Milestones

Somehow I managed to update sporadically this testament to a lack of priorities for almost one year. To be honest, I wrote foremost for myself so I didn't really bother to spend much time making these entries easily digestible for a wider audience. In particular, I found an excuse to apply some basic probability and statistics to FFXI, the playing of which is also a testament to a lack of priorities and extremely poor taste. On the other hand, I did try to focus my attention on the mechanics of the game so that these entries would have some informative value--at least some people thought so--instead of being just some masturbatory self-chronicle.

I would really like to maintain this conceit, anyway, but there is not much of an empirical mentality among the so-called playerbase to provide persuasive support for any theories that are developed or serendipitously discover non-trivial things about how the game works. Maybe some dead-enders take great pride in running their mouths without putting their bullshit to the test, but I find legitimizing claims with real data and observations to be far more interesting. I thought about turning this blog into a "digest" of sorts to summarize both new and old findings and give credit to the individuals that shed some light on some aspect of game mechanics, but actually it is just too tiresome to comb forums with crap search functions and garbage "intellects" for shiny nuggets of insight. So I will just continue talking about things that interest me enough to commit to blog, even though the posting frequency based on that criterion will be very low.

Anyway, this wasn't supposed to be just some navel-gazing exercise. Instead of making individual posts for the following topics, none of which really warrants standalone status, I decided to throw them all into a single entry.

Thoughts on Aspir

I managed to finish collecting some data to check the effect of Pluto's Staff and magic accuracy +12 on the potency of Aspir and updated the dot plot:

I think it's safe to say that INT or magic accuracy (MAB too, based on tarblm's results) have no role in the potency of Aspir (and by analogy, Drain). Note that I am not bothering with statistics and just arguing informally that none of MAB, macc, and INT increased the maximum in these samples.

As far as accuracy is concerned, that is much more inconvenient to check. The main purpose of my collecting data was to visualize the distribution of Aspir values. It seems here that the range of possible values of unresisted Aspir is fairly wide. The low values of Aspir observed may also be the result of a half-resist, which may cut the unresisted Aspir value in half. Unfortunately, you can see how partially resisted Aspirs are easily confounded with unresisted Aspirs if these ideas are true. Going back to tarblm's data though, the observed Aspirs generally have much greater variability, which could be attributed to partial resists.

Chocobo racing

Haven't talked about this in a while. A few months ago I actually canceled my content ID, but I let myself get pulled back into this pit of mediocrity that is FFXI. Since then I made some effort to maintain more detailed information on my Chocobo Circuit results, particularly whether my chocobo was competing against other PCs.

Not surprisingly, few of my C1 races were uncontested. In fact, 16 of the first 20 after I returned had at least one PC chocobo and 7 of those 16 had 2 PCs. I won only nine of those races, with a pretty abysmal 3-3-1-1 record against only one other PC.

During this time I came across a testimonial of another chocobo racer, also with a SS/B/B/B chocobo, who claimed to have won 67% of his races (128-41-22). This kind of pissed me off because farming chocobucks is extremely boring and here this guy was getting nearly 2 million more gil with the same chocobo profile and similar number of races. I thought perhaps he faced much less competition on his server and that his use of leather saddles may also have been a factor in his great success. But rather than shell out another $25 bucks to SE just for a server transfer, I tried the Sheep Leather Saddle for another month to see if taking the receptivity hit would be worth it in races with one or more other PCs.

My results were even worse with the leather saddle. In 20 races, I went 8-10-0-2 with 11 contested races, and in four of those contested races, an NPC chocobo won (I placed 2nd in all four) and in one case, two NPCs actually placed 1-2. (I finished out of the top 3 in this one.) Even worse, I won only four of the uncontested races, races in which I really "needed" to win to blunt the annoyance of losing chocobucks.

I then went back to the elm saddle and am now nurturing a nine-race winning streak (four contested), by far the longest streak I ever had. During this streak, I also reached the 10-million gil mark in net earnings. I am now going out of my way to race only in "off-hours" time slots to try to get my win rate back to 50%. My current record is 107-78-24-15.

Having reached 10 million in net earnings, I calculated an approximate rate of gil per hour earned in chocobo racing based on the time (one free race per 5 minutes) and gil spent to accumulate enough chocobucks (5,846) to enter the races and the gross earnings. Including this nine-race winning streak, chocobo racing has yielded an average of 74,644 gil per hour. (I admit this figure does not include time spent running to Chocobo Circuit.) Not as efficient as the guy winning 67% of his races, but still a nice reminder that even though chocobuck farming is a real pain in the ass, at least this huge barrier to entry allows chocobo racing to provide a steady income to those who actually put up with it... assuming the C1 races aren't so congested.

Thoughts on the possibility of chain 6 solo on Ebony Puddings without Novio and Manafont

I was extremely disappointed to find out that I had died 957 times between Adventurer "Appreciation" 2008 and A.A. 2009, the majority on black mage. (If I am really appreciated, can I get a Chocobo Wand in fewer than two weeks without being lucky?) I had considered myself more risk-averse over the past year (I did not even do Dynamis at all), but in retrospect this was not true, since you tend to die a lot in pickups, soloing, and poor event linkshells.

The pain of losing experience points on black mage (never mind the bullshit conceit that losing experience points on top of losing the time and resources you wasted is a reasonable penalty) can be blunted somewhat with efficient rate of gain of EXP. But what is considered efficient? From experience, the best I can do is around 8,000 EXP/hour (estimated by the time required to burn off an Emperor Band), and that's when being somewhat vigilant about achieving chain 5 (which is trivial if you are paying attention). Anyone who claims rates of 10,000 EXP/hr solo is full of shit until proven otherwise.

Is it possible to achieve chain 6 solo without Novio, though? By the time chain 5 rolls around I almost always have insufficient MP without Aspir to mount a chain 6 attempt, an indication that my maximum MP is not high enough. Moreover, even three "tier 4" nukes tend to leave a sliver of HP (on off-weather days), meaning that I have to rely on Drain to finish off a pudding. Casting Drain on chain 4 and 5 wastes MP that could be used for chain 6. These factors, along with half-resists and weather effects, conspire to make it really difficult to achieve chain 6. If it is easier than I am pondering, I'd like to know though, but not from shit Morrigan's users who still cast AM II on puddings.

Benevolent Despot

With the advent of Fields of Valor, the prospect of not spawning Despot in a timely fashion is less unpalatable since a training regime awards 1,550 EXP in about an hour of killing 11 placeholders. And maybe those tabs will actually be useful someday. Also, soloing without desirable rewards has grown pretty tiresome. I still have a Fenrir solo (ninja) on the back burner now that Lunar Roar supposedly does not dispel reraise, but I haven't been motivated to do that yet. At the moment, Despot is the only remotely appealing "get out there and kill shit" profit opportunity with a relatively high barrier to entry (actually being able to solo it under 30 minutes to lower the chance of vultures finding you and trying vainly to MPK you).

Though not quite as enjoyable as killing Despot and hardly a consolation prize, watching hapless groups kill Despot can provide some humor to brighten the day. Not a few weeks ago, I had the "pleasure" of witnessing this quartet of PLD/NIN, NIN/DRK, BLM and MNK struggle with Despot for over 40 minutes! Apparently, it didn't occur to these people to shed enmity via teleport in order to expedite the kill. Unfortunately, even inept players win eventually, a testimony to the dominance of the lowest common denominator in FFXI. Throw infinite time and resources at something and you can triumph! (Except for Absolute Virtue.)

Spending time farming gems of the west also has given me an opportunity to "get back" at the MPKing Tarutaru Duo That Shall Not Be Named by dispatching Despot in 22-27 minutes while those oblivious assholes continue to kill placeholders long after I'm gone.

Aspir data and observations

Edit (June 5): some attempts at clarification.

What affects the accuracy of dark magic? Skill only? How about potency? How can we describe the distribution of MP absorbed with Aspir? What data are out there to support the prevailing assertions? Finding old Aspir data sets (from 2006) was easy enough, and I also collected some Aspir data on my own.

This may seem like treading old ground if not for the B.S. I cited earlier in the week. At least there is some data you can cite when making an argument now.

Regarding the 2006 data set, the writer (whom I will call "tarblm" for now) collected Aspir data from King Buffalo (lv 79-82) over six trials. Each trial involved only a single buffalo. The data were collected under one of three configurations, all with a Pluto's Staff:

• "Dark magic skill": +40 dark magic skill (above 269) was the primary factor
• "MAB": +30 MAB from equipment (relative to control) was the primary factor
• Control: 269 dark magic skill
  

The writer also noted the experience gain for each buffalo. The data are presented in a dotplot:


First, the data give the impression that some amount of dark magic skill increases the average MP absorbed, whereas MAB doesn't, confirming previous beliefs. Certainly the maximum Aspirs are higher. Low values of MP drained seem fairly rare and set apart from the rest of the data, so describing the data as coming from a uniform distribution doesn't quite work.

Was "effective" magic accuracy capped on "very tough" buffalo? I would say yes. Otherwise, level difference would have confounded the results. If there is no difference in accuracy across the trials, one could attribute the average to an increase in so-called potency alone.

To try to avoid that uncertainty about capped magic accuracy for my data, I focused my attention on low-level Tunnel Worms and collected 50 Aspir samples for each of the following conditions without a Pluto's Staff:

• Control: 77 INT, 269 dark magic skill
  
• INT: +43 INT above control (120 total)
• Dark magic skill: +22 dark magic skill above control (291 total)

Since the worms are so low in level, I just assumed my effective magic accuracy was capped. This is a major assumption but a reasonable one given magic skill level. (Correction: I earlier used a level correction argument to make this assumption. It has not been established that level difference affects mobs in the same way that it affects PCs.) The data are illustrated in the following dotplot:


Similar to tarblm's data, some amount of dark magic skill seems to increase the average MP absorbed, although the increase is not statistically significant. As magic accuracy was probably capped in this scenario, it is probably safe to say that dark magic skill would increase potency by a statistically significant amount if I had more dark magic skill to pile on. In terms of the distribution of Aspir, it seems to shift the range of possible values to the right.

INT doesn't seem to cause any change in potency. That is not to say INT doesn't affect accuracy in some way! Low values of MP (here, below 50) were infrequent and I assure you they didn't result from capping total MP. A decrease in accuracy may manifest in a higher frequency of low values, resulting in a lower average if not a shift in the range of possible values.

Note that last time I gave an example of a data set (on FFXIclopedia) that showed INT increased the average Aspir, and I said this was a potency-only effect based on the assumption of capped accuracy. Perhaps there are other confounding factors that were not cited.

Also, data overall give an impression that Pluto's Staff affects potency (one, the 2006 data are more variable, Aspirs achieve higher values despite King Buffalo being 62-72 levels higher than Tunnel Worm).

From all this, it seems reasonable to conclude that

• Dark magic affects potency (still not sure about magic accuracy attribute, e.g., from equipment)
  
• MAB does not affect potency
• INT does not affect potency but it seems likely to affect accuracy in some way. Do not confuse accuracy with potency. In a sense, increasing one or the other should still increase the average drained up to a point, but the way each does that is different. An analogy to melee attack and melee accuracy should make sense.
  
• Magic accuracy probably affects accuracy but not potency, but I haven't found nor collected any data to check this.

You may also have noticed that the maxima and sample means in the 2006 data set are larger than those in the 2009 set. I'm pretty sure the difference can be attributed to Pluto's Staff.

Dark magic and INT

This is just going to be a quick and dirty post but may motivate a more enlightened post later, but just to reinforce the ignorance exhibited by the "player base," here's another chuckle-inducing, basically worthless discussion about what affects the accuracy and potency of Aspir. Here's another discussion from idiots talking about "tests" on the potency of Aspir, but where's the fucking data? Here's an obvious question. Did anyone ever actually disentangle accuracy from potency in a controlled experiment? Or how about, if you are at some hypothesized potency cap, why would you expect potency to increase with anything?

I mean, really, assertions like "Accuracy of [Aspir] is most highly affected by Dark Magic Skill, and is not affected by Magic Attack Bonus, or INT" are based on something rather than pointless anecdote, right?

Actually, in the talk discussion of that FFXIclopedia article on Aspir, there seems to be something like a controlled experiment with random sampling, with a RDM75 (200 dark magic skill) casting Aspir on a single worm between level 10 and 12. Assuming that "accuracy" is capped in some sense on such a low-level target, it appears that INT does affect potency (just do a quick two-sample t). Sure, type I error, blah blah, but it's better than total bullshit.

pDIF and obsession with polynomial fits

A recent thread on the BG forums about an investigation of "cRatio for two handers" really underscores the ignorance coming out of the "playerbase" that actively chooses to post on forums. To wit:

• You got some motherfucker implying the "center" of advanced knowledge about game mechanics lay among those who were banned for Salvage duping, when the "center" is actually maybe 10 people at best, and not all are necessarily English-speaking, much less posters on BG.
  
• Someone rightly points out that said motherfucker is some obsequious cock-gobbler (ok, those are my terms) since information on pDIF has been outdated since the "2-hander update" (well before the bannings) yet no one has actually bothered to do an honest investigation.
  
• Another one actually bothers to collect some data on damage frequency to see what kind of distribution the data follows, but is easily derailed with a fetish for polynomial fitting to the data and data following a normal distribution (polynomial fitting and normality are contradictions as I will discuss soon).

This inexplicable obsession with polynomial fitting and normality is misguided for several reasons:

• Normal distributions have obvious tails at the extremes. Moreover, the tails are neither too short nor too long. The data do not show evidence of any real tails.
• Normal distributions are not parameterized by extrema (minimum and maximum). The parameters are the mean (center) and variance (spread).
  
• A second-order polynomial fit cannot "account" for tails. This is obvious because normal distributions have inflection points. So you cannot use a polynomial fit and argue for "normality" at the same time.
• Coefficient of determination can be thought of as a summary of a model fit. It doesn't mean the model is actually good. You can draw a squiggly line through all the data points and that will give you a R² of 1, but that would be a terrible and useless model. Polynomial fitting is similarly terrible and useless for the above reasons.
  
• Why even bother with any kind of fitting? As long as the distribution is symmetrical, at least you know the minimum, maximum, and median (same as mean) for pDIF given some value of cRatio, so you can use an expected value argument for long-run damage.
  

That said, there were some useful comments about the "shape" of the data. One poster actually suggested the data may follow some trapezoidal distribution. This is actually quite plausible under probability theory!

Obviously, the data do not appear to follow a uniform distribution. Even acknowledging the discreteness of damage (due to rounding) such that the minimum and maximum might be observed rarely, a uniform distribution of pDIF (NOT DAMAGE) is not all that likely. Although we cannot observe the uniform distribution of pDIF directly, we can observe histogram of damage (NOT pDIF). For this histogram, if pDIF were actually uniform, one might see an extreme "discontinuous" jump from the minimum to the minimum plus 1, or from the maximum to the maximum minus 1. In other words, the underlying true distribution of damage (NOT pDIF) would appear to be uniform except at the endpoints.

However, from probability theory, it is known that

• The sum of two uniform random variables with the same variance (regardless of actual minimum and maximum) follows a triangular distribution
• The sum of two uniform random variables with different variances follows a trapezoidal distribution (so a triangular distribution can be thought of as a degenerate trapezoidal distribution)

How can I argue that the underlying random component of melee damage could follow a trapezoidal distribution?

• Does anyone actually expect the "developers" to have done anything particularly fancy with pDIF? In many cases, random number generation is basically "sampling" from a uniform distribution, usually Unif(0,1).
• If pDIF does follow a uniform distribution (conditional on cRatio) for some ranges of cRatio (I realize this has been shown not to be the case for certain ranges of cRatio), there could easily be another random component to introduce "jitter" into the damage calculation, which would increase the variability of damage output yet keep the mean the same. This would account for the "1.05x correction" on maximum damage I've seen bandied about from time to time.
• So, there could be an "effective" pDIF that includes jitter.
  

To illustrate the plausibility of the last two points, I simulated 9,885 realizations of non-critical melee damage given 55 "base damage," with pDIF that follows Unif(1, 1.8) and a "jitter" component that follows Unif(-0.1,0.1). Here, the random components are summed together so that the end result is that the fake data are trapezoidal. I plotted the frequencies and I also drew a nonsense curve through all the data points (in blue).


Yes, this is completely fake and is not meant to demonstrate the truth of anything, but merely the plausibility that pDIF follows (or has followed) a trapezoidal distribution for some values of cRatio. I even put in a second-order polynomial trend line, which has a very high coefficient of determination, which shows that R² cannot say anything about whether the model is even appropriate. Here, we know it is grossly inappropriate because I know what the underlying probability model is.

Here's the R code for the simulation. Data were exported to Excel. And so goes an hour of my life.

N = 9885
a = trunc(55*(runif(N,min=1,max=1.8)+runif(N,min=-.1,max=.1)))
dmg = seq(min(a),max(a))
N2 = length(dmg)
dmg.counts = numeric(N2)

for (i in 1:N2) {
dmg.counts[i] = length(a[a==(i+min(a)-1)])
}

Acknowledgement of comments received

Just a brief post acknowledging that I have read two comments made in the past few months when I wasn't doing anything with this blog.

Comments on data table header translations of Lodeguy's data. Technically, I did not really translate anything as I don't know Japanese (I didn't say I was translating anything), barring being able to read katakana, simple phrases and basic kanji.

Comments on my criticism of an alternative analysis of paralyze data. I do not have issues with the original analysis. The secondary analysis I nitpicked past its veneer of soundness. I made this post on a "whim," which kinda goes to show I seek out "fun."

Expected magic damage in terms of accuracy - more parlor talk

In some sense, having to hoard magic accuracy for so-called high-resist targets when nuking (or enfeebling, etc.) is an all-or-nothing proposition for various reasons I just made up that may incidentally be shared by others. One, these high-resist targets have such high magic "evasion" that it is completely untenable (from experience or whatever) to nuke with the same equipment you would use for Ebony Puddings. Two, even if the target of interest is not quite as resistant as, say, a wyrm or sky god, it can be difficult to ascertain what amount of magic accuracy is acceptable to reach some threshold (say 90% acc.) without personal experience (or the experience of others). Three, compared to mindless melee auto-attacking and WSing, nuking specifically is inefficient from the standpoint of theoretical damage dealt in the "long run" (MP being an important limiting factor), so it seems pragmatic to accept unconditionally the trade-off of lowering maximum magic damage for fewer resists when there is any doubt.

If there comes a time where it is easier to ascertain the magic evasion of any mob of interest (probably never given the FFXI "team's" fetish for making basic game mechanics as opaque as possible, and lack of information sharing among the "playerbase"), perhaps it can be useful to quantify the difference in overall magic damage between a "high-resist" setup (with the purpose of maximizing magic accuracy) and a normal setup for resistant NMs and whatnot. But realistically this is just another parlor talk.

A long time ago, I argued that levels of resistance for a single "nuke" can be modeled by a one-parameter categorical distribution, with the parameter being the probability that a nuke is not resisted at all (full damage). This probability will be called "overall magic accuracy" for the remainder.

To reiterate, the distribution can be described as

no resist: π
1/2 resist: π(1-π)
1/4 resist: π(1-π)²
1/8 resist: (1-π)³

This assertion was based on prior observations by me and others that multinomial count data for nukes, categorized by level of resist, seemed to conform to such a pattern. (I will not discuss the speculated motivation for the programmers to use this model, assuming it is true.) If this is a reliable model, it seems reasonable to think about the effect of overall magic accuracy on magic damage in terms of expected value.

Ignoring rounding, let X be the actual damage of a nuke (subject to being resisted) with unresisted damage D. The expected value of X can be expressed as

E[X] = D[π+0.5π(1-π)+0.25π(1-π)²+0.125(1-π)³]

Based on this expression, overall magic accuracy can be thought of as attenuating the unresisted damage of a single nuke in the long run, multiplying that damage by some factor less than 1 that is a function of π. Therefore, in making some assessment of overall magic damage as a function of magic accuracy, we don't have to consider the actual distribution of resists given π, just as players calculating physical damage don't consider the distribution of pDIF given a ratio of attack to defense.

Just as magic accuracy attenuates unresisted magic damage by some factor less than 1, magic attack bonus (MAB) amplifies magic damage by a factor greater than 1. This is illustrated and summarized with the following graph plotting these factors described (for magic accuracy and magic attack):



As you can see, when "long run" magic damage is considered, there is decreasing return to overall magic accuracy, π (the expected value computed earlier is a third-order polynomial with respect to π), and constant return to MAB. The endpoints also make sense, too. If you happen to have 100 MAB, your overall damage is twice as high. If you happen to have 100% overall magic accuracy (recognizing that this is impossible in FFXI for nukes), then there is no attenuating of your potential magic damage.

Using the model for levels of resistance I described, it is possible and simple to estimate the percent change in long-run magic damage between two equipment setups of interest. Suppose you have a normal setup with +70 MAB such that you know will achieve 60% overall magic accuracy on some target of interest (this means in the long run 60% of your nukes will be unresisted) and you are interested in assessing whether utilizing your "high-resist" setup is worth the tradeoff in potential damage. Suppose your high-resist setup has +63 MAB and +26 more magic accuracy than the normal one.

At this point, there should be no need for quantifying the relative performance increase, but perhaps you want to quantify it anyway.

Since the magic damage "formula" is just multiplying various factors together, it is easy to calculate a percent difference that is independent of base damage, INT, weather effect, etc. (all of which could be considered constant). One needs merely to identify the multiplicative factors associated with MAB (+63 and +70) and m. acc (60% and 86%). Through direct calculation,

(1.63)(0.924757)/[(1.70)(0.752)] - 1 = 0.179

In the "long run," the overall damage using the "high resist" setup will be almost 18% higher than that using the normal one.

Again, is this useful or practical? Not really. But it could serve as a theoretical framework for "theorycrafting" (oh how I hate MMORPG-related jargon).

One more time

I am fairly amused that the conclusions from lodeguy's magic accuracy experimentation and my data analysis have been used to support the shibboleth of "320 skill/120 INT" for direct-magic damage (just browsing FFXI forums periodically). Maybe "shibboleth" is too strong a pejorative, since at least this rule of thumb acknowledges that INT contributes to overall magic accuracy (even though this acknowledgment seemed to be supported mainly with anecdotes and collective experience rather than formal data collection).

Should we really care about attaining 120 INT?

As you may recall, lodeguy gave us data that suggest (informally) a critical point for ΔINT (caster's INT minus target's INT) that "connects" two distinct regimes of rate of change of overall magic accuracy with respect to INT. To summarize, before ΔINT +10, the rate of change is estimated to be 1% per 1 INT (actually a little less from statistical significance testing), and between ΔINT +10 and ΔINT +30, 0.5% per 1 INT. I only emphasize this range because there is no data to show what might happen beyond ΔINT +30. (Moreover, there was no data to suggest, as far as I can recall, the effect of INT below 50% overall m. acc. But, realistically speaking, no one is ever going to investigate these issues. This is the best we will ever get, probably.)

With that in mind, it might be interesting to get some sense of whether 120 INT is generally suitable in "endgame" to reach the second ΔINT range with the slower rate of change. To do this, one must compare 120 INT to the INT of various "endgame" mobs.

Regrettably, information about mob INT from English-language sources is either poorly documented (sequestered in obscure FFXI forum posts) or almost non-existent (seriously, does anyone give a fuck about anything other than Ebony Puddings?), and this annoyed me to the point that I attempted to calculate the INT (as well as magic defense bonus, or MDB, and reduction of magic damage taken, or MDT-) of various mobs that I faced over the past few months to get a sense of whether I was surpassing ΔINT +10 most of the time. As I said in the last post, magic damage is deterministic (level of resist is random), so it should be fairly straightforward to calculate mob INT in many cases. Of course, I could have made calculation errors or overlooked level variability for specific mobs. I will leave it to others to verify or refute my calculations.

There isn't much variety in what I do in FFXI, though. All I have is data for mobs in NW Apollyon and those for various ZNMs. First, NW Apollyon:

Monster	INT	MDB	MDT-
Bardha	75	0	0
Pluto	82	0	0
Mountain Buffalo	60	0	0
Apollyon Scavenger	62	0	0
Gorynich	72	0	0
Kronprinz Behemoth	74	0	0
Kaiser Behemoth	???	???	???

As you can see, most of the "normal" mobs have low INT so that ΔINT +10 is easily cleared. As for Kaiser Behemoth, I didn't gather enough information, but I am pretty sure it possesses some combination of MDB and MDT- traits. I also collected similar data on some ZNMs I fought several months ago:

Monster	INT	MDB	MDT-
Lil' Apkallu	60	0	1/4
Verdelet	115	0	0
Experimental Lamia	89	0	1/8
Mahjlaef the Paintorn	112	0	1/4
Cheese Hoarder Gigiroon	81	0	0
Vulpangue	78	0.20	0
Dea	62	0	0
Iriz Ima	70	0	0
Gotoh Zha the Redolent	92	0.28	1/8
Tinnin	85	0.20	0
Achamoth	65	0.16	0

Here, MDB is reported in terms of amount above 1.00. MDT- is reported in terms of fractional reduction of magic damage.

Other than Verdelet (an imp) and Mahjlaef the Paintorn (a soulflayer), all of the ZNMs have INT such that ΔINT is well above +10. Therefore, from the standpoint of optimizing overall magic accuracy (given what we know), it seems practical to exchange INT in excess of ΔINT +10 for elemental magic skill or magic accuracy. In particular, this could be useful for Tinnin, which seems to have higher magic resistance than the "lower-tier" ZNMs (probably a result of level difference) despite having "only" 85 INT.

Moreover, there could be some patterns to mob INT despite the limited information available. Beastmen and other "sentient" mob types (particularly soulflayers and imps) could have higher INT in general than other types. Magic users have higher INT in general than non-magic users (I will treat this as self-evident).

But concerning the main question, it appears, at least for most ZNMs that are worth nuking and mobs in NW Apollyon, that ΔINT +10 is surpassed most of the time. If you happen to get close to 120 INT incidentally, that's great, but not necessarily at the expense of possible improvements to magic skill/magic accuracy. For example, Dea has only 62 INT, but it is still prone to resisting Thunder IV (compared to Blizzard IV). Therefore, it would be appropriate to use Sorcerer's Petasos instead of Demon Helm +1 for the sake of improving accuracy.

None of these mobs even have INT above 120, so it's not like you would get much of an improvement to resist rates whoring INT (such that ΔINT +10 is satisfied) compared to whoring magic skill/accuracy (all things being equal).

So what about beastmen "kings" and HNMs? Bahamut ("The Wyrmking Descends") is reported to have 115 INT (from Studio Gobli, if you can actually find the documentation). (Bahamut is sentient, right? Check.) Also Jormungand is reported to have 120 INT (also from Studio Gobli). (Perhaps the example of Jormungand motivated the 120 INT figure?) Other than that, I have no other information.

Anyone can calculate mob INT, but...

... magic defense bonus (MDB) and reduction in magic damage taken (MDT-) can get in the way of calculating INT. These factors may play a role in determining overall magic damage for things like Sarameya and Tyger. Without knowing MDB and MDT- and considering the incessant flooring involved in these calculations, it is somewhat difficult to arrive at a unique set of MDB/MDT-/INT that allows you to calculate magic damage exactly without using formal optimization methods, and I am not interested in doing that.

However, this post offers some very useful facts to determine what exactly a mob's potential MDB or MDT- is. In particular,

• 1000 Needles is not affected by MDB.
• Quick Draw is not affected by MDT-.
• Damage calculations for both are independent of mob INT.

Unfortunately, I don't have access to blue mage or corsair, but these tools would be very useful if I had access to them. Practically speaking, it doesn't seem particularly appropriate to do this kind of testing during "serious" events (how seriously do you take Proto-Ultima?), but your mileage may vary (enough with the cliches!).