Unfortunately, a wider crit range is mathematically better than a higher multiplier at an even rate.
A natural 20 is a 5% chance, or 0.05, ×3 damage makes that 0.15
A threat range of 19-20 is 10% or 0.1, ×2=0.2, and 18-20 is 15%=0.15×2=0.3
If you double the threat range, it's 0
3, 0.4 and 0.6, respectively.
If you increase the critical multiplier, it's 0.2, 0.3 and 0.45
That's why, once you hit a certain flat bonus to damage, weapons with large critical threat ranges are the best choices, even if they do less base damage.
...assuming your opponent is vulnerable to critical hits, that is. But even if they're not, the axe-type weapons only come out slightly ahead.
Add in their same-or-worse damage and their more sunder-able stats, and the main advantage of an axe is usually a handful of gp.
(Sorry, I know it's not a direct answer, but I thought the information may be worth sharing anyway)
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Unfortunately, a wider crit range is mathematically better than a higher multiplier at an even rate.
A natural 20 is a 5% chance, or 0.05, ×3 damage makes that 0.15A threat range of 19-20 is 10% or 0.1, ×2=0.2, and 18-20 is 15%=0.15×2=0.3
If you double the threat range, it's 0
3, 0.4 and 0.6, respectively.If you increase the critical multiplier, it's 0.2, 0.3 and 0.45
That's why, once you hit a certain flat bonus to damage, weapons with large critical threat ranges are the best choices, even if they do less base damage.
...assuming your opponent is vulnerable to critical hits, that is. But even if they're not, the axe-type weapons only come out slightly ahead.
Add in their same-or-worse damage and their more sunder-able stats, and the main advantage of an axe is usually a handful of gp.
(Sorry, I know it's not a direct answer, but I thought the information may be worth sharing anyway)
I believe your analysis is a bit flawed.
If you assume a 19 on one attack and a 20 on the next and you automatically confirm any crits, you'll find both weapons do the same amount of damage:
- The axe does 4x damage total (one 1x hit, and one 3x crit).
- The sword does 4x damage total (two 2x crits).
- The axe does 8x damage total (two 1x hits and two 3x crits)
- The sword does 8x damage total (four 2x crits)
The major downside of 20/3x weapons is when you only need a 2x crit to down a foe: In that specific case you're effectively twice as likely to down your foe with the 19-20/x2 crit weapon.
I believe your analysis is a bit flawed.
I was just going off of the DPR calculator, which is pretty widely accepted as legit:
h(d+s)+tchd.
h = Chance to hit, expressed as a percentage
d = Damage per hit. Average damage is assumed.
s = Precision damage per hit (or other damage that isn't multiplied on a crit). Average damage is again assumed.
t = Chance to roll a critical threat, expressed as a percentage.
c = Critical hit bonus damage. x2 = 1, x3 = 2, x4 = 3
So if we assume, say, +30 to base damage with a 50% chance to hit...
Great sword: 0.5×27+0.1×2×0.5×22 = 16.2
Earthbreaker: 0.5×27+0.05×3×0.5×27 = 13.73
Falchion: 0.5×25+0.15×2×0.5×20 = 16.25
-- in earlier levels, the greatsword is going to be the lead with a larger base damage and a moderate crit range. But once your static bonus is high enough, the wider threat range counts for more.
I found only two cases where weapons with high crit multiplier are superior:
1) Coup de Grace (which can be delivered more often with a supporting caster and / or the Throat Slicer feat)
2) Enforced crits (flash of insight from Cyclopean Seer oracle etc.)
In at least one case the devs tried to throw players a bone with "the higher the multiplier, the more often you gain a +2 bonus", but I don't have the name right now. I think higher crit range was the superior option there anyway.
Still, the axe has a problem: There are weapons with multiplier x4. Sure, they have a slightly lower base damage, but this loses importance over the course of levels, unless you focus heavily on Vital Strike.
I believe your analysis is a bit flawed.I was just going off of the DPR calculator, which is pretty widely accepted as legit:
h(d+s)+tchd.
h = Chance to hit, expressed as a percentage
d = Damage per hit. Average damage is assumed.
s = Precision damage per hit (or other damage that isn't multiplied on a crit). Average damage is again assumed.
t = Chance to roll a critical threat, expressed as a percentage.
c = Critical hit bonus damage. x2 = 1, x3 = 2, x4 = 3So if we assume, say, +30 to base damage with a 50% chance to hit...
Great sword: 0.5×27+0.1×2×0.5×22 = 16.2
Earthbreaker: 0.5×27+0.05×3×0.5×27 = 13.73
Your c has to be 1 or 2, respectively. Also d is 27 in both cases, resulting in the same sum for both weapons.
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Oh, yes.
I started the equation with a Platonic character of lower level (hence the 22), then bumped it up a bit, but I forgot the second instance.
Greatsword 14.85, earthbreaker 14.85, falchion 15.375, I believe.
Axes aren't any better than comparable weapons in D&D and are worse than the best, so the trick is to cheat. Even back before d&d 3.0 was published it was noticed that many dwarves didn't bother with their traditional weapons; 3.0 made a dwarven waraxe which only dwarves could use easily. PF added a few more weapons in that vein. Those are better than comparable weapons, so long as you don't have to pay feats for them.
With the right feats a dwarf can TWF with dwarven waraxes, or at least with a dwarven waraxe and a dwarven maulaxe. A magus with a dwarven waraxe isn't a terrible idea; better non-crit damage can carry you. A swashbuckler who relies on kills to refill panache might work. Ventnor mentioned sliding axe throw, and you could probably build a warpriest with the air blessing around that.
Axes are not crit weapons, nor did the OP ask about crits...
Ventnor is on the right track with Sliding Axe Throw and Smashing Style.
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Axes are not crit weapons, nor did the OP ask about crits...
Ventnor is on the right track with Sliding Axe Throw and Smashing Style.
To be fair, the OP did bring crits into the conversation, though it wasn't the primary focus...
Back in the TSR days (D&D1.0 - D&D2.5), axes were generally subpar weapons due to the lack of a larger damage die versus Large+ creatures that (most) swords had and their horrible speed factor, so the only reasons to use one were flavor and 'this magic axe we found is a lot more powerful than the weapon you were using: Are you actually trained in Axes?'
In the WotC / Paizo era (D&D3.0 - PF2e), axes are 'fine' weapons: Not really better than any other 'fine' weapon, but generally up to whatever task you have. The largest exception to this is (somewhat ironically) PF2e's critical specialization for Axes, which is fairly atrocious, but that's another game entirely...
Alright, crits aside there are two more feats, at least for greataxes:
Cleaving Sweep: Basically a whirlwind trip without Dodge etc. as requirements, needs BAB 11 though
Orc Fury Style: Demoralize on hit, but take -2 on AB; Cornugon Smash is usually better but locks you into Power Attack
The problem with theorycraft is that it doesn't hold up at the table. I've found that x3 and x4 crit weapons can actually be a very strong player on the battlefield. Sure, you don't crit as often (and thus aren't good for crit-fishers) but having a 10% chance of 1-shot an enemy is nothing to sneeze at. Especially against hefty DR and other damage reducers.
Conversely, having a x3 or x4 weapon means you have a small chance of massive overkill, whereas an otherwise equivalent x2 weapon has a bigger chance of a kill. PCs benefit from reliable effects more than monsters do.
Where the x3 greataxe gets scary is in the hands of the RAW basic CR 1/3 Orc. Thankfully in PF it's been replaced by a falchion which means around 18 damage on the inevitable crit; in 3e it was a greataxe averaging 28.5 on a crit, a 1-shot death on any 1st level character and most 2nd level.
The problem with theorycraft is that it doesn't hold up at the table. I've found that x3 and x4 crit weapons can actually be a very strong player on the battlefield. Sure, you don't crit as often (and thus aren't good for crit-fishers) but having a 10% chance of 1-shot an enemy is nothing to sneeze at. Especially against hefty DR and other damage reducers.
Or those times where the encounter is what i like to refer to as "meaty chaff". Beatsticks with high hp and hd maybe 3 or 4 lower than your characters around mid level
One more thing for axes - though it would require a lot of feats to be useful - is that the Axes weapon group for fighters is (I think) the only weapon group with ranged, close and reach weapons in the one group.
You could potentially do a themed build with a Bardiche for AoOs and Throwing Axes for range and even a 2-level dip for Brawlers Flurry or something and still end up with +6 or so to all of them from Weapon Training. I don't know how viable it is but it's something.
Regarding crits, mathematically a ×3 crit weapon is equal to a 19-20/×2 crit weapon, and a ×4 crit weapon is equal to a 18-20/×2 crit weapon (and the few 19-20/×3 crit weapons are strictly superior). In my experience the crit-range is worth a little more than the crit-damage because there's less damage lost to overkill, but any vaguely-well-built martial should do enough damage that you won't feel underwhelming by taking a slightly less powerful weapon. Versatility us usually more important than a slight numerical advantage.
One more thing for axes - though it would require a lot of feats to be useful - is that the Axes weapon group for fighters is (I think) the only weapon group with ranged, close and reach weapons in the one group.
The monk, spears and thrown weapon groups all meet this qualifier too.
You could potentially do a themed build with a Bardiche for AoOs and Throwing Axes for range and even a 2-level dip for Brawlers Flurry or something and still end up with +6 or so to all of them from Weapon Training. I don't know how viable it is but it's something.
It's still a problem at mid-levels and later with the whole 'how do I keep all these weapons enchanted properly' problem. Axes make terrible missile weapons with the 10' range increment (too low for even far shot to fix) too; the sliding axe throw warpriest I mentioned in passing fixes it with air blessing, but that's a standard action until level 10+. I'm not sure it's practical.
IME if your build isn't leaning heavily on landing crits for some reason other than raw damage, you're not likely to notice much performance difference just for picking an axe over a sword.
So I was wondering if there was any feats / features that specifically Beifit a character for using an Axe.
There're two traits that specifically benefit axes, and the four aforementioned feats (Cleaving Sweep, Sliding Axe Throw, Orc Fury Style, and Smashing Style), and the dwarfen racial proficiency with battleaxes might make them a better choice than other weapons (although longspear is a simple weapon that's highly likely to be better in practice).
That's basically it. Machanically, using an axe is practically always suboptimal. Usually not cripplingly so, but still.
Everyone forgets about the Tongi...
19-20/×3 one-handed piercing axe...
Axe-wielding Swashbuckler...?
Everyone forgets about the Tongi...
19-20/×3 one-handed piercing axe...Axe-wielding Swashbuckler...?
Well, it's a great weapon after some levels. Since it adds ~10% on DPR but costs you a point of average damage, you will have to get above ~10 damage on hit to make it superior to a battleaxe. And precision damage won't cut it, since it doesn't get multiplied.
Finally the weapon has to be legal for the campaign to be an option. I expect "19-20/x3" to make some GMs nervous, even though it's suboptimal at crit fishing and doesn't do that much additional damage. You might have to fall back to a pata for a swashbuckler.
The Tongi is Paizo content, I don't see why it wouldn't ever be legal. There are other 19-20/×3 weapons out there, it's not like the Tongi is unique in that... the PelletBow is 19-20/×3 at range.
The player would likely be out of luck with any other 19-20/x3 weapon, too. And depending on individual GM, "Paizo legal" is more or less of an argument. I hold the company in high regards usually, but that doesn't stop me from banning Leadership, Dazing Spell and Sacred Geometry...
So, to get back to topic, IMO tongi certainly is something to consider, but not always the best answer.
I expect "19-20/x3" to make some GMs nervous
If an exotic 1d6 weapon makes the GM nervous, I'd suggest switching to decaf. Or to learn some math. Probably both, come to think of it.
Axe-wielding Swashbuckler...?
Swashbuckler doesn't care about crit multiplier (not the least because Precise Strike doesn't get multiplied), but rather about confirming crits for panache recovery. Which puts your ordinary rapier way ahead of the tongi.
For anyone not caring about piercing weapons (so everyone but Swashbuckler/Virtuous Bravo/Daring Champion), falcata is the same but with 1d8. Swashbuckler and Virtuous Bravo really need an 18-20 weapon, and Daring Champion has no reason to pick up Improved Critical (without which other weapons are better), so...
I was rather surprised by the whole 19-20/×3 weapons making GM's nervous... like, why?
There's no use sweating martials when there's 7th, 8th, and 9th level spells to deal with. Especially martials that aren't archers.
Now that's where the 19-20/×3 PelletBow comes in... 5 levels of Bolt Ace Gunslinger makes it a 19-20/×4... with Improved Critical it's 17-20/×4... AT RANGE! Now it's starting to get interesting, but I wouldn't ever even consider banning it.
As for a Swashbuckler with a Tongi... it's just an option. Not optimal, nothing involving axes (or Swashbucklers) really ever is. But we were talking about axes being used for flavor, not efficiency, so I figured I would throw out an option that hadn't yet been discussed. Not that I like the flavor Swashbuckler brings to the table, but it is an option
I was rather surprised by the whole 19-20/×3 weapons making GM's nervous... like, why?
I guess every fight eventually comes down to hitpoints, so whatever other options are available a high damage character can end encounters faster than you think they should.
If your Demon with 8 natural attacks, AC:40, 400hp and DR:30/- gets killed in 2 rounds by a Paladin with a bow who doesn't have any bow-related feats you're gonna feel pretty bad.
It's also possibly the easiest metric to quantify - teleporting is amazing, but calculating a PC's teleport abilities into the CR of your encounters is more abstract than looking at the damage numbers.
So if we go back to the demon example, if the wizard manages to teleport the party round the battlefield, kiting the demon so it only gets 1 attack per round and the party kills it after taking minimal damage the party might actually be better off (less resouces spent, less chance of character death) but it doesn't feel as bad for the GM or as disappointing for the other characters who didn't participate.
I'm not saying that you should penalise martials for their damage output, but it's an easier metric to see when a character is overpowered, and often a more difficult one to balance if there's more than 1 damage dealer in the party.
It's also the easiest to counter/negate... it being martials, in general, overpowered or not.
Throw good weapons and gear at them, give them all the help they can get... because come level 13, it's rocket tag with big boy spells, and martials are all but irrelevant. Martials require overpowered gear just to participate.
Limiting or removing access to such gear is a detriment to the game....
What, I can't have nice things? I should have just been a Wizard.
I was rather surprised by the whole 19-20/×3 weapons making GM's nervous... like, why?
There's no use sweating martials when there's 7th, 8th, and 9th level spells to deal with. Especially martials that aren't archers.
Now that's where the 19-20/×3 PelletBow comes in... 5 levels of Bolt Ace Gunslinger makes it a 19-20/×4... with Improved Critical it's 17-20/×4... AT RANGE! Now it's starting to get interesting, but I wouldn't ever even consider banning it.
As for a Swashbuckler with a Tongi... it's just an option. Not optimal, nothing involving axes (or Swashbucklers) really ever is. But we were talking about axes being used for flavor, not efficiency, so I figured I would throw out an option that hadn't yet been discussed. Not that I like the flavor Swashbuckler brings to the table, but it is an option
I have a perverse desire to go bolt ace 5/Weapon master fighter 15 ranged crit fishing build with fighter critical feats.
Oh hey Julius, that weird wall decoration you were asking about a while back? In PF it's called a tongi. I'd never noticed it before VM mentioned it above. It looks like it'd work for a str-based swashbuckler or kensai magus, maybe for a TWF crit-fisher.