Updated Ninjutsu Damage Formulae

Node 465

Nice testing!

Your residuals in the third regime of the Ni and Ichi best fits implies that your slope is wrong, quite possibly because you're fitting discrete measurements with a continuous model.

In addition, if you get the correct order of operations / floor steps and the right constants, then you should end up with 0 residuals. Ninjutsu damage in FFXI isn't something biological/human behavior. It should be algorithmic/deterministic. Mougurijin is that one that primarily did this for black magic, although, to your point, he didn't leave much raw data around. There aren't that many multipliers here (particularly with 0 MAB), so you should be able to do it basically through trial and error.

I agree with this entirely. Even though there are only 2~3 possible locations I can truncate or rearrange terms, I was unable to exactly reproduce the damage seen in game. This was frustrating so I decided I would return to it at a later date after I'd made this post. The values here are good enough approximations for general use, and my publicly-available data set may allow others to solve the issue of "order of operations" for me in the mean time.


Thanks for the link. I hadn't seen this page yet. I'll look into it further to try to solve the issues with my residuals.

I have tried recruiting Ninja with capped Ninjutsu Skill and 0 job points to further explore the issues with my Ichi/Ni residuals. Being a mastered Ninja, I have +28 Matk and +40 Magic Damage that partially complicate the equations. Unfortunately, nobody was available within my linkshell that satisfied my requirement at the time of testing.


Edit 2022 June 21: I think I solved the issue already. See my next post.

I had the same sets pretty much in my sheet for nukes. Have you checked Nyame path C just to see how crazy upgrade it is? R25 body/legs/hands are like 30%+ damage for free nukes and like 50%+ magic bursts.

Also R25 feet and head are touching (head might even beats Relic+3 for Magic burst) Relic+3 and assuming datamined stats for R30, head will be even for free nukes and significantly better for MB, while feet will be marginally worse for free nukes, but slightly better for magic bursts.

Now imagine path C will get INT +10 as 4th stat or something... (or Magic Critical hit rate II +%...)

Is there any reason you felt the need to make 3 separate sets for Ichi/Ni/San? The only difference in the free nuke set is Shiva Ring +1 instead of Dingir, and all 3 sets are exactly the same for bursting.

Well done.

For free nuking, how would a pair of max-augmented Malevolences compare?

	Ambu Katana/Dagger	Malevolence
INT	15+15	10+10
Magic Accuracy	40+40	35+35
"Magic Atk. Bonus"	16+16	44+44
Magic Damage	217+217	118+118
Magic Accuracy skill	250/250	201/201

Not even close. Pair of Ambus is far ahead (~33% on :ni and ~27% on :san)

Does Perfect Ochu (from Sinister Reign) still have a place somewhere in the burst sets? If not, how far behind is it in the tier list of useful weapons for Ninjutsu bursting?

Same question for Perfect Samnuha Coat. Any use for that, supposing you can cap burst damage with the other slots.

Like 10% behind Ambu.


It's very close to base Nyame (same on :Ni and slightly worse on :San) in current sets. That's assume 4%MBBI is from Nyame Body. You would need to tell me specifically what item you would want to use to get that 4% elsewhere, because I dont see any.

Thanks for your patience.

I've updated the main post to reflect the following changes since yesterday. Let me know if you see any errors.


1) I've explored the issue mentioned by Byrth about some of my residuals showing a pattern and not being randomly distributed around the residual=0 line. I believe that these patterns are actually expected to occur given that we are fitting truncated data to a non-truncated, interpolated, model. Additionally, the shape of the patterns present in the residuals are determined by my model grid step size (i.e. by exactly where the model grid interpolation lands as its "best" fit).

Given that my data was not taken from nature, and technically has zero formal uncertainty, it should not necessarily follow a Gaussian or Poisson distribution centered on 0 residual. It should follow a more uniform distribution, with roughly an equal number of data points above the residual=0 line as there are below. Data points being weighted more above or below the residual=0 line suggests a slightly incorrect "V" value, while a constant and linear slope across the residuals suggests a slightly incorrect "M" value (certainly off by less than 0.01 if you consider the values obtained from the fits - minus the M=0.45 for the smallest dINT range for "Ichi" spells. That one is clearly off by 0.05...), as pointed out by Byrth. Ideally you want them all to be exactly 0, though.


2) I found and corrected two typos in my published data tables:

- dINT=59 showed 248 damage instead of 250 damage
- dINT=203 showed 1298 damage instead of 1296 damage.

My data collection was entered manually after every one to three ninjutsu casts. I'm glad there only appear to be two typos considering how tedious this task was. The data tables in my GitHub repository have also been updated.

3) After correcting the two data typos, I am now able to exactly recover the damage for all nukes across the entire observed dINT range using a simple spreadsheet, based on the values obtained through my minimization fitting. See the main post's new "Spreadsheet Manipulation" subsection for the details.

Unfortunately, I am only able to obtain a perfect match if I set the "Ni" and "San" ninjutsu skill caps to 349 and 499, respectively. A "San" ninjutsu skill cap of 499 directly conflicts with two separate data sets I've collected that each demonstrate an increase in damage at 500 skill compared to 499 skill (see my Data Collection ""San" ninjutsu skill upper limit data table." spoiler for details). The simple solution I speculate on is the "San" Ninjutsu Skill Potency Bonus using ("Ninjutsu Skill" - 1) in its equation. I do not plan to explore this further for now, but I invite somebody else to take up the challenge.



I find similar results: perfect malevolence are far behind the ambuscade weapons. Magic damage is a relatively rare stat. The extra +99 magic damage on each of the ambuscade weapons is potent when you consider how much it increases your base damage. This extra magic damage then gets multiplied by the various multipliers, such as magic attack bonus ratio, ninjutsu skill potency, Orpheus's Sash, magic bursts, etc.

That's interesting to see that V = 28.5 for Ichi because I always had it at 28 before, but I just did some testing on a lower lvl job with nin sub and 28.5 is the only number that works, while 28 didn't fit my numbers. I never see a V with a decimal in it, but only looked at Ninjutsu and Regular Nukes on BG Wiki.

As for the San Skill Lvl Capping at 500 and not 499, is it possible that the lower Skill Lvl actually starts at 276 and not 275? If so, your numbers should still work, since the multiplier will be 2.12 instead of 2.125 at capped skill and also your friend's dmg not changing at 275 to 276 would suggest it starts to increase at 277, since there was no change in dmg. Also, I think the multiplier is floored to two digits after the decimal point. The only number I can't get to work from your friend's San lower skill table is the 297 skill being 299 dmg using the 276 skill as the lower skill value.