Thief Weapon Skill Damage Guide by Malizia

__TOC__
=What is the purpose of this Guide?=
I wanted to know how to equip my Thief to maximize Weapon Skill damage when I use Sneak Attack and/or Trick Attack. Answering that involves a lot of number crunching, so I decided to publish my results in a guide here rather than make everyone else figure out the same numbers. Also, this way people can correct my math if I'm wrong.
The basic type of question I had was, "well, I have a Garrulous Ring with STR and AGI +3, and a Spinel Ring with DEX +4... which should I use?" This guide answers that question.
This guide does not determine how Attack or Accuracy affect damage.
=What Stats Should I Emphasize?=
Assuming you're level 75, have 100% accuracy, 0% critical hit chance, and always use your weaponskills at exactly 100% TP:
*If you only use Sneak Attack with your weaponskills, ignore AGI and stack DEX. 1 DEX = 2 STR (unless you primarily use Shark Bite, where 1 DEX = 3 STR) for equipment comparisons.
*If you only use Trick Attack with your weaponskills, still focus on DEX and supplement with AGI. For Dancing Edge, 1 DEX = 1 CHR = 1.5 AGI = 1.5 STR. For Evisceration, 1 DEX = 1.5 AGI = 1.5 STR. For Shark Bite, 1 DEX = 1.8 AGI = 2.3 STR.
*If you use both job abilities with your weaponskills, focus mostly on DEX. For Dancing Edge, 1 DEX = 1.5 CHR = 2 AGI = 2 STR. For Evisceration, 1 DEX = 2 AGI = 2 STR. For Shark Bite, 1 DEX = 2 AGI = 3 STR.
*See the discussion page for explanations of damage mechanics for Sneak Attack and Trick Attack. The only unknown still needing verification right now is Dual Wield mechanics relative to these job abilities.
The charts on the right show how each attribute adds to damage as your pDIF (essentially, attack/defense ratio) goes from the minimum of 0 to the maximum of 2.4.
==Mercy Stroke==
If you are lucky enough to be able to use Mercy Stroke, stack STR and Attack regardless of your SATA preferences. STR adds far more damage than DEX or AGI, regardless of pDIF. Focusing on STR also frees you from the burden of relying on Sneak Attack or Trick Attack for the majority of your damage. DEX and AGI still add significantly to damage, however, if you run out of +STR to add. 1 STR = 2.7 DEX = 2.7 AGI.
*Accuracy should not be an issue at all, since if you use either Sneak Attack or Trick Attack your first attack and your off-hand attack should be guaranteed hits.
*Without Dual Wield, 1 STR = 2.25 DEX = 2.25 AGI.
==Adjustments==
*Without using Trick Attack, AGI does not factor into weaponskills.
*Without using Sneak Attack, DEX only factors into weaponskill damage via the WSC, and of course accuracy / critical hit chance.
*DEX is more valuable than calculated because it increases accuracy as well as Critical Hit chance for hits after the first hit on a multi-hit weaponskill. The calculations used in this guide assume both accuracy and critical hit chance are constant.
*STR increases Attack, which increases pDIF. This change in pDIF is very minor, but is still nonzero. Thus, STR is slightly more important than calculated here.
*If the subjob is Warrior, there will be a smaller chance of having an extra hit in the weaponskill, but also a small chance of having more extra hits than just one. Any other subjob will only have the normal number of hits in each weaponskill, and not have the single extra hit I assumed here. This means for non Ninja or Warrior subjobs, AGI is slightly less valuable, since it impacts the multiple hit calculations the most.
==What if I'm not 75?==
*Viper Bite has the exact same WSC and fTP as Evisceration, but only one hit. Here, 1 DEX = 5/4 AGI = 5 STR.
*Wasp Sting has no WSC, is one hit, and has an fTP of 1. The majority of the time you use Wasp Sting, you have no access to Trick Attack, so things are pretty simple: 1 DEX is equivalent to 4 STR.
*Fast Blade and Combo have a 20% DEX and 20% STR WSC. Like with Wasp Sting, you won't be using Trick Attack much. Here, about 1 DEX = 3 STR.
*If your level is between 60 and 75, the WSC is ever so slightly more pronounced due to α. This does not cause any significant change in the damage calculations.
==Which Weapon Skill does more damage?==
That depends entirely on your character, your equipment, and what you are fighting. Because each weaponskill has its own WSC, fTP, and more importantly number of hits, you would not only need to plug in your own personal STR, DEX, AGI, and CHR numbers, but also know how accuracy affects each weaponskill and its damage. Also, remember TP changes the amount of damage dealt in significantly different ways for each weaponskill. Determining this is out of the scope of this guide.
=SATAWS Damage Analysis=
This analysis relies on information taken from the Calculating Weapon Skill Damage page and its various links.
Damage = WD * pDIF.
WD = Weapon Damage and pDIF is dependent on the attack/defense ratio and the level difference.
WD = floor((D + fSTR + WSC) * fTP) + AGI + DEX.
D is the base damage listed on a weapon.
fSTR is the STR/VIT difference function.
*max: floor(D/9) + 8
*min: - floor(D/9)
*FSTR = (your STR - monster VIT + k)/4, where k ranges from 4 (STR >> VIT) to 13 (VIT >> STR).
*Note the Blau Dolch has D = 26, and the Mandau has D = 39. This gives maximums of fSTR = 10 and 12, respectively.
:Assuming STR >> VIT, this implies additional gains in STR will not affect fSTR for STR = VIT + 36 and STR = VIT + 44, respectively.
:For an XP or higher level mob, this seems... unlikely to happen.
WSC is the weapon skill attribute modifier.
*In general, WSC = floor(floor(A * A% + B * B%) * α),
:where A and B are the weapon skill attributes multiplied by their corresponding percentages.
:α = 0.83 at job levels 74 and 75.
*For Dancing Edge, WSC = floor(floor(0.3 * DEX + 0.4 * CHR) * α).
*For Shark Bite, WSC = floor(floor(0.5 * DEX) * α).
*For Evisceration, WSC = floor(floor(0.3 * DEX) * α).
*For Mercy Stroke, WSC = floor(floor(0.6 * STR) * α).
fTP is the TP multiplier. At 100% TP,
*Dancing Edge fTP = 1.1875.
*Shark Bite fTP = 2.00.
*Evisceration fTP = 1.00.
*Mercy Stroke fTP = 3.00.
pDIF = c + 1.2 * (character Attack/monster Defense),
:where c is based on the level difference between the character and the monster.
*For the below calculations, I determine the marginal gain in damage if a single attribute is increased by one point. In other words, I calculate the increase in damage after increasing an attribute by 1, assuming everything else is kept constant.
*I assume the character is level 75, and uses SATA with every weaponskill. Floors are ignored for the purpose of calculation. I assume every hit connects (making Accuracy irrelevant), even though this is often not the case for multi-hit weaponskills. I also assume TP is at 100% when the WS is used.
*pDIF is taken to be constant, because changes to pDIF due to stats are insignificantly small. Assume the monster Defense is 200 for a level 75 monster: an increase of STR by 1 would mean the pDIF increases by 0.6/200 = 0.003. That change is too small to be compared to the other changes under consideration.
*Critical Hits increase the pDIF by 1, up to a maximum pDIF of 3. The first attack of a SATAWS is always a critical hit. I assume later hits in the weaponskill are not critical hits.
*Calculating the marginal gain in damage due to an increase in Attack would be incomparable to the results below, since an increase in Attack only changes the pDIF (which is taken to be constant in the below calculations), and thus requires actual knowledge of D, fSTR, WSC, and monster Defense instead of just relative values. Note the below calculations never actually determine the actual numbers for those variables.
*Hits in a multihit weaponskill after the first hit are calculated by setting the fTP to 1 and ignoring the SATA modifiers. Although they can be critical hits, they are not guaranteed like the first hit, so I assume none of them are (see Adjustments for how this changes results). This is taken from information on VZX FFXI Doc.
*I assume a Ninja subjob, meaning one extra hit in the multihit weaponskill. The Double Attack job trait from a Warrior sub gives the same end result if it procs.
==Dancing Edge==
Dancing Edge is a 5-hit weaponskill, with fTP = 1.1875. WSC = (0.3 * DEX + 0.4 * CHR) * 0.83.
The first hit will use a pDIF of (pDIF + 1), and the next 5 hits (because of NIN subjob) use an unmodified pDIF.
The damage equation is thus:
first hit: (1.1875(D + fSTR + 0.83(0.3 * DEX + 0.4 * CHR)) + DEX + AGI)(pDIF + 1)
later hits: + 5(D + fSTR + 0.83(0.3 * DEX + 0.4 * CHR)) * pDIF
===STR===
D, WSC, DEX, CHR, and AGI are constant. fSTR = STR/4 + a constant.
Damage = (STR/4) * 1.1875 * (pDIF + 1) + 5(STR/4) * pDIF + a constant = (0.296875 * pDIF + 0.296875) * STR + 1.25 * pDIF * STR + a constant.
An increase of 1 to STR equates to an increase of about (1.55 * pDIF + 0.3) damage.
===DEX===
D, fSTR, CHR, and AGI are constant. WSC = 0.83 * 0.3 * DEX + a constant.
Damage = (1.1875 * 0.83 * 0.3 * DEX + DEX) * (pDIF + 1) + 5(0.83 * 0.3 * DEX) * pDIF + a constant = (1.2956875 * pDIF + 1.2956875) * DEX + 1.245 * pDIF * DEX + a constant.
An increase of 1 to DEX equates to an increase of about (2.54 * pDIF + 1.3) damage.
===AGI===
D, fSTR, WSC, DEX, and CHR are constant. fTP is irrelevant since it is only multiplied by constant values.
Damage = AGI * (pDIF + 1) + a constant.
An increase of 1 to AGI equates to an increase of (pDIF + 1) in damage.
===CHR===
D, fSTR, DEX, and AGI are constant. WSC = 0.83 * 0.4 * CHR + a constant.
Damage = (1.1875 * 0.83 * 0.4 * CHR) * (pDIF + 1) + 5(0.83 * 0.4 * CHR) * pDIF + a constant = (1.39425 * pDIF + 0.39425) * CHR + 1.66 * pDIF * CHR + a constant.
An increase of 1 to CHR equates to an increase of about (2.05 * pDIF + 0.395) in damage.
At pDIF = 1 and above, about 1 DEX = 1.5 CHR = 2 AGI = 2 STR.
==Shark Bite==
Shark Bite is a 2-hit weaponskill, with fTP = 2.00 at 100% TP. WSC = 0.5 * DEX * 0.83
Like with Dancing Edge, the first hit will use a pDIF of (pDIF + 1), and the next 2 hits (because of NIN subjob) use an unmodified pDIF.
The damage equation is thus:
first hit: (2(D + fSTR + 0.83 * 0.5 * DEX) + DEX + AGI)(pDIF + 1)
later hits: + 2(D + fSTR + 0.83 * 0.5 * DEX) * pDIF
===STR===
D, WSC, DEX, and AGI are constant. fSTR = STR/4 + a constant.
Damage = 2(STR/4) * (pDIF + 1) + 2(STR/4) * pDIF + a constant = (0.5 * pDIF + 0.5) * STR + 0.5 * pDIF * STR + a constant.
An increase of 1 to STR equates to an increase of (pDIF + 0.5) in damage.
===DEX===
D, fSTR, and AGI are constant. WSC = 0.83 * 0.5 * DEX.
Damage = (2 * 0.83 * 0.5 * DEX + DEX) * (pDIF + 1) + 2 * 0.83 * 0.5 * DEX * pDIF + a constant = (1.83 * pDIF + 1.83) * DEX + 0.83 * pDIF * DEX + a constant.
An increase of 1 to DEX equates to an increase of (2.66 * pDIF + 1.83) in damage.
===AGI===
D, fSTR, WSC, and DEX are constant. fTP is irrelevant since it is only multiplied by constant values.
Damage = AGI * (pDIF + 1) + a constant.
An increase of 1 to AGI equates to an increase of (pDIF + 1) in damage.
At pDIF = 1 and above, about 1 DEX = 2 AGI = 3 STR.
==Evisceration==
Evisceration is a 5-hit weaponskill, with fTP = 1.00. WSC = (0.3 * DEX) * 0.83.
Since fTP is now the identity multiplier, we no longer need to consider it in these calculations.
The first hit will use a pDIF of (pDIF + 1), and the next 5 hits (because of NIN subjob) use an unmodified pDIF.
The damage equation is thus:
first hit: (D + fSTR + 0.83 * 0.3 * DEX + DEX + AGI)(pDIF + 1)
later hits: + 5(D + fSTR + 0.83 * 0.3 * DEX) * pDIF
===STR===
D, WSC, DEX, and AGI are constant. fSTR = STR/4 + a constant.
Damage = (STR/4) * (pDIF + 1) + 5(STR/4) * pDIF + a constant = (0.25 * pDIF + 0.25) * STR + 1.25 * pDIF * STR + a constant.
An increase of 1 to STR equates to an increase of (1.5 * pDIF + 0.25) in damage.
===DEX===
D, fSTR, and AGI are constant. WSC = 0.83 * 0.3 * DEX.
Damage = (0.83 * 0.3 * DEX + DEX) * (pDIF + 1) + 5 * 0.83 * 0.3 * DEX * pDIF + a constant = (1.249 * pDIF + 1.249) * DEX + 1.245 * pDIF * DEX + a constant.
An increase of 1 to DEX equates to an increase of about (2.5 * pDIF + 1.25) in damage.
===AGI===
D, fSTR, WSC, and DEX are constant.
Damage = AGI * (pDIF + 1) + a constant.
An increase of 1 to AGI equates to an increase of (pDIF + 1) in damage.
At pDIF = 1 and above, about 1 DEX = 2 AGI = 2 STR.
==Mercy Stroke==
Mercy Stroke is a 1-hit weaponskill, with fTP = 3.00. WSC = (0.6 * STR) * 0.83.
Like with Dancing Edge, the first hit will use a pDIF of (pDIF + 1), and the next hit (because of NIN subjob) uses an unmodified pDIF.
D is always 39, since you can only use Mercy Stroke with the Mandau or Batardeau.
The damage equation is thus:
first hit: (3(39 + fSTR + 0.83 * 0.6 * STR) + DEX + AGI)(pDIF + 1)
later hit: + (39 + fSTR + 0.83 * 0.6 * STR) * pDIF
===STR===
D, DEX, and AGI are constant. fSTR = STR/4 + a constant. WSC = (0.6 * STR) * 0.83.
Damage = 3(0.25 * STR + 0.498 * STR) * (pDIF + 1) + (0.25 * STR + 0.498 * STR) * pDIF + a constant = (2.25 * pDIF + 2.25) * STR + 0.75 * pDIF * STR + a constant.
An increase of 1 to STR equates to an increase of (3 * pDIF + 2.25) in damage.
===DEX===
D, fSTR, WSC, and AGI are constant.
Damage = DEX * (pDIF + 1) + a constant.
An increase of 1 to DEX equates to an increase of (pDIF + 1) in damage.
===AGI===
D, fSTR, WSC, and DEX are constant.
Damage = AGI * (pDIF + 1) + a constant.
An increase of 1 to AGI equates to an increase of (pDIF + 1) in damage.
At pDIF = 1 and above, about 1 STR = 2.7 DEX = 2.7 AGI.
=Disclaimer=
*If you quote these numbers, please do so in context, or link back to this page.
*These calculations cannot be taken too literally. For example, if increasing DEX by 1 increases damage by 5, and increasing STR by 1 increases damage by 2, this does not mean increasing DEX by 1 and STR by 1 increases damage by 7. More interestingly, this also does not mean increasing DEX by 2 increases damage by 10. The numbers will be close, but if you stretch them too far they will no longer be reliable.
=Links=
*Calculating Weapon Skill Damage
*VZX FFXI Doc
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