With all the mess that happened I forgot to post my (unwanted?) opinion -.-
Trying to get back in topic now, some time ago I calculated 3 different possible combinations for the third atma.
Of course RR and Apoc aren't in discussion.
For the third I calculated the overall damage with:
1) Voracious Violet
2) Gnarled Horn
3) Sanguine Scythe
I didn't factor my automaton at all on these calculations, which was probably a big mistake D:
I also split those calculations in two, first considering Stringing Pummel as the main WS, then with Victory Smite.
Of course these results are somehow bound to my personal equipment at the time and other close combinations. Anyway I found out the following:
- With a close to unbuffed character (no haste, no march, no food, no berserk up etc) VV produces slightly better results than the other two. It also has to be noted that VV produces other advantages that are hard to factor inside formulae. For example the utility of the 2tp/tic regain during times when you are not fighting. It may sound stupid, but you won't be constantly engaged 100% of the times. It's also an added utility if you want to hold back and proc stuff for some reason.
- GH offers a nice + crit rate % which is always useful since we won't be capped. The AGI won't do much (probably capped on AGI eva with just cruor buffs, and no primary/secondary mod on any WS). The +counter is nice but without native counter (like MNK) it doesn't become a particularly interesting edge. It also has to be noted that if you're using Sharpshoot, ranged attacks won't benefit from the +crit, but they would benefit from AGI (r.acc, and also it's also supposed to be the primary modifier for Armor Shatterer). Similarly, the +counter could be useful for Valoredge if you use Galvanizer for some reason. From all of this it sounds that GH is a nice option, but slightly behind the other two, wether you're using Pummel or Smite, wether your character is fully buffed or fully unbuffed.
- SS offers the utility of more HP for both you and your pet (which doesn't benefit from cruor buffs). Doesn't directly affect your damage but personally it's a stat I really like, especially for my pet (altough since when they added Deus Ex Machina, Automaton survivability became much less of an issue than it was before). Damage-wise it seems to affect your overall dps more than VV when you start getting some buffs (Zerk, food, etc), it's behind VV when you're completely unbuffed, but with a small difference.
Of course as a choice for third atma I didn't consider "Atma of Alpha & Omega" which, in theory, is better than any of the above under any possible circumstance. But I don't really like the -HP so I usually skip considering A&O.
tl;dr
Buffed: SS > VV > GH
Unbuffed: VV > SS > GH
Same thing for either Pummel and Smite.
SS probably wins when you're buffed (with an increasing margin the more you're buffed) because, correct me if I'm wrong, it's not a static damage increase but a % one. Hence the more your basic damage is (increased by buffs) the higher return the % gives.
Also as you get close to the attack cap the +25 you get from VV loses its relevance.

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