Verified BLM Spell Damage Formula!

[Nobusan]

Terminologies
=============
Elemental spell damage (ESD)
INT Difference Factor (IDF)
Spell Damage Factor (SDF)
Spell Damage Bonus (SDB)
Elemental Staff Bonus (ESB)
Spell Damage Constant (SDC)
Magic Attack Bonus (MAB)

Main Formulas
=============
ESD = [ (IDF * SDF) + SDC ] * MAB

IDF = (Caster INT - Enemy INT)

SDF = SDB * ESB


INT Difference Factor (IDF) Explained
=====================================

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 --

Spell Damage Factor (SDF) Explained
===================================

SDF = SDB * ESB

ESB = 1.0 for no elemental staffs equipped (or not for the right spell)
1.1 for Normal Quality elemental staffs (matches with spell)
1.15 for High Quality elemental staffs (matches with spell)

Spell SDB
===============
I Series 1.0
II Series 1.0
III Series 1.5
III(ga) 1.5
IV Series 2.0
Ancient 2.0

Magic Attack Bonus (MAB) Explained
==================================

MAB Table
=========
Level Job MAB
10 BLM 1.2
30 BLM 1.24
50 BLM 1.28
70 BLM 1.32
20 RDM 1.2
40 RDM 1.24

Moldavite Earring (+0.05 to MAB)
Zenith Glove (+0.05 to MAB)

Spell Damage Constant (SDC) Explained
=====================================

Spell Earth Water Wind Fire Blizz Thunder
I 5 11 20 30 41 55
II 78 90 108 128 150 173
III 210 236 265 295 320 345
IV 381 410 440 472 506 541
III(ga) -- -- -- -- 642 697
Ancient 577 630 552 657 526 603


Elemental Day Effect on Damage
==============================

If day is the same as spell element:
ESD = ESD * 1.1 (i.e. Fire Day casting Fire Spell)

If day is the opposite of spell element:
ESD = ESD * 0.9 (i.e. Fire Day casting Blizz Spell)


How to verify this formula
==========================

Go to just outside of bastok, use burn to lower those newbie bees so their INT becomes 1.

Without equipping any weapons, Level 75 BLM with INT 129, wearing Moldavite Earring, casting Thunder IV.

Since,

ESD = [ (IDF * SDF) + SDC ] * MAB

IDF = (Enemy INT - Caster INT)

SDF = SDB * ESB

Therefore,

IDF = 129 - 1 = 128

SDF = 2 * 1 = 2.0

ESD = [ (128 * 2) + 541 ] * 1.37 = 1091.89 (drop decimals) = 1091

You're welcome to try them yourself, and find the other SDB and SDC values that were not listed here. Finding the PTV and UTV values will be more challenging, but it is still doable too.

These results has been verified by many other BLM and are obtained from JP boards. (I've verified myself as well)

Please feel free to test and find the other missing contants and post them here. Any feedback is welcome!

Thanks!

[Balodoth]

Impressive

I'll be bookmarking this page to see the discussion on this. I would like to point out, however, that there is going to be a random factor in there somewhere, it's what allows a spell to be cast twice and not do the same damage twice. It's also what allows S-E to keep the real algorithm somewhat shady.

I'm also interested in what you have found out in relation to MB's.

[Kirara]

your formula

ESD = [ (IDF * (ESB * SDB)) + SDC ] * MAB

your formula with out staff->

ESD = [ (128 * (2 * 1) + 541 ] * 1.37 = 1091.89 (drop decimals) = 1091

your formula with normal staff ->

ESD = [ (128 * (2 * 1.1) + 541 ] * 1.37 = 1126.962 (drop decimals) = 1126

your formula with HQ staff ->

ESD = [ (128 * (2 * 1.15) + 541 ] * 1.37 = 1144.498 (drop decimals) = 1144

[Nobusan]

You can try to verify those numbers if you would like by testing it with the method I mentioned. You would be able to get the same numbers as calculated.

[Kirara]

i am at work now, however i will do the test once i get off (if i am nto dead enough from moving)

but from my previous experiences, the damage difference is bigger than what the formula calculated (and that's for an elvaan with way less int)

[Nobusan]

Any additional testing done to help refine this formula is highly welcomed. Make sure you pick low level newbie mobs and use burn to lower its INT to 1 to help accurately test this formula (bees outside bastok will be one good candidate).

Thanks!

[csBahamut]

I haven't done any testing, but part of that just seems inefficient from a programming perspective.

The way in whih IDF is found would require multiple lines of code, as oppsed to using an eponential formual, like say (some factor)^(caster's INT - enemy's INT). That way, you don't have to deal with checking if the difference is negative. It'd still be possible to keep the formula difficult to figure out, but still simple to program. Simple is always better. (Not saying what you have there IS wrong, but it could be off. Curve fitting isn't always easy when there's so many variables)

What about resistences to a particular element(i.e. equipment or bar-spells)? How does any randomness fit in? How about Magic Defense Bonous? Does wheather have an effect?

[AtraposBLM]

He mentioned the effect of weather.

As far as the equation being exponential..I highly doubt it. Everything I've done with dealing with spell damage has lead me to believe there is a hard cap on damage, not a gradually decreasing amount of bonus. Notice that while your higher level spell damage fluctuates, if you pick a lower series, it will do the exact same damage every single time. Also note that your max damage is VERY consistent. With Blizzard III, at lv69, I hit 567 damage 9 times out of 10 (that might not have been the exact number to tell you the truth, but it almost always hit for one number and one number alone).

[csBahamut]

Oops!(about the weather) I didn't read carefully enough.

I wasn't implaying that damage increase exponentially, but that the intelligence factor could be exponential.

example:

e^(52 - 50) = e^2 ~= 7.389056
e^(50 - 52) = e^-2 ~= 0.135335

now, it's quite easy to put a hardcap on the modifier/damage still.
Of course, the right numbers would have to be inputted to make it work right, but it'd be possible.

Monster difficulty(in regards to solo mainly), Monster HP, EXP for next level, and probably some other things all *seem* to increase at an exponential rate, as opposed to PC HP, MP, stas, etc. growing at a pretty linear rate.

If you could provide a chart(perferably an excel table) of damage done on a type of mob over a range of intelligence differences, we could probably single out the effect and truly tell if it's linear of exponential. Just make sure to include enough samples to remove randomness and the effect of different level mob types.

Also, how does shell come into play?

[Nobusan]

INT effect is linear, read the post carefully. PTV and UTV are meant to be used as their way of capping damage.

[csBahamut]

And how did you come to this conclusion? What data do you have to support this? Charts, graphs, and tables are appriciated, along with the logic used to come to these conclusions. Links would work too.

[kazuri]

Wowie, this is certainly an interesting topic, I've never seen anything like this before. I'll be sure to read it all once it's finished printing. XD

But, like csBahamut said, it'd be really nice to see charts/graphs/tables along with this equation. ^^

[Nobusan]

I didn't came up with the logic on my own, this is information that is extracted from a asian board that has many BLM tested and verified. I merely translated the information that I found and post it here.

I did verify the info based on the method I mentioned, and with the few test cases I tried, it is working as it says.

[csBahamut]

You have got to consider how this group of asians is going about finding these equations. Sure, maybe the data fits, but it could still be wrong. There's bound to be more than one curve that will fit the data samples. Because of the randomness in FFXI, the best R^2 curve fit could be wrong. Bad data samples could also provide a slightly incorrect curve fit. Are they even doing curve fits? Are they approaching this in a professional manner, or are they just guessing? If you could give a link to the board(s) you got this info, maybe I could try to find it myself, though I'll be limited to what the web can translate.

There's a set way to go about finding an equation, and simply making up an equation that seems to fit is NOT the best way to get the correct answer. Of course, it could be right, by pure chance.

With some data to backup the equations, the rest of us could use that, along with our own tests to verify it. The more data samples we have, the better the chance we have of finding a curve fit(more data will take the effect of randomness out).

[Kirara]

equipment i have that relates tothis (not counting int+)
i will use ice spell to test int difference will be asumed to be averaged at 65 for this

i have zenith glove moditive ice staff

with out anything, damage: 873
by calculation: 872

with zenith glove only, damage: 906
by calculation: 906

with zenith glove and moditive, damage: 940
by calculation: 940

with all 3 items, damage: 1042
by calculation: should been 954 only

with just ice staff and nothing else, damage: 983
by calculation: should have been 889

i am guessing the way how you calculate what you call "ESB" is not correct