FFXI Equations/Statistics Thread

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FFXI Equations/Statistics Thread
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 Phoenix.Dabackpack
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By Phoenix.Dabackpack 2011-12-07 16:47:59
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Hey all, since I haven't really seen one here yet, I was thinking of having one thread where we can compile a database of equations for damage calculations and whatnot. I think it would help to have one centrallized location for this stuff; I like doing FFXI math, but it's still pretty annoying to have to switch through wiki pages for finding optimimum attributes for whatever WS or spell.

I think it would help for people less familiar with the game mechanics as well. So, to the mathematicians out there, if you want to post something, I'll move it to this post under a bunch of spoilers.

Thank you :)

Under construction

Physical Attack Damage Calculation
The expected damage of one's physical attacks (excluding Ranged Attacks for now) is expressed in a formula as follows:
Physical Damage = Base Damage * pDIF
Further calculations are needed to find the two terms above:
1.) Base Damage
Base Damage is the sum of two values:
Base Damage = Weapon Base Damage (D) + fSTR
Weapon Base Damage is just the number listed on the weapon (for Hand-to-Hand weapons, this number is added by three).
fSTR is a term relating the attacker's STR value and the defender's VIT value. For higher values, this is approximated as
fSTR = (character STR - enemy VIT+4)/4
There is a limit (or perhaps 'range') to the value of fSTR. To describe this, another variable is needed: Weapon Rank.
Weapon Rank is a value held by a weapon (duh) and is
Weapon Rank = Weapon Base Damage / 9
(This value is an integer, so you must round down.)
You need this value to determine fSTR's upper and lower bounds:
The lower cap of fSTR is the weapon's Weapon Rank.
The upper cap of fSTR is the weapon's Weapon Rank + 8.


Using fSTR and Weapon Base Damage, you can compute Base Damage.

2.) pDIF
This becomes a bit more complicated.
You can take a look here for more detailed information on the topic. It is not entirely known at the moment.
What we do know:
  • It depends on the ratio between your Attack and the opponent's defense. This ratio has an upper cap: 2.0 for one-handed weapons and 2.25 for two-handed weapons.

  • A Level Correction Function is placed on this ratio.
    cRatio (corrected ratio) = Ratio - (target's level - attacker's level) * 0.05


In other words, you experience a damage penalty when attacking higher-level enemies.

As for calculating your average pDIF (this is what goes into the equation), refer to the following approximations, courtesy of the BGWiki:
If 0 ≤ cRatio < 0.3 → pDIF = 1.0585 × cRatio ^ 2 + 0.3391 × cRatio + 0.0239
If 0.3 ≤ cRatio < 1.3 → pDIF = -0.12311 + cRatio × 1.129179
If 1.3 ≤ cRatio < 1.5 → pDIF = 0.7486 × cRatio ^ 2 - 1.5814 × cRatio + 2.1349
If 1.5 ≤ cRatio → pDIF = 1.129573 × cRatio - 0.24878


Furthermore, the following equations are applied for critical hits:
If 0 ≤ cRatio < 1.63 → pDIF = 0.948491 + cRatio × 1.045043
If 1.63 ≤ cRatio → pDIF = -0.7153 * cRatio ^ 2 + 3.4303 × cRatio - 1.0385

Remember that these are average pDIF values, and that there are upper and lower values for the term. For more information on pDIF, refer to the link above.

What does this mean for you?

  • It pretty much confirms the obvious: Higher damage weapons will increase your damage. Every 9 weapon damage, though, your fSTR range increases, further increasing your damage potential. If you want to maximize fSTR, you might want to consider adding more STR to accomodate to your current weapon rank (don't sacrifice important stats like haste though~).

  • You will generally deal less damage against higher-level monsters as opposed to lower-level monsters.

  • The attack value determines the value of pDIF on your end, further increasing your general damage.



Which stats to stack for a TP build?
Haste.
Not kidding, the potency of Haste only increases as you stack it. You should shoot for the 26% gear cap of Haste (explained later) as soon as you can. It gives increasing returns. You should make this your highest priority, after accuracy is high enough.

Accuracy.
Sure, you can hit fast/hard, but that amounts to nothing if you're not touching anything. You want to make sure your hit rate is close to 95% if you can. This is an easy way to increase your DPS. Sure, you can always use accuracy food, but you could be using attack food! Just be sure to not overdo it, since hit rate does cap at 95%.

Double Attack/Triple Attack/Quadruple Attack.
Be careful with these. I mean, they don't hurt. They can definitely help you with gaining TP. You want to make sure that you're not putting too much into these stats. They have dimishing returns - in other words, the higher your current values of DA/TA/QA, the less gain you get by adding more.
I'm not saying these are bad. The change from 0% DA to 1% DA is enormous (since it actually grants you the ability to attack twice) but I would not use DA as a substitute for Haste while Haste is uncapped, ever. These are sometimes subject to different opinions, but this is the general consensus.

Attack/STR.
These won't benefit you as much as the others as far as DPS goes, but each point of Attack or STR will help you with pDIF. Generally, attacking faster is better than hitting harder.

Store TP.
This guy right here is another really important one for 2-handers. I don't know about you, but I find it really annoying when I find myself sitting at 98% TP on DRG or SAM. You have to calculate for yourself how to gear for Store TP, since each weapon has its own characteristics. Slower jobs will require less STP to hit an x-hit build than a faster job will. Don't forget to count in delay reduction from Dual-Wield or Sword Grip if you want to reach that x-hit. More info on Store TP later.

Dual Wield.
Once again, be careful. Haste beats an equivalent level of Dual Wield, because Dual Wield actually reduces your TP per hit; it's just usually easier to find higher levels of Dual Wield. You really do want to reach the delay reduction cap, but concentrating on Dual Wield when Haste is equally efficient option will result in an unnecessary loss in TP.

Depending on the job, several other factors comes into play. Be sure to find out what is good for your job besides these. Ranged Attack jobs follow a different set of rules.
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 Ramuh.Sagittario
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By Ramuh.Sagittario 2011-12-07 16:56:16
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I am sure you can find every database you could possibly want on BG. Would be cool to have them here too, but BG is known for this sort of thing.
 Carbuncle.Asymptotic
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By Carbuncle.Asymptotic 2011-12-07 17:03:22
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Maybe if more of this stuff waso
Ramuh.Sagittario said: »
I am sure you can find every database you could possibly want on BG. Would be cool to have them here too, but BG is known for this sort of thing.

Maybe if more of this stuff were on FFXIAH directly, people might not try to defy logic so much during gear discussions.
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 Ragnarok.Sekundes
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By Ragnarok.Sekundes 2011-12-07 17:04:16
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Many of the posters on the BG threads post here as well, though AH doesn't have a specific forum dedicated to math and game calculations. Wouldn't hurt to have more eyes seeing good information and perhaps commenting on or adding to the knowledge base. What we really need is some very bored people to help extract info from threads and put it in to the BG wiki.
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 Phoenix.Sehachan
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By Phoenix.Sehachan 2011-12-07 17:05:34
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Nothing wrong with spreading useful info.
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 Phoenix.Dabackpack
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By Phoenix.Dabackpack 2011-12-07 17:08:55
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Also, if I end up doing this right, will be in layman's terms. A lot of numbers are scary. That is probably what drives a few people away.

Though, of course, I won't downplay the complexity of the entire system.
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 Ragnarok.Sekundes
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By Ragnarok.Sekundes 2011-12-07 17:13:33
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I'm pretty sure if you start adding information like that first one, you aren't going to have enough room in the OP to keep it going for very long. I'd keep it above FFXI: Remedial courses.
 Phoenix.Sehachan
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By Phoenix.Sehachan 2011-12-07 17:14:46
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There's a limit for spoilers in one post I think.
 Fenrir.Niniann
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By Fenrir.Niniann 2011-12-07 17:18:01
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Phoenix.Sehachan said: »
There's a limit for spoilers in one post I think.

Probably. Should have it unspoilered. You can have a ton of information in just one OP, I've never had an issue with running out of space.

Also, I think most of the math people probably have better things to do than post about equations and the like. You'll probably have to look it all up yourself on BGwiki, or sift through BG.
 Ragnarok.Sekundes
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By Ragnarok.Sekundes 2011-12-07 17:18:32
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5 Per post. Mods can edit your post to fix that but regardless there is still a per post character limit that I don't think can be overrided.
 Phoenix.Sehachan
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By Phoenix.Sehachan 2011-12-07 17:20:52
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You expect him to have everything compiled within 30 minutes?
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 Fenrir.Skadoosh
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By Fenrir.Skadoosh 2011-12-07 17:21:50
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Didn't expect the community to do 99.9% of his work lol
 Phoenix.Sehachan
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By Phoenix.Sehachan 2011-12-07 17:22:41
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He's just adding bit by bit :|
 Ragnarok.Sekundes
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By Ragnarok.Sekundes 2011-12-07 17:23:35
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Phoenix.Sehachan said: »
You expect him to have everything compiled within 30 minutes?
Plus,this isn't a copy the wiki post, this is an equation/statistics thread. No one's going to read it if you put crap like that in here.
 Fenrir.Skadoosh
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By Fenrir.Skadoosh 2011-12-07 17:24:50
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Isn't that comparable to saying:

"Hey guys! I have a question, but I don't have it formulated yet. Just going to post here for now, and when I think of what to ask, I'll already have this designated thread for it."

IDK
 Phoenix.Dabackpack
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By Phoenix.Dabackpack 2011-12-07 17:25:04
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Fenrir.Skadoosh said: »
Didn't expect the community to do 99.9% of his work lol

Well, considering that I made this thread thirty minutes ago, and it'd be HELP I AM TRAPPED IN 2006 PLEASE SEND A TIME MACHINE just to copy+paste things, and I'm the only regular user allowed to modify my own post...

Rome wasn't built in a day, you know.

Thanks for the comments, I realized when writing it that "if you don't know what AGI is, then it's not hard to look it up".

So, it'll probably take a while.

(Also, what I meant about "contribution" is if anybody wanted to give something useful, I'd include it, but most information is already out there for me to compile)
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 Phoenix.Sehachan
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By Phoenix.Sehachan 2011-12-07 17:25:04
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I'd wait for the final post before throwing judgments, no point in doing it on something under construction.
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 Fenrir.Niniann
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By Fenrir.Niniann 2011-12-07 17:27:07
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Phoenix.Sehachan said: »
I'd wait for the final post before throwing judgments, no point in doing it on something under construction.

^

It takes a while to make a guide, especially something like this. Also it's nice to start with a blank slate and edit it so you can see what it looks like/you don't end up having your computer crash while you're writing it and lose everything.
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 Valefor.Prothescar
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By Valefor.Prothescar 2011-12-07 17:36:56
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Calculations for physical blue magic and weaponskills:

Blue Magic

Base Damage = floor(D+fSTR+WSC)*fTP

Where -

D = floor(Blue Magic Skill * 0.11)*2 + 3

fSTR = fSTR caps at 26 for Blue Magic. Assuming you have a semi-decent STR, (attacker STR - defender VIT+4)/4 can be used to find your fSTR. This changes based on your STR vs. the monster's VIT at lower STR values, however.

WSC = Your secondary modifiers. floor((A * A%) + (B * B%))*α
*A = stat 1, B = stat 2
*A% = % of modifier A, B% = % of modifier B
*α = the alpha. This varies by level, but for current levels the alpha is 0.85.

fTP = Damage multiplier. This varies from spell to spell.

So an example:

Quadratic Continuum has a 32% STR modifier and 32% VIT modifier. It has an fTP of 1.25 per hit for an overall fTP of 5. Let's also assume capped fSTR and a Blue Magic skill of 447.

D = floor(447 * 0.11)*2 + 3
D = 98 + 3
D = 101

fSTR = 26

WSC = floor((A * A%) + (B * B%)) * α
WSC = floor(floor((159 * 32%) + (89 * 32%)) * 0.85)
WSC = floor(floor(50.88 + 28.48) * 0.85)
WSC = 67

fTP = 5

Base Damage = floor(D+fSTR+WSC)*fTP
Base Damage = floor(101+26+67)*5
Base Damage = 970



Damage = base damage * pDIF

pDIF is essentially a multiplier based on you attack and the opponent's defense. It is not 100% known how this functions, however there is a general understanding of how it does. There's too much information regarding pDIF to list here, so I will direct you to http://wiki.bluegartr.com/bg/PDIF for information regarding how to find a pDIF value to use to calculate weaponskill damage.

It's important to note that blue magic attack = Blue Magic Skill + floor(STR/2) + 8


Weaponskill damage is similar but there are a few key differences.



Damage for weaponskills is calculated the same way as it is for physical blue magic, except for the D value and fSTR caps being different. D = weapon base damage and fSTR lower cap = weapon rank while fSTR upper cap = weapon rank + 8. Weapon Rank = (D/9), or in the case of hand-to-hand, Weapon Rank = (D+3/9).

Also, for ranged weaponskills, you will be using fSTR2 and will also be adding ammo damage to your base damage calculation.

Base Damage = floor((D + (aD) + fSTR + WSC) * fTP)

fSTR2 is calculated in essentially the same manner as fSTR, however the caps are different.

The lower cap of fSTR2 is (Weapon Rank) * 2.

The upper cap of fSTR2 is (Weapon Rank+8) * 2


Hope that helps you out a bit. Can add in magic stuff later if you need help with that.
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 Lakshmi.Byrth
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By Lakshmi.Byrth 2011-12-07 17:39:57
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You could just link the bgwiki pages if you want, haha.

* Damage Taken
* fTP
* pDIF (I need to review what Motenten just posted on BG and revise it)
* fSTR
* This guide for calculating physical damage that I started writing a few days ago and forgot about. There is a reason it isn't a real page yet
* Resists / Magic Hit Rate / Magic Evasion / Magic Accuracy
* Critical Hit Rate
* Attack Speed/Haste
* Job Traits
* Job Abilities
* Monster TP Gain
* Player TP Gain
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 Carbuncle.Asymptotic
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By Carbuncle.Asymptotic 2011-12-07 17:41:40
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Once you get all the equations compiled, I'll be glad to help you re-explain things in ways that are easier for people to understand.

That's probably the biggest skill I've gotten out of my math degree (which is useful because it means big $$ tutoring freshman engineers!)
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 Carbuncle.Asymptotic
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By Carbuncle.Asymptotic 2011-12-07 17:56:18
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@Byrth:

Links to the information sources @ BGWiki are good, but I think detailed explanations on-thread would help too, just because people are lazy @ link clicking and generally math HELP I AM TRAPPED IN 2006 PLEASE SEND A TIME MACHINE.
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By Valefor.Prothescar 2011-12-07 18:01:07
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Blue magic "efficiency":

Difficult to quantify as each spell has different mods. Assuming 100 of every stat, 100MAB, a lv 95 monster with 70 of every stat and no special resistances. Only counting "useful" spells:

Physical (based on maximum possible damage) -
Heavy Strike 29.15625 dmg/1MP
Delta Thrust 26.07142 dmg/1MP
Quad. Continuum 15.69230 dmg/1MP
Disseverment 14.81081 dmg/1MP
Vanity Dive 14.55172 dmg/1MP
Goblin Rush 9.59210 dmg/1MP

Magical -
Regurgitation 10.58 dmg/1MP
Dark Orb 10.55 dmg/1MP
Thunderbolt 8.93 dmg/1MP
Water Bomb 8.63 dmg/1MP
Charged Whisker 7.49 dmg/1MP
Everyone's Grudge 7.73 dmg/1MP
Mind Blast 7.27 dmg/1MP
Firespit 7.24 dmg/1MP
 Lakshmi.Byrth
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By Lakshmi.Byrth 2011-12-07 18:03:12
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idk, it's kind of hard to get more basic than most of those pages.
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By Valefor.Prothescar 2011-12-07 18:05:54
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Yeah, it's not really possible to break it down further than those wiki pages or my post tbh.
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By Siren.Kalilla 2011-12-07 18:10:45
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If you really want to do this Dabackpack then I could help you out with formatting the look of your OP so you can have as much information as possible without taking much space up.
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By Phoenix.Dabackpack 2011-12-07 18:46:43
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Siren.Kalilla said: »
If you really want to do this Dabackpack then I could help you out with formatting the look of your OP so you can have as much information as possible without taking much space up.

Thank you everyone so far for the comments.

And yeah, I might need help with formatting, just the part on physical damage takes up a lot of space. I'll see how far I decide to take this though.
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By Fenrir.Schutz 2011-12-07 18:52:44
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Phoenix.Dabackpack said: »
Siren.Kalilla said: »
If you really want to do this Dabackpack then I could help you out with formatting the look of your OP so you can have as much information as possible without taking much space up.

Thank you everyone so far for the comments.

And yeah, I might need help with formatting, just the part on physical damage takes up a lot of space. I'll see how far I decide to take this though.

Yah Kalilla is a BBCode guru, LOL. :p

Like in this thread...

http://www.ffxiah.com/forum/topic/26795/dev-utsusemi-icon-hard-to-read/2#1614525

...I was really impressed with the use of the "[ div class="spoiler" ]" BBCode to get around Scragg's hardcoded limit on the use of "[ spoiler ]".

That sort of thing should really help out in making your OP very presentable and easy-to-read.
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By Siren.Kalilla 2011-12-07 19:04:19
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Fenrir.Schutz said: »
...to get around Scragg's hardcoded limit on the use of "[ spoiler ]"...
You make it sound like I'm doing something bad :(
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