There have been some questions popping up lately over differences in numbers between the formula in Elmoreb's thread and what people actually see in game. We've learned a few things in the year since it was posted, so I'm going to revisit the formula, change what I think needs updating, and hopefully make it a little easier to read. (pardon the plagiarism of format)
Terminologies
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Elemental Spell Damage - hereafter just called "damage."
Magic Attack Bonus - abbreviated as "MAB."
Spell Damage Constant - abbreviated as "SDC."
Elemental Staff Bonus - abbreviated "ESB."
Day/Weather Bonus - abbreviated as "DWB."
INT - you should know what INT stands for.
Caster INT - abbreviated as "cINT."
Target INT - abbreviated as "tINT."
Tier INT Multiplier - abbreviated as "TIM."
Main Formula
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Damage = [(cINT - tINT) x TIM + SDC] x MAB x ESB x DWB
This is the hard and fast formula, and will apply in the vast majority of situations. You may notice that I did away with the INT Difference Factor from the original equation...I'll explain why below.
Individual Factors Explained:
Caster INT - Target INT (cINT - tINT)
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This is fairly straightforward. At the heart of the damage equation lies INT. In general, the more INT you have, the better. Since INT can work against you if the enemy has greater INT, it is good to keep this stat high. If you get a negative in this part of the equation, the multipliers found later on will work against you.
Tier INT Multiplier (TIM)
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Tier I: 1.0
Tier II: 1.0
Tier III: 1.5
Tier IV: 2.0
Ancient Magic: 2.0
This is the first multiplier to amplify your damage. Your INT will serve you to different degrees depending on what tier spell you cast, and this is also why (at least theoretically) some Ancient Magic spells can outdamage -ga III spells. In the previous formula, this stat was called SDB...I changed the name to avoid confusion with the stat below, and because the Spell Damage Factor it was a part of was greatly flawed.
Spell Damage Constant (SDC)
===========================
Spell Earth Water Wind Fire Blizz Thunder
I 5 11 20 30 41 55
I -ga 43 -- -- 119 -- 172
II 78 90 108 128 150 173
II-ga -- -- -- 312 350 --
III 210 236 265 295 320 345
IV 381 410 440 472 506 541
III-ga -- 479 526 588 642 697
Ancient 577 630 552 657 526 603
This is essentially the most controversial part of the equation. In order to get these numbers, we go out and cast Burn on a level 0 mob and the strip away the other factors in the equation to get the constant. The accuracy on these numbers depends on there being no such thing as negative INT, and also doesn't account for the rounding that SE does. I'm also suspicious of the arbitrary numbers for some spells...I don't see why SE would make the damage constant for Thunder IV 697 instead of 700, or 603 for Burst instead of 600. I'd appreciate any testing people would do to verify or update these numbers.
Also, I will be adding numbers for -ga, II-ga, and the unprovided III-ga spells shortly.
Magic Attack Bonus (MAB)
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Level Job MAB
10 BLM 1.20
30 BLM 1.24
50 BLM 1.28
70 BLM 1.32
20 RDM 1.20
40 RDM 1.24
60 RDM 1.28
Note: Main job and sub-job MAB DO NOT stack!
Ahhhh my favorite stat. Equipment that adds to MAB stacks with this stat. For instance, if you are level 70 with a Moldavite Earring, you MAB will be 1.37 (1.32 natural + .05 equipment). If an item says it adds +5 MAB, treat it as a percent turned into a decimal for the purpose of math. For instance, +5 MAB to +5% to + .05 MAB.
Elemental Staff Bonus (ESB)
===========================
NQ Elemental Staff: 1.10
HQ Elemental Staff: 1.15
An Elemental Staff is the single most important piece of equipment when it comes to determining the damage of your spell. The Staves have their own multiplier, and even the NQ versions give the greatest single constant boost to your damage.
Note: Using the wrong Staff for your spell can count against you. If you use a Fire Staff for casting Blizzard, the modifiers will be:
NQ Elemental Staff: 0.90
HQ Elemental Staff: 0.85
Day/Weather Bonus (DWB)
=======================
Base Multiplier: 1.00
Same Element as day: +.10
Same Element as weather: +.10
AF2 Pants and proper spell: +.05
Correct Obi & proper spell: +.10 to +.30 (replaces day & weather bonus)
Weak Element to day/weather: -.10
This is potentially a massive bonus to your damage. It is also the most random bonus. If casting on the proper day, there is a roughly 10% chance to get the bonus, same for casting during weather. Casting during multiple weather is a bit trickier: You have a 10% chance of getting each bonus, so in double weather, you have a greater chance of getting the bonus, as well as a chance of getting double the bonus. Combine that with the day effect, and it is possible to get +30% damage, though it will be rare. Note that like the staves, if you cast the wrong spell, this will work against you in the same manner.
The AF2 Pants will add to your damage every time you cast a spell that is the same element as the day. Thanks to Keberoz and others for comments on the Obis: They guarantee that you recieve all the day/weather bonuses 100% of the time, and also stack with the AF2 pants.
Comments on the old formula:
IDF, And Why It Doesn't Matter
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In the old formula, there is a section that concerns what happens when your INT is way over that of the enemy's. It calls this the INT Damage Factor. After a threshold point, INT begins to have diminishing returns up to the point where you hit the Damage Cap, after which no addition in INT will result in more damage being done to the monster. This is very noticeable to any high level Black Mage who has cast Stone I for sh*ts and/or giggles. The damage seems to stay in one spot no matter what you do with your INT.
The fact of the matter is, beyond Thunder I, you will never have such an advantage over your enemy that you even hit the point of dimishing returns. The threshold value for Thunder I is 79 INT over that of your enemy, and unless you are killing bunnies in Ronfaure, you'll rarely have this advantage. For those that are curious though, I've quoted the information below. I will not be adding to any of these tables in the future.
[quote:91abc]INT Damage Factor (IDF) Explained
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It is possible that enemy INT is higher than caster INT, in that case the resultant value will be negative from the subtraction.
If the difference between enemy and caster INT exceeds Preliminary Threshold Value (PTV), then the damage growth rate will decreate. (i.e. the following formula will be used for IDF instead)
IDF = [ (Caster INT - Enemy INT) + PTV ] / 2
For I series spells, here are their PTV values:
Spell PTV
===============
Earth I 21
Water I 30
Air I 41
Fire I 51
Blizz I 62
Thunder I 79
3. If the INT difference exceeds the Ultimate Threshold Value (UTV), then the IDF value will be capped and the following formula applies:
IDF = (UTV + PTV) / 2
For I series spells, here are their UTV values: (-- indicates not tested yet)
Spell UTV
===============
Earth I 53
Water I --
Air I --
Fire I --
Blizz I --
Thunder I --