What's the proc rate for virtue weapons? How do you know?

One "line" of evidence: checking with Justice Sword

Taken at face value, the estimate 555/1000 indicates the "occasionally attacks twice" (OAT) rate of Justice Sword is significantly higher than 50% and could be considered 55% (source). But is the OAT property the same for all so-called "virtue weapons"?

Another line of evidence: checking with Fortitude Axe... and WAR

The rest of this post discusses how to estimate the OAT rate of Fortitude Axe in the presence of the double attack trait from WAR. But first, I needed a good idea about how Fortitude Axe OAT actually interacts with the DA trait. In the past, I blabbed a lot about how Fortitude Axe might interact with double attack, but my "conclusion" was based on very weak evidence. After collecting some more count data with kparser under 12% DA (source), which ruled out my previous weak hypotheses about the DA/OAT interaction, I got a better idea about how to explain these results (assuming kparser was working correctly...).

It appears (not exactly "proof") that OAT can process on both the normal hit (which is guaranteed to occur for a given attack round, if not actually land) as well as the hit from the possible DA proc (with a major caveat to be discussed soon). More specifically, the hit from the DA proc occurs independently of whether an OAT proc occurs. (Not probabilistically, of course, but "mechanistically.")

It is worth noting that conceptually the order of DA and OAT could easily be reversed, such that the hit from the OAT proc occurs independently of whether a DA proc occurs, but I will just say the resulting probability calculations are not supported by the data when OAT is mechanistically independent of DA.

Anyway, one way to show pictorially all "possible" outcomes where DA and OAT can interact is with the following "tree":


There are six hypothetically "distinct" outcomes, but it is very inconvenient to monitor the equipment menu for virtue stone expenditure. More important, though, is the fact that Fortitude Axe cannot quadruple attack, so the case of expending two virtue stones is impossible. (This makes sense, noting that triple attacks are impossible with zero DA rate.)


So what "happens" to this 2-virtue stone attack round that is impossible? It appears that even if a DA proc occurs, only one virtue stone can be expended anyway, so the "tree" simplifies further:


The resulting probability model of the number of hits in an attack round (ignoring the distinction between hits and misses) is specified as follows. Let X denote the number of hits in a given attack round, d the probability of a double attack proc, and π the probability of an OAT proc. Then,

Now that we have a reasonable probability model describing the interaction between double attack and the OAT property of Fortitude Axe ("reasonable" based on chi-square goodness of fit to the data given 12% DA rate and posited virtue weapon proc rates of 50% and 55%), we can now estimate the OAT rate. Proceeding with maximum likelihood estimation is not really necessary when an obvious unbiased estimator can be based off the observed number of single hits (denoted as X₁) in n attack rounds:


It follows that the unbiased estimator is


with variance


Note that when d = 0, the variance reduces to that for the estimator for a simple binomial proportion (marginal in the context of the multinomial distribution). (Note to self: from simulation, this estimator is only very slightly less efficient, from an MSE standpoint, than the MLE, which I would bet is UMVUE even if an analytical expression for the MLE and the CRLB is annoying to obtain.)

The estimated proportion of single hits (per attack round) is 1 - 595/1425/.88 = .5255183, with corresponding 95% confidence interval (.4964218, .5546148). Given the specified probability model (which cannot be "proven" to be true at this time) and the data, it is not possible to conclude that the OAT rate of Fortitude Axe is either 50% or 55% (both are plausible given the confidence interval), unfortunately. But it should be possible to rule out one or the other with further data collection (with the hope that the probability model is correct), using the estimator specified above.

A third way: Faith Baghnakhs

Among all virtue weapons, it would be fastest to determine the OAT rate of Faith Baghnakhs by counting the number of triple attacks and quadruple attacks. It would be easier to do this on ninja because you wouldn't have to pay attention to kick attacks (because you want to use a parser instead of counting manually). If the OAT rate for Faith Baghnakhs can be shown to be 55%, that, along with the observed proc rate for Justice Sword, could be used as evidence for a common OAT rate of 55% across all virtue weapons.

A hierarchy of great axes?

This is a rehash of a previous post comparing Bonesplitter and the good Luchtaine, two "Magian" great axes, to that old standby Perdu Voulge and Fortitude Axe, the presumptive weapon of choice for Campaign (even though Waltz recast ends up being the rate-limiting factor for curing yourself), but new evidence, both for Fortitude Axe (see first relevant BG post and second relevant BG post for details that I won't go over here) and Luchtaine (to be discussed later, perhaps), show that I underrated Fortitude slightly and overrated Luchtaine significantly.

In particular, evidence indicates Luchtaine behaves similarly to Joyeuse such that regular DA and Magian OAT are "directionally" exclusive, which is different than mutually exclusive. Suppose that the DA rate were 20%. Then, mutually exclusive would mean P(OAT) = .40, P(DA) = .20, and P(OAT and DA) = 0. On the other hand, directionally exclusive would mean that either P(OAT|not DA) = .40 and P(DA) = .20 OR P(DA| not OAT) = .20 and P(OAT) = .40. Consequently, given 20% DA and 40% OAT rate, the effective DA rate would be .20 + .80*.40 = .40+.60*.20 = .52.

Also, I decided to repeat the previous analysis using Raging Rush. Even if Raging Rush's three base hits (in other words, those not arising from double attack) are the only ones that have a chance to be critical hits, it's still generally better than King's Justice. One consequence: because RR's STR modifier is lower than KJ's, the relative difference in damage between a Perdu RR and Fortitude RR is more than that between a Perdu KJ and Fortitude KJ, so the relative difference between Perdu and Fortitude "overall" would be less with RR than KJ "all other things being equal."

I find it is worth including Rune Chopper in the discussion, too, along with Hephaestus with STR +4 and attack +15 as a basis of my pontificating about what kind of effort is warranted to get "good enough" (not the most). Since I have 19% haste normally, I will use that as a haste baseline before Rune Chopper, so the full haste bonus of Rune Chopper is not fully realized. On the other hand, I will also consider having Rune Chopper with only 1 MP refresh such that the latent is active one out of every two rounds (as it appears to be anyway). I will also consider the situation of having a "typical" double March (~20% haste with March +2 instrument and 8/8 merits in both wind and singing skill), Haste spell (~15%), and Hasso (~10%).

I will also account for the concept of time delay between the initiation of a weapon skill and the start of the next attack round, as it apparently is fundamental to the game and not associated with human reaction time or laziness (not that I really noticed or cared), kind of like how the delay associated with Curing Waltz screws up Drain Samba actually working properly (something that is easy to notice and that I find very annoying). This could also be considered the time delay associated with execution of a weapon skill that must elapse before the start of the following auto-attack round, or "WS delay" for short. It's something worth considering because this delay is unavoidable, but since I don't know what is actually the so-called WS delay, I will do this comparison for 0, 1, 2, 3, and 4 second delays.

Finally, I find it really unnecessary to go into excruciating detail about what goes in the calculations, so I will just report something I call "relative efficiency" ratios relative to the baseline of Perdu Voulge, which are merely ratios of damage rates. In the end, one should focus only on the gross differences, rather than whether something is really 2.15% more as opposed to 2.2% more, for example.

Relative efficiency of great axes relative to Perdu Voulge (in terms of damage rate)

Weapon	No WS delay	1s delay	2s delay	3s delay	4s delay
Rune Chopper (latent active always)	1.097	1.082	1.070	1.059	1.049
Fortitude Axe	1.037	1.008	0.984	0.964	0.947
Hephaestus (6 hits to 100 TP)	1.032	1.029	1.026	1.023	1.021
Bonesplitter	1.017	1.017	1.017	1.017	1.017
Perdu Voulge	1	1	1	1	1
Rune Chopper (latent 1/2 active)	0.997	0.991	0.986	0.981	0.977
Luchtaine	0.985	0.972	0.961	0.952	0.944
Hephaestus (7 hits to 100 TP)	0.953	0.961	0.968	0.974	0.980

Again, these ratios are based on 19% equipment haste before Rune Chopper, along with double March (~20% march), Hasso, and Haste spell.

The ratios under the hypothetical situation with zero WS delay can represent the "intrinsic" relative efficiency of weapons that have a higher WS frequency that Perdu Voulge (notice that Bonesplitter has the same relative efficiency regardless of WS delay because it has the same WS frequency as Perdu), but intrinsic doesn't mean actual or true. The higher the WS delay, the more disproportionately affected are weapons with higher WS frequency compared to Perdu.

(Note that the concept of WS delay can be generalized to job abilities that interrupt or postpone attack rounds, but I did not account for that here.)

Implications for Fortitude Axe: wonder why Fortitude Axe doesn't actually appear to be better than Perdu Voulge in practice? WS delay could explain it. In particular, if you plan to use Fortitude Axe in a maximum haste situation (~80% haste), spamming weapon skills might be relatively counter-productive (for Fortitude compared to Perdu) because of WS delay, but WS frequency is pretty much the only benefit of using Fortitude Axe (aside from TP gain without using WS), so why not just use a high-damage great axe (Perdu or even Berserker's Axe)? Using Fortitude Axe for a zerg basically means having hope that you get more hits per round in a small time frame compared to the long-run average, e.g., stringing together several 3-attack rounds. Having 80% haste is usually the decisive factor in a max-haste zerg because you probably have max attack and accuracy as well. Maybe if you had a BLM land Choke and got some STR etudes... things you could do to compensate for the low base damage.

Implications for Rune Chopper: On the other hand, Rune Chopper with latent always active (if you somehow manage to achieve this; not a trivial thing) is still substantially better than Perdu even with significant WS delay (4 seconds), and this is under the situation where the 9% haste bonus isn't fully realized (it could be if you switched out other haste equipment to increase other damage-related factors), albeit under the double March/Hasso/Haste spell situation. On the other hand, Rune Chopper with only 1 MP refresh is rather pointless. If you had an Ares Cuirass lying around and RDM accommodating you, it would be good.

Implications for Luchtaine and other Magian great axes: SE really needs to allow Luchtaine to attack 3 times or even 4 times in the future or increase the base damage dramatically. At least there is hope that SE might do this later, whereas with Fortitude Axe, SE will never allow 4 attacks per round. You don't get much out of the others (as the final forms currently are) considering the time investment required, compared to spending IS on a Perdu Voulge. Hephaestus 6-hit is not terribly reasonable because of the 29 store TP requirement alone.

Didn't I say something about a hierarchy? Stick with Perdu Voulge in general...

How to check if a Teiwaz has superior accuracy to Terra's Staff

Obviously, I am talking about the Teiwaz with elemental affinity: magic accuracy +3, not so much that I am talking about the earth-aligned Teiwaz.

It is thought that earth affinity: magic accuracy +1 is equivalent to the accuracy bonus of Earth Staff, and earth affinity: magic accuracy +2 equivalent to the accuracy bonus of Terra's Staff. If you ever read this blog, you would know that elemental NQ staves are considered to have +20 magic accuracy for the specified element, and HQ staves, +30 magic accuracy. It is postulated that elemental affinity: magic accuracy +3 corresponds to +40 magic accuracy.

Without discussing the evidence underlying the following experiment to check whether the earth Teiwaz is superior to Terra's Staff, I will describe a superiority "trial" involving relatively few casts.

Location: Alzadaal Undersea Ruins (Nyzul Isle Staging Point)
Target monster: Level 78 Qiqirn Poulterer (ranger)
Spell to cast: Stone (I)
How many casts: 100.
What to count: number of non-resisted Stone I, number of half-resisted Stone I, number of quarter-resisted Stone I, number of eighth-resisted Stone I (should be easy to identify from the magnitude of damage)

How to identify the level 78 Qiqirn Poulterer: one way to check you have found the correct level Qiqirn is to set your accuracy score to 263 and use the "check" function to find the right Qiqirn. One way to achieve this is to equip a weapon type for which you have 230 combat skill (example: BLM with max club skill). 230 combat skill corresponds to 227 accuracy. Suppose you also have 62 DEX. For a one-handed weapon (club), this means you have +31 accuracy. Then equip +5 accuracy worth of equipment (example: Chivalrous Chain) to achieve a total accuracy score of 263. Level 77 and 76 Poulterers will check "low evasion," while the level 78 Poulterer will give no evasion message. Incidentally, this implies the level 78 Poulterer has at least 293 total evasion. You can confirm the level after killing the Poulterer by noting EXP yield (200 base EXP for level 78, 230 given 15% Sanction bonus).

Total magic accuracy for this experiment: it is known reasonably well (I will not cite evidence at this time) that having 65 INT, 290 elemental magic skill, +5 magic accuracy (from equipment), and no elemental staff corresponds to having about 55% magic accuracy rate for the Stone I spell. (The level 78 Qiqirn Poulterer has 65 INT.) If your elemental magic skill is higher or lower (say 292), make the appropriate adjustments to INT and/or magic accuracy. Here, +/-1 INT is considered +/-1% magic accuracy rate (up to a point), and +/-1 magic accuracy (from equipment) is considered +/-1% magic accuracy rate, too.

Given the above, equipping a HQ staff like Terra's brings your magic accuracy up to ~85%. A "quickie" trial I ran gave 57/71 non-resisted Stone I, strong evidence of uncapped magic accuracy rate. As postulated previously, equipping a Teiwaz with earth affinity: magic accuracy +3 could bring your magic accuracy up to ~95% (the maximum rate).

Why 100 casts of Stone I on a level 78 Qiqirn Poulterer? 100 is an arbitrary figure as I am too lazy to do a power calculation, but since we know a priori that Terra's Staff doesn't even give a capped magic accuracy rate (and it shouldn't since I said it would be ~85%), it will be very easy to show that, if the Teiwaz earth affinity: magic accuracy +3 really has +40 magic accuracy, the observed data will indicate a capped magic accuracy rate. Of course, if the accuracy bonus were higher than +40, this test wouldn't be able to show that, but the in-game constraints described by the current magic accuracy "model" and a desire for a "minimal" sample size (the further away from 50%, the smaller the standard error) led to the above experimental conditions.

Considerations: avoid Qiqirn Goldsmith links. To minimize damage from ranged attacks, it is preferable to be RDM. If not, have someone spam heal you while you hammer out 100 casts in short order. It really doesn't take that long.

Questions and desired clarifications about experimental conditions may be fielded in the comments, if anyone actually gives a shit.

Credit to pchan on BG for previous work on Qiqirn Poulterers that allows for a fairly straightforward and not-onerous experiment.

Two years of chocobo racing

Crystal Stakes (C1) results

Time period	1st place	2nd place	3rd place	4th or lower	TOTAL
Period of angst	98	78	24	15	215
Period of relative prosperity	52	28	11	3	94
Since Chocobo Circuit changes	40	24	9	6	79
Since March 2010 update	5	4	5	1	15
	195	134	59	25	413

I made some gil. How about you?

Katanas from Trial of the Magians

This post is patterned after "great axes from Trial of the Magians," but with a minimum of tedious commentary. These are explicit damage calculations that should match up closely with simplified, one-minute "paper napkin" analysis when WS damage is dropped as a damage component. It should be obvious what katanas are of interest (Kuina with STR and attack bonuses, for example). See FFXIclopedia entry for final forms of katanas.

Givens, assumptions, and simplifications for analysis

• Basic rates: 95% hit rate, 15% double attack rate, 0% haste, 40% dual wield delay reduction, 24% critical hit rate
• Store TP +5
• Blade: Jin used as the WS of interest
• At 100 TP, a critical hit rate bonus of +10% (added to base critical hit rate) exists for Blade: Jin (questionable assumption by analogy: Evisceration shown to have a critical hit rate bonus at 100 TP)
• All hits in Blade: Jin can critical hit (unfounded assumption)
  
• For WS, double attack can occur once for main hand and once for off hand (unfounded assumption)
  
• 40% "occasionally attacks twice" OAT rate for Isatu
• Effective double attack rate is the sum of the OAT and DA rates (unfounded assumption)
  

Probability distributions for required number of hits to 100 TP after Blade: Jin

TP per hit	22 hits	21	20	19	18
4.6 TP	.00245	.09330	.88770	.01654	-
4.7	.00018	.00919	.15338	.83725	-
4.8	-	.00245	.09330	.88770	.01654

Remarks: these are required to account for variability of TP return to determine average time to 100 TP. 4.6 TP (201/190 delay combo), 4.7 TP (227/190, 227/201, 232/190, 232/201), and 4.8 TP (227/232) cover all katana combinations presented in this post.

Average time to 100 TP in the long run

Weapons	Average no. of rounds	Average no. of hits	Average time (s)
Senjuinrikio/Perdu	9.081	19.842	37.87
Mozu/Perdu	9.081	19.842	37.87
Mozu/Isatu	7.780	19.955	35.71
Mozu/Kuina	9.081	19.842	38.87
Isatu/Perdu	7.815	20.045	32.98
Isatu/Kuina	7.815	20.045	33.84
Kuina/Perdu	9.497	20.752	37.13

fSTR and average pDIF (both auto-attack and WS)

Used baseline fSTR 4 and 9 for auto-attack and weapon skill, respectively (5 and 10 for Kuina), and +53 to Blade: Jin base damage from secondary modifiers (+54 for Kuina).

Used baseline average pDIF 1.452 (from 450/300 attack to defense... yes, I know that equals 1.5) and 2.552 for non-critical and critical hits, respectively. Average critical pDIF is taken to be 1.1 plus average pDIF (very rough estimate that can slightly overestimate the effect of critical hits).

Weapon	Phase	Average pDIF (no critical)	Average pDIF (critical)
Senjuinrikio/Perdu	TP	1.491	2.591
	WS	1.571	2.671
Mozu/Perdu	TP	1.491	2.591
	WS	1.571	2.671
Mozu/Isatu	TP	1.452	2.552
	WS	1.533	2.633
Mozu/Kuina	TP	1.506	2.606
	WS	1.586	2.686
Isatu/Perdu	TP	1.491	2.591
	WS	1.571	2.671
Isatu/Kuina	TP	1.506	2.606
	WS	1.586	2.686
Kuina/Perdu	TP	1.544	2.644
	WS	1.624	2.724

Average damage in a single cycle

Weapons	Avg. hits	Avg. TP dmg.	Avg. WS hits	Avg. WS dmg.	Avg. total dmg.
Senjuinrikio/ Perdu	19.842	758.796 + 626.823	2.9925 + 1.0925	820.638	2206.258
Mozu/Perdu	19.842	818.353 + 626.823	2.9925 + 1.0925	829.362	2274.540
Mozu/Isatu	8.499 + 11.455	685.489 + 746.999	2.9925 + 1.0925	817.325	2249.815
Mozu/Kuina	19.842	825.347 + 719.984	2.9925 + 1.0925	848.606	2393.939
Isatu/Perdu	11.507 + 8.538	767.446 + 539.427	2.9925 + 1.0925	775.131	2082.006
Kuina/Isatu	8.538 + 11.507	619.599 + 774.006	2.9925 + 1.0925	810.714	2204.320
Kuina/Perdu	20.751	769.145 + 675.347	2.9925 + 1.0925	822.067	2266.560

Remarks: Isatu effective DA rate is taken to be (40 + 15)% = 55%, which is subject to verification. Isatu's OAT rate is thought not to affect weapon skills.

Damage per second

Weapons	Proportion of total dmg. in auto-attack phase	Damage per second
Senjuinrikio/Perdu	.628	58.260
Mozu/Perdu	.635	60.063
Mozu/Isatu	.636	63.004
Mozu/Kuina	.645	61.592
Isatu/Perdu	.627	63.130
Kuina/Isatu	.632	65.141
Kuina/Perdu	.637	61.036

Remarks: Auto-attack damage proportions may be lower than what should be expected (closer to 2/3)

Some comments

It should have already been obvious that Mozu/Perdu would generally be better than Senjuinrikio/Perdu, especially in a max pDIF context. Fudo was already (barely) better than Senjuinrikio (for auto-attack damage alone)... Mozu/Kuina is the best of the non-Isatu pairings (OAT rate still in question; take with a grain of salt), particularly better than Kuina/Perdu because 4.7 TP per hit is better than 4.6 TP per hit. Kuina/Isatu still gives 4.7 TP per hit, making it a formidable combination on paper (again pending OAT rate verification).

Great axes from Trial of the Magians

[Update: forgot delay +10 on Luchtaine.]

New update, more junk to waste time on, like the new quest "Trial of the Magians." I'd take a 100-damage Bonesplitter over Perdu Voulge anyday if I didn't have to camp the same lottery spawns over and over, and a 76-damage Luchtaine that "occasionally attacks twice" sounds even better and, not unexpectedly, even more tedious to obtain. (How about compared to Fortitude Axe?) Then again, so does Bravura, but that's something I'll never bother trying to get.

With that in mind, this post attempts to answer how much better these new great axes are compared to Perdu Voulge to inform the decision on whether to get one of these new great axes. This will be determined by calculating average rates of damage for the previously mentioned great axes (except Bravura).

This post is constructed in a similar fashion to my comparison of a 33-damage Tsukumo to Senjuinrikio (in a dual-wield context).

Some basic "givens" and assumptions

• 95% hit rate
  
• 22% double attack rate
• 24% critical hit rate
  
• 0% delay reduction (literal delay reduction or haste)
  
• "Sufficient TP" to accumulate at least 100 TP in only six hits
• King's Justice used as the WS of interest
  
• WS damage based only on 100 TP (where TP modifiers apply)
• 50% "occasionally attacks twice" rate for Fortitude Axe
• 40% "occasionally attacks twice" rate for a 76-DMG Luchtaine
  
• Luchtaine CANNOT attack three times in an attack round

Points 1 and 5 together imply a 95% chance to reach 100 TP in only 5 hits after any weapon skill, because any additional hits in the WS don't affect this probability.

The TP bonus on Raging Rush is still not understood well (and probably never will be), and King's Justice has more application anyway, so I will just go with KJ here. KJ has its own problems with "spike damage," but it is not characterized well at all, so how could I really account for it?

The last two points have yet to be substantiated for 2-handed Magian weapons as far as I know. Actually, determining how the DA trait interacts with the "occasionally attacks twice" property for the Magian weapon warrants its own post. For now, I will assume that the DA rate and OAT rate are additive (so effective DA rate of 62%) based solely on this BG post. The Clopper-Pearson 95% confidence interval is (.378, .528) (n = 179) and there were no reported triple attacks, much less quadruple attacks. I also think it's safe to say that the 62% rate, if true, would not be applicable to weapon skills.

I will update this post if those assumptions are invalid.

Average time to 100 TP in the long run

Weapon	Average no. of rounds	Average no. of hits	Average time (s)
Perdu Voulge or Bonesplitter	4.505	5.221	37.84
Luchtaine	3.531	5.434	30.24
Fortitude Axe	3.247	5.571	27.28

This whole analysis is based on consideration of a cycle of TP generation to reach 100 TP immediately followed by a weapon skill (no delay between cycles). The "long run" refers to the fact that the initial cycle, starting at 0 TP, has a infinitesimal effect on the ideal average time to 100 TP, given previously stated conditions. It is possible, though, to miss the first hit on a weapon skill, so the averages do account for that.

Also, it is well established (by me) that Fortitude Axe can triple attack in a single round, and the DA trait interacts with Fortitude Axe's OAT in a way that is not obvious. (Refer to a previous post on this if you're interested in the details. I didn't provide strong evidence the OAT rate is 50% though...)

fSTR and average pDIF (both auto-attack and WS)

I will just use fSTR 6 and 11 for auto-attack and WS damage (based roughly on my own character).

As always, pDIF for 2-handed weapons is a pain in the ass to consider.

For now, I will use an attack/defense ratio of 1.5 (450/300) as an arbitrary baseline for Fortitude Axe, in the auto-attack or TP phase. Then, the ratios for Luchtaine, Bonesplitter, and Perdu Voulge are 1.52, 1.52 (attack +6 with Fire Bomblet), and 1.553 (attack +16), respectively.

Ratios for weapon skills will be based on my own equipment (attack +8 except for Fortitude Axe, which will be attack +14 to account for Fire Bomblet).

For the range of attack/defense ratios considered, at least there are no pDIF floors or ceilings to account for. Therefore, the distribution of pDIF (given attack/defense ratio) is symmetrical.

For the sake of clarity, I will not justify the following at this time (would anyone really care though?) and assert that, partly given what I just stated in the last paragraph, average non-crit pDIF is approximately equal to attack/defense ratio and crit pDIF is approximately equal to non-crit pDIF + 1.1. (This is a rough simplification, to be generous, but one based on data.)

Weapon	Phase	Average pDIF (no critical)	Average pDIF (critical)
Perdu Voulge	TP	1.553	2.653
	WS	1.58	-
Bonesplitter or Luchtaine	TP	1.52	2.62
	WS	1.546	-
Fortitude Axe	TP	1.5	2.6
	WS	1.546	-

Since KJ is the weapon skill of interest, critical pDIF is irrelevant here.

Average damage in a single cycle

Weapon	Avg. hits	Avg. TP dmg.	Avg. WS hits	Avg. WS dmg.	Avg. total dmg.
Perdu Voulge	5.221	967.698	3.268	790.366	1758.064
Bonesplitter	5.221	987.382	3.268	795.036	1782.419
Luchtaine	5.434	794.924	3.268	669.3747	1464.298
Fortitude Axe	5.571	687.882	3.268	607.278	1295.160

King's Justice has a damage modifier of STR 50%, so I added 42 to WS "base" damage (again, based on my own character). Also, I accounted for the fTP bonus from a sea gorget (first WS hit only).

Damage per second

Weapon	Proportion of total dmg. in auto-attack phase	Damage per second
Perdu Voulge	.55o	46.457
Bonesplitter	.554	47.101
Luchtaine	.543	48.410
Fortitude Axe	.531	47.481

The proportion of total damage from the auto-attack phase is one way to check to see if these calculations are remotely rooted in reality (comparing to parser output), and the corresponding figures for each weapon seem reasonable. They are rather "far" from 50%, but I haven't merited in a non-Colibri situation in a long, long time, so I can't say for sure. Note that the given double attack rate, 22%, is higher than I have used in the past. As DA rate increases, the auto-attack proportion of damage necessarily increases. (I have used either 17% or 19% in the past.) I also used a maximum critical hit rate, which would increase auto-attack damage relative to King's Justice damage.

Now, consider paper-napkin calculations. For auto-attack damage alone, I could argue that Bonesplitter is about (106/102-1)*100% = 3.92% better, but I didn't account for the attack difference, much less differences in WS damage, so 1.38% might be a better indication of how much better overall Bonesplitter is than Perdu Voulge where attack still contributes to damage (even where average pDIF is rather high as in this example).

Fortitude Axe is often touted as superior to Perdu Voulge, and a previous analysis corroborates that notion. However, that analysis presumed that Fortitude could attack up to four times in a single attack round, which we know now obviously isn't true, so the gap between the two is even less than I showed.

Luchtaine appears superior to Fortitude Axe, not only in average rate of damage (not by much though) but also in average TP fed per attack round (if that is ever a concern). Now only if there were some corroboration on the 40% OAT and how the DA trait interacts with OAT...

Conclusion

Luchtaine appears to be the best option on paper, pending confirmation on its "occasionally attacks twice" rate and how that interacts with the normal double attack trait. Now, I can show how much something is better, but whether it's worth getting one thing over another is a matter of priority depending on how much you value the marginal improvement (over Perdu, Fortitude, whataever).

The requirements for Luchtaine, including 10 of an exclusive item that drops off a Vampyr that probably requires an alliance of two parties to kill efficiently (see "Voidwalker Notorious Monsters"), seem rather onerous, so I would need some good evidence concerning Luchtaine to bother upgrading it, and I would do so only as part of "nothing better to do" activity, which means it could take a year to get it.

I didn't even consider the various final forms of Hephaestus, either, including one with 91 DMG, 482 delay, STR+4 and attack +15, which looks good until you remember that you need +29 store TP for a 6-hit setup. I might update this post to include that great axe later.

Topic generation

My motivation to post is closely related to my motivation to play, even though what I actually do when I play tends to have little direct relationship with what I post about. Considering this, until (if) I have motivation to blog again about FFXI, maybe passersby can leave something in the comments to this post about what they might be interested in having me discuss at a later time. (While I do have an idea about showing whether Poisson regression is more appropriate than a simple difference of two binomial proportions for a particular FFXI-related data set, as I do not have any intuition about what would be "better," that would be interesting only to me, really.) Perhaps to stimulate generation or recall of ideas, I will reflect briefly about this blog:

One of the things I wonder about is what a reader of this blog, whether someone who has actually perused most of it or is coming from a link from a FFXI forum, actually applies anything he/she may have gleaned from the multifarious range of topics I've discussed. In some cases, I merely describe simple facts that are, surprisingly, not widely known, like the attack bonus on Yellow Curry Buns compared to Coeurl Subs (why else would you waste your gil buying subs instead of buns?) and chocobo raising/racing information. In other cases, I apply basic statistics to data collected by other players to support or refute things about game mechanics that are either "known" from anecdotal observation or merely assumed without any legitimate evidence. Sometimes I even do probability exercises to compare tactics (optimizing Phantom Roll "algorithms") or differences in equipment as precisely as possible.

In all cases, though, what really motivated me to create these posts was irritation with ignorance. (Many times this irritation was profanely expressed.) Yeah, maybe you can't read Japanese. I can't either, but it doesn't stop me from hitting up the major Japanese wikis to see if there is any information that doesn't show up on FFXIclopedia. And considering that the core of MMORPGs is a random number generator, I would hope the savvier players would have some appreciation that applications of probability and statistics can be very useful to understand how to play the game beyond lootwhore-agonizing about poor drop rates, or just have a better understanding of FFXI and of probability and statistics in general.