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.
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