penalty]] for a full list of zones without level correction. 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) {{math|times}} 0.05
* '''Ranged attacks have 0.025/level ratio penalty'''
: cRatio = Ratio - (target's level - attacker's level) {{math|times}} 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{{math|times}}.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.

[[Image:Verification.png|Verification Needed]] '''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
**[[Image:Verification.png|Verification Needed]] 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.
{| border="0" cellpadding="0" cellspacing="0" style="width: 100%; vertical-align: top;"
|-
|

{| class="wikitable" cellpadding="3" style="width: 100%; max-width: 610px; text-align: center;"
!colspan="1" |[[wRatio]]
!colspan="1" |UL Equation
!colspan="1" |Min
!colspan="1" |Max
|-
|style="background: #eef3f7; width: 30%;"|0 ≤ wRatio < 0.5
| style="width: 38%;"|wRatio + 0.5
| style="width: 16%;"| 0.5
| style="width: 16%;"| < 1
|- 
|style="background: #eef3f7;"|0.5 ≤ wRatio < 0.7 
|1
| 1
| 1
|- 
|style="background: #eef3f7;"|0.7 ≤ wRatio < 1.2
|wRatio + .3 
| 1
| < 1.5
|- 
|style="background: #eef3f7;"|1.2 ≤ wRatio < 1.5
|(wRatio {{math|times}} 0.25) + wRatio 
| 1.5
| < 1.875
|- 
|style="background: #eef3f7;"|1.5 ≤ wRatio
| wRatio + 0.375 
| 1.875
| (varies)
|}

{| class="wikitable" cellpadding="3" style="width: 100%; max-width: 610px; text-align: center;"
!colspan="1" |[[wRatio]]
!colspan="1" |LL Equation
!colspan="1" |Min
!colspan="1" |Max
|-
|style="background: #eef3f7; width: 30%;"|0 ≤ wRatio < 0.38
| style="width: 38%;"| 0
| style="width: 16%;"| 0
| style="width: 16%;"| 0
|- 
|style="background: #eef3f7;"|0.38 ≤ wRatio < 1.25
|(wRatio) {{math|times}} (1176/1024) - (448/1024) 
| 0
| < 4083/4096
|- 
|style="background: #eef3f7;"|1.25 ≤ wRatio < 1.51
|1
| 1
| 1
|- 
|style="background: #eef3f7;"|1.51 ≤ wRatio < 2.44
|(wRatio) {{math|times}} (1176/1024) - (755/1024)
| 0.9968359375
| 2.064882813
|- 
|style="background: #eef3f7;"|2.44 ≤ wRatio
|wRatio - 0.375
| 2.065
| (varies)
|-
|}

|
[[Image:2016 PDIF.jpg|thumb|min and max pDIF curves|right]]
|-
|}

* '''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 and Great Katana qRatio caps at 3.5 for non-crits and 4.5 for crits
*** Great Sword, Staff, Great Axe, and Polearm qRatio caps at 3.75 for non-crits and 4.75 for crits
***Scythe qRatio caps at 4 for non-crits and 5 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

{| border="0" cellpadding="0" cellspacing="0" style="width: 100%; vertical-align: top;"
|-
|
{| class="wikitable" cellpadding="3" style="width: 100%; max-width: 610px; text-align: center;"
!colspan="1" |[[cRatio]]
!colspan="1" |UL Equation
!colspan="1" |Min
!colspan="1" |Max
|-
|style="background: #eef3f7; width: 30%;"|0 ≤ cRatio < 0.9
| style="width: 38%;"|cRatio {{math|times}} (10/9)
| style="width: 16%;"| 0
| style="width: 16%;"| 1
|- 
|style="background: #eef3f7;"|0.9 ≤ cRatio < 1.1
|1
| 1
| 1
|- 
|style="background: #eef3f7;"|1.1 ≤ cRatio
|cRatio
| 1.1
| 3.5
|}

{| class="wikitable" cellpadding="3" style="width: 100%; max-width: 610px; text-align: center;"
!colspan="1" |[[cRatio]]
!colspan="1" |LL Equation
|-
|style="background: #eef3f7; width: 30%;"|0 ≤ cRatio < 0.9
| style="width: 38%;"| cRatio
| style="width: 16%;"| 0
| style="width: 16%;"| 0.9
|- 
|style="background: #eef3f7;"|0.9 ≤ cRatio < 1.1
|1
| 1
| 1
|- 
|style="background: #eef3f7;"|1.1 ≤ cRatio
|cRatio{{math|times}}(20/19) - (3/19)
| 1.1
| 3.5
|-
|}

|
[[Image:Ranged_pDIF.png|thumb|Ranged pDIF Min and Max curves|right]]
|-
|}

=== 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 {{math|times}} 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.

== References ==
* [http://www.bluegartr.com/threads/108161-pDif-and-damage?p=5007405&highlight=wratio#post5007405 Motenten's pDIF graphs and testing (Motenten, BG Forums)]
* [http://www.bluegartr.com/threads/108161-pDif-and-damage?p=5310540&viewfull=1#post5310540 Pchan's pDIF testing (Pchan, BG Forums)]
* Most of the information for Masamune's pDIF model was obtained from a long-term large-scale effort by Masamune of BG (or Masamunai on some other forums). It is currently represented in an excel sheet, which makes it difficult to cite as the wiki cannot host it and it contains personally identifying information. Send him a PM for information.
** [http://www.bluegartr.com/threads/71816-cratio-for-two-handers?p=2577673&viewfull=1#post2577673 Old cRatio tomfoolery (Cadasune, BG)]
** [http://www.bluegartr.com/threads/84304-RNG-updates?p=3230651&viewfull=1#post3230651 pDIF cap post-adjustment (Masamune, BG)]
** [http://www.bluegartr.com/threads/87774-pDIF-testing-and-Damage-formulas pDIF formulas post-adjustment, first pass (Masamune, BG)]
* [https://www.bluegartr.com/threads/127523-pDIF-Changes-%28Feb.-10th-2016%29 pDIF formulas 2-2016 adjustment (Fwahm and Byrth, BG)]
* [https://www.ffxiah.com/forum/topic/33470/the-sealed-dagger-a-ninja-guide/152/#3423239 GKT is not the same cap as other 2H weapons (Asura.Snapster, FFXIAH)]
* [https://www.ffxiah.com/forum/topic/35174/dont-fear-the-reaper-a-dark-knight-guide/178/#3475063 Scythe's new pDIF cap (Asura.Veikur, FFXIAH)]
[[Category: Game Mechanics]]