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...