Stupid posts

Sadly, I wasted a bit of time combing English-langugage forums this weekend looking for anything interesting, but it's not as wasteful as actually posting on forums. If only I knew Japanese, then I'd be able to make this blog a lot more informative instead of cluttering it with arithmetic junk. Here are some threads amusing enough to waste 20 seconds commenting on each.

(FFXIclopedia) Playing the logic card in a video game when considering the possibility of cutting up Marinara Pizza into slices for convenience. "How do you end up with more pizza than you started out with?" How about, how the fuck do you fuck up cutting a pizza into slices? (Recall that you can HQ curry buns.)

(Allakhazam) How do you get a Kikoku when you're this ignorant? Never mind, you actually upgraded Kikoku as opposed to something useful and parasitized your Dynamis LS or RMT'ed it in the process or sat on a fat pile of gil before general deflation.

(BG) Dick-riders actually defend the Quicksand Caves map requirement for "Moogle Kupo d'Etat," like you dipshits didn't look up the mission info beforehand to save time (the smart thing to do) and actually finished this particular mission through trial-and-error. This is from someone who has all the maps and didn't leech some of them (like the useless Promyvion maps) like you probably did. No, most maps are completely useless.

(BG) Typical Fenrir "player" contributing nothing of value (asking about possible ANNM solos), except the valid point that vBulletin's search function is complete shit, and the premise that we should even search the forums for highly fragmented information is complete shit, too.

(Allakhazam) What is it with bards and Alkalurops anyway? Not that you should actually read this, but take my word for it that I just cannot have a legitimate conversation about magic accuracy with anyone in that thread except two people. There is still a lot to learn and confirm in theory (how about the "developer" team of monkeys not being so fucking opaque about everything?), but it's not getting done with some stupid back-and-forth.

(FFXIclopedia) Again, why does anyone care about beating StarOnion/InvincibleLeg/MeteorBrian?

(Allakhazam) Are players really that invested in becoming a great [insert job here]? Considering all the inane hero worship that surrounds so-called "celebrity" players in FFXI, no, no one who's played long enough should be all that surprised. Still, being a knowledgeable, even "skilled" (to the extent that skill is involved) player involves a bit more than micromanaging a single job. Not that leveling only one job is a bad thing (why throw even more good time after bad in a MMORPG?), but I guarantee that one-job only types who talk a game about "perfecting their craft" had to leech at some point or another. Especially thieves.

Tsukumo

The nature of recent posts hardly belies the fact that they are not at all interesting to construct. While they could easily be construed as a form of showing off, they were also motivated by my interest in analyzing the game in a more simpler way than just hand-waving about shit like everyone else. To me, it juts makes a lot more sense to deal with averages, which are a nice way to ignore variability in both damage and attack frequency and really simplify quantitative comparisons. Sometimes you just have to do the boring shit yourself since few others are capable and even fewer willing.

Aside from the posts concerning samurai weapons, everything else I had some degree of "personal" interest in, including this one about Tsukumo. Should I even bother trying to get a Tsukumo? I attempted to assess the viability of Tsukumo as a replacement for Senjuinrikio in the main hand.

Could Tsukumo with DMG +5 alone supplant Senjuinrikio in the main hand? The way I'm currently (not) using ninja, 190 delay and a decent damage rating on the main hand would be enough to let Senju collect dust, but all the hand-wringers can't seem to let go of the 6% crit rate and 38 base damage, never mind that you'd be better off with Fudo if you want higher average damage in the fantasy land of high pDIF.

Whatever your idea of high pDIF is for ninja, there is a way to show quantitatively whether Tsukumo/Perdu Blade is relatively less (or more) efficient (I'm starting to hate this term) than Senjuinrikio/Perdu in terms of spamming Blade: Jin. The case of dual wielding requires just a little more work than single weapons.

From the standpoint of spamming weapon skills, TP return from the previous WS looms large in terms of determining how many hits, on average, it will take to get to 100 TP. The fact that the off-hand weapon contributes a full-TP hit to Blade: Jin's TP return makes it more difficult to determine the "true" average number of hits to 100 TP after a Blade: Jin, but there is a way to calculate it.

Given the following...

• 95% hit rate
  
• 15% double attack rate
  
• 5 Store TP (Rajas Ring)
  
• 40% delay reduction from Dual Wield

... what is the probability distribution of the required number of hits to 100 after a Blade: Jin (with TP return being a random variable)? This information is necessary to calculate exactly the average number of hits to 100 TP along with the average number of rounds to 100 TP.

So far, I have gotten away with assuming there is always sufficient TP return from the previous WS to get to 100 TP in n - 1 hits for a n-hit setup. Ignoring the 5% of the time that there isn't sufficient TP return is not really necessary, but it is convenient.

While this simplification may be tolerated for two-handed weapons, this is not acceptable for the dual-wield situation. Nominally speaking, both Tsukumo/Perdu (4.6 TP) and Senjuinrikio/Perdu (4.7 TP) require 22 hits to 100 TP starting from 0 TP. (I hope these TP values are correct as they are the linchpin of this "analysis.") After a Blade: Jin, which can take on any of a finite set of TP values, the required number of hits to 100 TP is broken out as follows:

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

Weapon	22 hits	21 hits	20 hits	19 hits
Senjuinrikio/Perdu (4.7 TP)	.0002	.0092	.1533	.8373
Tsukumo/Perdu (4.6 TP)	.0025	.0933	.8877	.0165

It shouldn't be surprising that even a 0.1-TP difference results in dissimilar distributions. Most of the time, the Senjuinrikio/Perdu combination requires 19 hits to reach 100 TP. In contrast, the Tsukumo/Perdu combination requires 20 hits to reach 100 TP most of the time. We can use these probabilities to obtain a weighted average of the average number of hits to 100 TP after Blade: Jin.

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	37.84
Tsukumo/Perdu	9.497	20.752	36.09

These figures are based on spamming weapon skills continuously, showing that Tsukumo/Perdu doesn't have much of an advantage. Note that this a different viewpoint than just looking at the rate of TP gain (Tsukumo/Perdu being the obvious "winner"), which is not very meaningful for assessing spamming efficiency because, from this point of view, TP return from the previous WS is meaningless (like in Campaign).

If you've read this far, congratulations! I posted a spreadsheet that calculates the average number of rounds to 100 TP and average number of hits to 100 TP based on hit rate, DA rate, and whether you're dual wielding or not. While making a comprehensive, user-friendly spreadsheet for melee damage calculations is not very interesting to me, I can see where these calculations can be incorporated into one.

(Note: simulation was used to validate these averages.)

Calculating average damage to 100 TP

Weapons	No. hits to 100 TP	AA dmg	Hits/WS (main/sub)	WS dmg	Total dmg
Senjuinrikio/Perdu	19.842	691.708 + 571.463	2.9925/1.0925	701.261	1964.433
Tsukumo/Perdu	20.752	1195.305	4.085	652.783	1809.689
Tsukumo/Perdu (5% crit)	20.752	616.329 + 597.652	2.9925/1.0925	666.847	1880.829

Now that the average time to 100 TP has been taken care of, all that's left is to calculate average damage per hit and damage per WS. Hey, why not consider Tsukumo with 5% critical hit rate, too?

Here, I am assuming an average of 1.6 pDIF given 20% base critical hit rate across the board (still delving in fantasy, obviously) except where modified by weapon properties, 4 fSTR for auto-attack, and 9 fSTR for weapon skills. Given Blade: Jin, I used a WSC value of 53.

As I understand it, during a weapon skill double attack procs once for the main weapon and one for the sub, so that there are up to 6 hits possible for Blade: Jin. Therefore, it is necessary to split the average number of hits for Blade: Jin to account for any base damage (or expected damage) differences.

Another assumption I made with absolutely no concrete evidence is that that there is a critical hit rate bonus of +10% at 100 TP (analogous to Evisceration) on top of the 20% base rate and weapon crit rates, and that it applies to all hits. Assuming there is even a bonus, does it even apply to the off-hand hit, or does the off-hand hit crit at the normal rate? Is the second potential double attack from the off-hand swing? Obviously, I never closely examined these subtleties. Anyway, these details aren't terribly important.

Damage per second

Weapons	AA prop. total dmg	DPS
Senjuinrikio/Perdu	.643	51.916
Tsukumo/Perdu	.647	51.207
Tsukumo/Perdu (5% crit)	.646	52.114

The auto-attack proportion of total damage is just under 2/3 for WS spamming, which seems rather low. Maybe the assumption of a critical hit bonus at 100 TP is wrong. Tsukumo/Perdu with 5% crit rate barely edges Senju/Perdu, which is similar to Fudo barely edging Senju given high pDIF.

Final thoughts

Since Tsukumo is really only acceptable in the main hand if at all, I would consider Tsukumo with DMG +5 (any other augments being gravy) for both TP-holding (Campaign) and weapon-skill spamming. Frankly, if ninja users actually cared about optimality, why weren't they using Fudo for high pDIF?

Second to one?

Fay weapon augmentation seems so popular these days that players will even organize pick-up parties to spam the Grauberg (S) fight, which apparently is one of the easier ones. As embarrassing as it is to admit, I myself did a couple of pick-up runs to try to get a good Tsukumo for ninja, which I hardly use because I don't solo much on it anymore (I dusted it off to solo one of the latest Wings of the Goddess missions, though), when I could probably get a lot more mileage from a properly augmented Erlking's Kheten for warrior. But is it worth it when warriors already have access to Perdu Voulge as an all-purpose weapon? I attempt to provide some insight on this by playing with numbers.

Looking at possible Erlking's Kheten augments, we see that base damage can range from 3-6, STR from 3-5, attack from 5-7, and even double attack is possible (1-2). Some combination of base damage, STR, attack, and double attack (say, three out of four of these attributes) seems pretty competitive with Perdu Voulge. But would a strong Erlking's Kheten actually surpass Perdu Voulge, which has 5 accuracy (below 100 TP) and therefore might be better to use when hit rate isn't already at 95%?

Before doing the number-crunching, first recognize that is easy to calculate the percent difference between the two on a per-hit basis alone. It should be easy to see that Perdu is still better. A corny calculation could be (.925*108)/(.95*106) - 1 = -0.0079 in favor of Perdu. But let's see how we can account for the decrease in rate of TP gain relative to Perdu Voulge.

To put it another way, does the higher "potency" of a properly augmented Erlking's Kheten overcome the accuracy advantage of Perdu Voulge?

Using this example of a competitive Erlking's Kheten, which has total base damage 97 (DMG +6), STR +5 (effective base damage at least 98 given high STR relative to mob VIT), and attack +5 (either +8 or +9 effective attack rating), we can compare this particular Kheten to Perdu Voulge at various hit rates to get a sense of how fast these great axes get to 100 TP on average and how different average weapon skill damage could be.

This specific comparison follows the same template as a previous comparison among Fortitude Axe, Perdu Voulge, and Engetsuto, which was meant to serve as a proof of concept of how to simplify the calculations by first considering the average frequency of attacks and then considering the average "potency" of individual attacks to arrive at some answers--the proportion of total damage in weapon skills in particular--that can theoretically be compared against reality through parser output.

First, start off with calculating average frequency of attacks. Assume 19% DA rate and no delay reduction. Also assume sufficient TP from the previous WS to get to 100 TP in five hits.

Calculating average time to 100 TP for a "six-hit setup" - Perdu Voulge

Hit rate	Average no. of rounds	Average no. of hits		Average time (s)
70%	6.136	5.111		51.547
80%	5.386	5.127		45.244
90%	4.802	5.143		40.342
95%	4.557	5.151		38.278

I chose 70% overall hit rate as the lowest acceptable hit rate for meleeing anything. Notice that the average number of rounds and average time to 100 TP appears to decrease with increasing hit rate at a decreasing rate. As hit rate approaches 100%, the average number of rounds approaches 4 about 4.336. (Remember that double attack is present.) Also notice that the average number of hits increases with hit rate at a constant rate. Observing these trends is just to help verify that I didn't screw up the calculations. (Of course, I'm doing this all with spreadsheets.)

Calculating average time to 100 TP for a "six-hit setup" - Erlking's Kheten (DMG +6, STR +5, attack +5)

Hit rate	Average no. of rounds	Average no. of hits		Average time (s)
67.5%	6.358	5.107		53.414
77.5%	5.555	5.123		46.667
87.5%	4.936	5.139		41.463
92.5%	4.676	5.147		39.283

In this exercise, I am assuming that Perdu Voulge has received the full benefit of accuracy +5 to attain 70%, 80%, 90% and 95% hit rate, so that the hit rate difference for Erlking's Kheten is relative to Perdu Voulge. I am also assuming that changes in hit rate is not discretized by units of 1% hit rate as calculated by the game.

Now, it's time to compare the "potency" of Erlking's Kheten to Perdu Voulge, keeping in mind the whole point here is to see whether the augmented Kheten overcomes its accuracy deficit relative to Perdu Voulge.

Calculating average damage to 100 TP - Perdu Voulge

Hit rate	Avg. no. hits to 100 TP	Average AA damage	Avg. no. hits per WS	Average WS damage	Total damage
70%	5.111	812.771	2.616	592.524	1405.295
80%	5.127	815.310	2.854	646.431	1461.741
90%	5.143	817.850	3.092	700.338	1518.188
95%	5.151	819.121	3.211	727.291	1546.413

Let's suppose fSTR is 10 and average pDIF is 1.500. By considering some arbitrary average, I don't have to care about critical hit rate or the distribution of pDIF or anything like that. Let's also suppose a WSC value of 45 for King's Justice. (Of course, if you are attacking some mob for which you have poor hit rate, it is doubtful your average pDIF against that mob will be as high as 1.500.) I am also assuming you maintain exactly the same hit rate and average pDIF for WS'ing as you do for TP'ing and 95% hit rate for the first hit of KJ, along with no fTP bonus from a gorget or TP in excess of 100.

For the average number of hits per WS, notice that the average increases with hit rate at a constant rate. Also, the percent difference in number of WS hits between any two levels of hit rate is going to be the less than the percent difference in hit rate because the first WS hit is assumed to have 95% hit rate.

Calculating average damage to 100 TP - Erlking's Kheten

Hit rate	Avg. no. hits to 100 TP	Average AA damage	Avg. no. hits per WS	Average WS damage	Total damage
67.5%	5.107	825.804	2.5565	593.197	1419.002
77.5%	5.123	828.386	2.7945	648.421	1476.808
87.5%	5.139	830.969	3.0325	703.646	1534.615
92.5%	5.147	832.261	3.1515	731.258	1563.519

For this great axe, suppose fSTR is 11 and average pDIF is 1.497 relative to Perdu Voulge (-1 attack; for -2 attack, use 1.493). Unfortunately, this average must depend on how you think it changes with attack, which in turn depends on your target's defense rating as well as your critical hit rate, which also depends on your target's AGI. Still, I think it's inappropriate, since I have come this far, to avoid the nuisance of calculating the change in pDIF. Also assume WSC of 47 (+2 higher than with Perdu Voulge).

Damage per second - Perdu Voulge

Hit rate	AA prop. total dmg	DPS
70%	.578	27.26
80%	.558	32.31
90%	.539	37.63
95%	.530	40.40

Counter to the silly notion that there is "diminishing return" when it comes to accuracy, the computed damage per second here (average amount of damage output in a "cycle" of 5 hits to 100 TP plus damage from the executed weapon skill) appears to increase with increasing hit rate at an increasing rate. (Funny phrase.) This should make sense when you consider that accuracy not only increases the average damage of King's Justice, it also increases the frequency of WS (kind of like a delay reduction). The two-fold effect of accuracy could be considered "synergistic."

Damage per second - Erlking's Kheten

Hit rate	AA prop. total dmg	DPS
70%	.582	26.56
80%	.561	31.64
90%	.541	37.01
95%	.532	39.80

On paper, alas the "potency" advantages of the augmented Erlking's Kheten (DMG +6, STR +5, attack +5) do not overcome the accuracy bonus (+5) on Perdu Voulge when you receive the full bonus of Perdu Voulge. There is no "critical value" of hit rate at which the two weapons are equivalent. If Perdu Voulge is at 95% hit rate and receives the full effect of accuracy 5, on paper it is (40.40/39.80 - 1)*100 = 1.507% more efficient. Based on the previous comments about the effect of accuracy both on average WS frequency and average WS damage, this value should be higher than the rudimentary calculation [(.95*106)/(.925*108) - 1]*100 = .801% for auto-attack damage alone.

So, even though the Kheten is more potent, it must be slower to WS when hit rate is not capped and that is the decisive factor to the extent that accuracy matters for you.

Maybe if I got DA +2% on Erlking's Kheten (along with those other augments, though? Yeah, right) I could redo the calculations.

Conclusion

Erlking's Kheten: sorry, try again! If accuracy matters with "most other things being equal," Perdu should always be better. If you're always at 95% hit rate (not unlikely given the practicality of marinara pizza)... then why did you read this post?

Comment potpourri

More comments on the relationship between INT and effective magic accuracy

Last week I got into this "debate" about magic accuracy (BG) regarding the results of casting Stone "a bunch of times" (massive understatement) on Qiqirn Poulterers. After inspecting lodeguy's elemental magic data back in December 2008, I speculated about a model for elemental magic to explain lodeguy's results, not expecting to find any other data to provide independent confirmation for this "model." But thanks to pchan, we now have even more data for which this model agrees (assuming I'm not being irredeemably biased in my perspective) along with some new insights that I describe rather turgidly in one of my posts there.

For example, it is known that the effects of additional magic accuracy, elemental staves, and elemental magic skill appear to be cut in half when "effective" magic accuracy or "hit rate" (the output that depends on the aforementioned inputs) is sitting below 50%. This latest data shows that the effect of INT appears also to be halved below 50% (for ΔINT ≤ 10).

Perhaps more relevant is the observation that, given this data, the effect of INT could be attenuated even further as ΔINT goes further and further beyond 10. That is, it could be (statistically) significantly less than +0.5% "hit rate" for every one-point increase in INT above ΔINT > 10. However, my naive analysis is based on statistical control and not experimental control of levels of INT, the latter of which seems preferable to minimize the influence of potentially confounding factors (as unlikely as they may seem).

Curry buns

Unless RMT are dumping inventory, I don't see why anyone would still craft Coeurl Subs instead of Yellow Curry Buns. From a crafter's standpoint, crafting Yellow Curry Buns will give a slightly better yield on the average because it's only a level 54 recipe ("tier 3" achieved at 105 cooking skill) and the most typical HQ result is 8 buns instead of 6.

But the real nail in the coffin, assuming that it's true, is that the buns retain the hidden bonus of the corresponding curries. Apparently, (hope I'm interpreting this Google translation correctly), the attack cap on Yellow Curry rises to 85 when eaten in the presence of four or more people in the same party as the consumer, among other attribute differences. Amazing that it's 2009 and players still don't know this. (Well, I never used yellow curry so I didn't know.) For Red Curry, the condition is apparently the same, but the attack bonus rises from 23% to 25% (still capped at 150). If the buns retain these hidden bonuses, why wouldn't there be higher demand for Yellow Curry Buns?

Note: the bonus from eating yellow curry (buns) while in a party does not wear off upon leaving the party. Using one while not in a party yields only 75 attack, and it probably does not increase upon joining a party of sufficient size.

The quaintness of dual wielding

It's been almost two years since the pivotal two-handed weapons adjustment, which, among other things, was the beginning of the end for dual-wielding as a mainstream option for warrior.

Before the update, the rates of TP gain and auto-attack damage were generally superior for dual-wielding configurations "most things being equal," as the multi-hit properties of Joyeuse and Ridill amply compensated for lower native sword skill and 8 axe/8 sword seemed to be a popular merit option anyway, leaving no room for great axe merits.

There does not seem to be any simple quantitative comparison of dual-wielding configurations with great axe in terms of rate of TP gain and damage per second, so I did some quick calculations. The following is a "most things being equal" comparison of four canonical dual-wield weapon pairs with Perdu Voulge and Fortitude Axe from the standpoint of auto-attack efficiency, as represented by base damage per second (a modification of the usual "DPS" ratings assigned to weapons per FFXIclopedia accounting for double attack and 95% hit rate) and TP per minute.

Comparison of theoretical auto-attack efficiency of various weapon configurations at 95% hit rate and given 15% double attack rate (no Store TP)

Configuration	Hits/round	Hits/sec	Base DMG/sec	TP/round	TP/min
Maneater/Ridill	2.91175	.4271	18.52	16.01	140.96
Maneater/Joyeuse	2.548375	.3822	15.67	13.76	123.85
Ridill/Joyeuse	3.275125	.5339	20.17	16.37	160.19
Maneater/Iron Ram Pick	2.185	.3013	14.46	12.67	104.88
Perdu Voulge (17% DA)	1.1115	.1323	12.70	15.22	108.76
Fortitude Axe (17% DA)	1.6535225	.1968	12.59	22.65	161.80

All of these values are averages. Base damage per second could be considered a measure of "damage over time" potential. If (average) pDIF and hit rate were held constant across all these options, then Ridill/Joyeuse is the clear choice, which is basically saying if you're farming too-weak mobs. As for rate of TP gain per unit time, which has nothing to do with weapon damage ratings, it was always pretty obvious that axe/sword and Ridill/Joyeuse were more efficient in this respect.

Of course, the aforementioned update eviscerated the normally silly notion of most things being equal as the adjustment brought ample attack and accuracy bonuses (accuracy affecting rate of TP gain when accuracy actually matters, duh!) and Raging Rush was modified to be able to critical hit. Given how parsimonious the "development team" generally was (and is), it was almost unfathomable that the STR-to-attack and DEX-to-accuracy "ratios" were "increased" to 1:1 (from 2:1) before they were scaled down to 4:3.

How about another measure of efficiency, like TP "fed" to a mob per unit time or ratio of damage to TP given to a mob? To the extent that it matters, dual-wielding options were generally worse than great axes (Fortitude Axe aside), which could have been considered an acceptable trade-off back then. But, since the two-handed weapon adjustment really undermined the relative efficiency advantages of dual wielding, the trade-off is not that appealing now for mid-level events like Einherjar or Limbus where you not necessarily be at maximum hit rate. The first floor of Central Temenos is a good example of where dual-wielding would be a complete joke. Again, you didn't have to crunch numbers to have realized that.

Comparison of average TP "fed" to mob per attack round (no attack speed reduction, no Subtle Blow)

Configuration	TP fed/ round	TP fed/ min	Base DMG/ TP fed
Maneater/Ridill	24.75	217.84	5.10
Maneater/Joyeuse	21.40	192.65	4.88
Ridill/Joyeuse	26.20	256.31	4.72
Maneater/Iron Ram Pick	19.22	159.12	5.45
Perdu Voulge (17% DA)	18.56	132.58	5.74
Fortitude Axe (17% DA)	27.61	197.24	3.83

Black mage solo EXP in Xarcabard [S]

This may have gone under the radar for many considering the hype surrounding fay weapons, Igqira Weskits with INT+6 that you'll never get, and the rat race to finish A Moogle Kupo d'Etat (what's the acronym? AMK? MKE?), but this latest version update actually provided an alternative to Ebony Puddings as a solo EXP fodder for level 75 black mages and scholars in the form of the five or so LV 75+ Gigas's Tigers with only 1,400 or so HP within striking distance of the Xarcabard [S] teleport point at (H-9).

Considering the interval between the start of the ToAU expansion and now, this is totally (un)characteristic of SE depending on your point of view, whether you're a fucking retard for fulminating about the "exploiting" the generally low HP of BST pets or a realist.

Perhaps "alternative" is a gross understatement since chain #19 has been achieved on these tiger pets with BLM/SCH (and the attendant MP-efficiency advantages) and the ability to one-shot these tigers with the appropriate weather (ice) or day (Iceday or Lightningday). Not only that, there was the suggestion that these can be chained indefinitely! This seems like a pretty good case for /SCH at this camp if you can one-shot (you have Bind and Sleep anyway).

As for the bread-and-butter /RDM sub, I don't know about you, but even attaining chain #5 on Ebony Puddings (even though I can't three-shot, as in three tier IV), my average EXP/hour doesn't even approach 10K per hour (more like 8K).

In contrast, even without day or weather bonuses and basically lolly-gagging, after trying my hand at these Gigas's Tigers I still managed to average about 8K/hr over two chains with BLM/RDM as summarized in this parser output:

Experience Rates
Total Experience : 2538
Number of Fights : 17
Date             : 7/26/2009
Start Time       : 11:46:32 AM
End Time         : 12:05:28 PM
Party Duration   : 0:18:56
Total Fight Time : 0:04:33
Avg Time/Fight   : 66.85 seconds
Avg Fight Length : 16.07 seconds
XP/Fight         : 149.29
XP/Minute        : 134.00
XP/Hour          : 8039.97

Moreover, after achieving a chain #10 (cheating with Manafont), I averaged over 9.6K/hr on this chain while still not being able to one-shot tigers:

Experience Rates
Total Experience : 1773
Number of Fights : 11
Date             : 7/26/2009
Start Time       : 12:12:18 PM
End Time         : 12:23:18 PM
Party Duration   : 0:11:00
Total Fight Time : 0:03:31
Avg Time/Fight   : 60.03 seconds
Avg Fight Length : 19.20 seconds
XP/Fight         : 161.18
XP/Minute        : 161.10
XP/Hour          : 9665.87

I would argue that, at least for me, at worst the EXP/hr in Xarcabard [S] is equivalent to that in Mount Zhayolm, with the potential to clear 10,000 EXP/hr easily with /SCH and enough oomph to one-shot these tigers.

Personally, I would rather not rely on the crutch of having the benefit of the right weather or day effects to be able to one-shot tigers, but my gear or merits do not give me the flexibility to one-shot anytime. After determining that these tigers have 55 INT, I determined that I would need to acquire Selenian Cap with INT+4 and MAB+2, a Novio Earring, and 4 INT merits to clear 1,400 damage with Thunder IV.

With this in mind, those players with Novio and full Morrigan's would have a field day at this camp.

Properties of virtue weapons like Fortitude Axe

Edit (Aug. 5): mixed up scenario labeling but the conclusion is the same.

A few days ago I forwarded these cheesy analyses of the relative "efficiency" of so-called virtue weapons (Fortitude Axe and Love Halberd), which I hope are not taken all that seriously even though I made some attempt to reconcile it with my own experiences or others'. My primary goal with these posts I made over the past week was to demonstrate yet another application of probability theory to simplify such cheesy "analysis" while being somewhat rigorous about it. At least it's better than presenting some ugly arithmetic and retarded hand-waving, as I explicitly stated the major assumptions involved. (But you would have to trust I am doing calculations correctly.)

I bring up the comparisons involving the virtue weapons to point out that I made the assumption that double attack can proc both on the main hit and virtue weapon proc, yielding the possibility of a round of 4 attacks. Actually, I have no basis for assuming such a thing other than flimsy hearsay. With this in mind, I set out to collect data to support the notion that a 4-attack round is possible with Fortitude Axe, and I obtained the following count data after 236 rounds. (I ran out of virtue stones.)

No. of hits	0	1	2	3	4
Counts	5	96	100	35	0
Est. proportion	.0212	.4068	.4237	.1483	.0000

It so happened that I didn't observe a 4-hit round with Fortitude Axe, but is this because it is rare or because it's impossible?

If we assume DA can proc independently of one another for both the initial attack and the virtue weapon proc, the probability of a 4-hit round is .01796 (given 95% hit rate) and the probability that zero 4-hit rounds occur in 236 attempts is .01388. Put another way, the probability that at least one 4-hit round occurs in 236 attempts is .98612.

Thus, if this "mechanism" of interaction between DA and virtue weapons is true, I was unlucky not to see a 4-hit round. But, if it is wrong, not seeing a 4-hit round is exactly what I should expect.

How else would DA and virtue weapons interact such that a 4-attack round is not a possibility?

One scenario, which I call "A," is that there is exactly one DA proc possible and that it's independent of the virtue weapon proc. In this case, DA has only one chance to proc.

Another hypothesis is that whether DA procs on the virtue weapon depends on whether the DA has processed on the initial attack. I call this scenario "B." If DA has processed on the first attack, it will not process after the potential virtue weapon proc; otherwise, DA may process after the virtue weapon swing. In this scenario, there are up to two chances for DA to proc.

Both of these scenarios are not far-fetched, so the question of which one agrees more with the data depends on knowing the hypothetical distribution of number of attacks per round under each scenario given the rate of DA trait and overall hit rate. These distributions are determined for 95% hit rate, 21% DA rate, and 50% virtue weapon proc rate, as shown below.

No. of hits	0	1	2	3	4	Expected value
(A)	.0210	.4235	.4655	.0900	0	1.6245
(B)	.0208	.4162	.4018	.1611	0	1.7033025
(C)	.0208	.4161	.3991	.1460	.0180	1.72425

To summarize, scenario "A" allows DA exactly one opportunity to proc. This DA proc is independent of whether the virtue weapon procs.

Scenario "B" allows DA up to two opportunities to proc. If it procs on the first attack, it won't on the (potential) virtue weapon proc. If it doesn't proc on the first attack, it can on the virtue weapon proc

Scenario "C" allows DA exactly two opportunities to proc (DA and virtue weapons "stack") as explained toward the beginning. The language to describe these may be confusing, but the associated probability distributions are a pretty convenient distillation. Checking the actual data against these hypothetical distributions can give us insight as to which scenario is most reasonable of the three. The "expected value" column shows the average number of attacks per round under each scenario. My initial impression is that (B) seems to be the most realistic.

I already discussed scenario "C." The probability of observing zero 4-hit rounds in 236 attempts is .01388, so scenario "C" is unlikely.

Start with scenario "A." Instead of focusing, say, on comparing the observed proportion of 3-hit rounds to the hypothetical proportions under (A) and (B), it makes more sense to consider all of the data at hand. I can use Pearson's chi-square statistic to examine the "goodness of fit" of the associated probability distribution to the observed data. Under scenario "A," the approximate p-value is .02017, indicating that scenario "A" is not particularly likely given the data.

How about scenario "B" then? The associated p-value is .898 (approximately). Under the scenario that DA is permitted to proc up to two times, the probability of observing count data as "extreme" or more extreme than the data actually observed is about .898, an indication that this mechanism is very plausible.

It bears reminding that in all of these hypothetical cases, I assumed that the virtue weapon proc rate was 50%. This is not necessarily a good assumption. For example the Joyeuse proc rate is more like 45%, contradicting the long-held assumption that it is 50%.

After acknowledging that scenario "B" is the best way to explain my data, it may be useful to see how the probability distributions "shift" by changing the virtue weapon proc rate in increments of 5% in either "direction" of 50%.

Hypothetical probability distributions for the number of hits in a single round, assuming that DA has up to two opportunities to proc on a virtue weapon

Given a virtue weapon proc rate of...	0 hits	1 hits	2 hits	3 hits	p-value
40%	.0246	.4870	.3593	.1289	.08418
45%	.0227	.4516	.3806	.1450	.52411
50%	.0208	.4162	.4018	.1611	.898
55%	.0189	.3808	.4231	.1773	.66298
60%	.0170	.3453	.4443	.1934	.13281

It is easy to see that the probabilities under each column decrease or increase at a constant rate. It is also easy to see what while a virtue weapon proc rate of 50% is highly probable given the data at hand, there is insufficient statistical power to rule out a proc rate as low as 40% or as high as 60%.

Conclusion

Based on an observed sample of 236 attack rounds with Fortitude Axe, it appears that the double attack trait can proc either on the first attack or on the virtue weapon attack, but not both. If it procs on the first attack, it won't on the potential virtue weapon attack. If it doesn't proc on the first attack, it may proc on the potential virtue weapon attack.

The obvious implication is that claims of a four-attack (or four-hit) round with Fortitude Axe and other virtue weapons are highly suspect. If you think you observe a four-attack round with Fortitude Axe or another virtue weapon that cannot be explained by high attack speed, that observation must be considered in the context of the relative frequency of 0-, 1-, 2-, and 3-hit rounds that you probably didn't even bother to record. Idiot.

Also, the proc rate of a virtue weapon might be 50% but there was an insufficient sample size to "prove" it.