[
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.