( D + fSTR + WSC) * fTP * PDIF = 1283

FFXI numbers are big and scary. I mean, look at this shit.

( D + fSTR + WSC) * fTP * PDIF

That's the equation for WS damage. Putting meaning to the variables...

D = DMG
fSTR = Function of STR vs VIT
WSC = WS modifiers
fTP = Certain WS have a damage multiplier
pDIF = Ratio of Attack vs Def plus randomizer.

In the end, all that means is that stacking STR boosts raw DMG, and some WS double-dip into STR with WSC. Attack is important, but a lot of WS have attack multipliers (Steel Cyclone and Tachi: Gekko double your attack). Some WS have big fat fTP modifiers, which multiply the damage done.

DMG needs no further explanation, it's written right on your weapon.

fSTR is, more precisely, capped at Rank + 8, with a minimum of -Rank. Weapon Rank, is just DMG / 9. So a DMG:90 weapon is rank 10.
So Hagun is 75 / 9 = rank 8 + 8 = fSTR cap of 16.
Perdu Voulge is 91 / 9 = rank 9 + 8 = fSTR cap of 17.
(Note that 91, the base damage, not 96, the latent damage, is used to calculate rank. The only exception to this is Destroyers-style latents, which are always active and thus change the rank)
If you're breaking 100 STR on WS, it's a pretty safe assumption you're capping fSTR on normal targets.
If you're wearing STR+0 while hitting Kirin, you're probably capping fSTR in the other direction, which is around -5. (It takes Koenig or something to get below that)
/wordy
All of that boils down to getting free DMG:+X on your weapon from stacking STR, around 4-5 for one-handed jobs, 15-18 for 2-handers. Ranged Attacks gets double the effect of any STR with a high cap.

WSC is fairly simple. I'm sure you've heard of weapon skill modifiers. STR 75%, DEX 30%, AGI 60%, etc etc.
If you've got 100 STR and a STR 75% modifier, M = 75 (Arbitrary variable to keep things straight)
100 * .75 = 75.
Using Dragon Kick as a more real example here, STR 50% VIT 50%.
MNK has STR 68+38, VIT 66+30. 106 and 96. Multiplied by .5 is 53 and 48, M of 101.
Finally, that modifier is multiplied by .83, a balancing penalty for being level 75.
M * .83 = WSC, so 101 * .83 = 83.
/wordy
Sum modifiers * .83 = WSC

fTP is also written right out, this time on the wiki.
Tachi: Gekko is 1.5~ at 100% TP, 1.8~ at 200% TP, and 2.5 at 300%
Dragon Kick is 2.0, 2.75, 3.5
Raging Rush is 1.0, 1.0, 1.0

Add D, fSTR, and WSC together, multiply by fTP to get final weapon damage, WD.

WD * PDIF is the actual damage done.

PDIF is the complicated part of all of this.

First, cRatio is calculated.
Then, level correction is applied.
Finally, PDIF adds a couple things and adds randomization to get the variable melee damage we all see.

cRatio. Simply the ratio of your attack to the target's defense. Level 82 Greater Colibri have 327 defense, I have 450-something attack, roughly 1.37. Add in food, minuet and such, closer to 600 attack for a 1.8 ratio.
Remember, some WS have attack bonuses. Gekko doubles your attack, so if this was Gekko, I now have 1200 attack and a cRatio of 3.6 well beyond any cap that on cRatio, which is estimated to be 2.2 for 2-handed and 2.0 for 1-handed. Crits are a free +1.0 cRatio, with a cap of 3.0. Oh, and rangers cheat here, with ranged crits multiplying PDIF by 1.25 with an effective 3.75 cap.
cRatio caps: 2.0 for 1-h, 2.2 for 2-h, 3.0 for crits.

Level correction is then applied to cRatio.
cRatio - (0.050 * level difference), or cRatio - .05 per mob level over 75.
Rangers yet again cheat here, with ranged attacks being cRatio - (0.025 * level difference)
Using level 82 colibri as an example, level correction is cRatio - .35, so this capped cRatio on Tachi: Gekko becomes 1.85.
It's worth noting that no, players don't get any sort of level correction while being hit by targets lower level than themselves.

Finally, this is fed into the PDIF calculation, which looks up the cRatio on a chart and adds a 5% randomization. Assuming the currently known numbers are correct, the example 1.85 will have a value between 1.42 and 2.22. A capped 2.2 would range between 1.84 and 2.64. The 5% randomization added after means a final cap of 2.77.

Going through the entire sequence, we have

Weapon DMG
+
More DMG from STR
+
More DMG from WS modifiers * level penalty
*
fTP multiplier
=
WD

Attack / Defense ratio
-
Level correction
+/-
Randomizer
+/-
Randomizer #2
=
PDIF

WD
*
PDIF
=
The Greater Colibri takes 1283 damage.

Important points:
STR is important on any WS where you can't fill in with the primary mod.

STR is even more important on WS that it's a primary mod (which is to say, the majority of them)

STR cheats on ranged attack, as ranged has literally double effect from STR.

It takes a lot of Attack to make a difference once you break mob DEF. Wearing Ochiudo's Kote (20 attack) on a theoretical colibri WS will only increase its damage by... (cRatio = 600 / 327 = 1.834~, 620 / 327 = 1.896~) 3%. Even unbuffed, the difference between 400 and 420 attack is still only 4%. Ranged attack cheats here too, being able to benefit from much higher levels of cRatio than other weapons.

Level correction is a bitch, and Ranged Attack cheats yet again, only taking half penalty.

Ranged Attack cheats.



This is Mai Ikari, and with any luck, you arn't more confused now than when you started reading this post.