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.
Sunday, August 16, 2009
Friday, August 7, 2009
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...
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:
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.
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
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
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?
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
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
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 approaches4 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)
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
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
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
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."
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.
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
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?
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