Sunday, December 1, 2024

Napkin Math: Mauls vs Greatswords vs Greataxes

 In 5E, if you want to hit the absolute hardest with a melee weapon, the options that have the highest damage potential have always been the Maul, Greatsword, and Greataxe (this used to include the Lance, but that was brought closer in line with the other reach weapons in the 2024 update. Also, we should note that Muskets also have the same damage maximum, but those are ranged, so we'll exclude them here, as well as all modern and futuristic firearms).

There have always been some subtle distinctions, of course. Mauls, unlike the other two, deal bludgeoning damage (which historically has been slightly better than the other kinds of "kinetic" damage, but only slightly) and Greataxes, while they can still cap out at a roll of 12, do have a slightly lower average damage thanks to just being 1d12 rather than 2d6 (2d6 has a minimum roll of 2, while a d12 can get down to 1).

But generally, in D&D14, you could pick any of these and pretty much do well regardless, with very little difference in your overall experience.

That has changed.

Weapon Mastery has created distinctions between weapons that didn't used to have any. The Halberd and Glaive, for example, in the 2014 rules, were mechanically indistinguishable (the same in everything from damage to weight to properties to price). Weapon Masteries came around and created new distinctions between similar weapons. And these three classic "great weapons" now each have a different weapon mastery.

So, I wanted to know: how good are they in comparison to one another?

Greatswords have the simplest mastery, but the one that I think stands a good chance of being the most powerful overall, which is Graze. Graze (found, I believe, just on Greatswords and Glaives) allows you to deal damage equal to the ability modifier  you used to make the attack when you miss. So, while you'd typically be dealing 2d6+3 on a hit as a first level Fighter, say, even if you totally whiff it, you will still deal 3 damage.

Mauls have the Topple mastery. This forces any creature hit by the weapon to make a Constitution saving throw (the DC equal to 8+PB+the modifier you used to make the attack, most likely Strength.) Dropping a foe will of course convey advantage on future attacks (along with other issues). Advantage isn't terribly hard to get in D&D, but it's also a very powerful thing to get.

Greataxes have Cleave, which is the most niche of these features, and allows you to, after you hit with this weapon, make an additional attack against a target within 5 feet of the target. If this hits, you roll the damage die as normal and can add any bonuses from things like Rage or a magic weapon, but you don't add your ability modifier. So, you might hit a target for 1d12+3 on your action, and then another for 1d12 (only getting one extra hit per turn).

My suspicion is that Graze is going to wind up the most effective, though its value of course diminishes as your chance to hit increases. Still, the way 5E is structured, you'll still generally have decent chance to miss, and this will help smooth out your damage and ensure you're always moving the fight along. By the time you get a +5 to your Strength (or Intelligence or Charisma if you're a Battle Smith or Pact of the Blade Warlock, respectively, requiring a feat or multiclass to get the mastery, of course) you'll be guaranteed 10 damage done every turn once you have Extra Attack or the equivalent thereof.

Graze will also be the simplest to plug in for average damage, as the others will require some assumptions.

For Topple, we're going to make a couple assumptions. The first is that we're not getting advantage from any other source. The second is that our target has a 50% chance to succeed on their saving throw. The third is that our foe will stand up on their turn, meaning that we'll only benefit from this on our second attack.

For Cleave, we'll assume that there's an eligible target for the Cleave attack 50% of the time.

As we'll be using two attacks, we're going to assume that our character has a +7 to hit with their attack (reasonable at level 5) and that our target has a 16 AC. Thus, we have a 40% to miss, and then a 55% chance to hit normally and a 5% chance to crit.

Greatsword/Graze:

Our average damage with a mundane Greatsword is going to be 2d6+4, which comes out to 11 on average. We can actually just add 2d6x.05 to our overall damage per attack to account for the bonus crit damage. Our misses, however, will deal 4 slashing damage thanks to Graze. So, what we're looking at per attack is:

Miss: 40% x 4, or 1.6

Hit: 60% x 11, or 6.6

Crit Damage: 5% x 7, or .35

So, this gives us an average damage per attack of 8.55.

With two attacks, then, this becomes 17.1 damage per turn.

Maul/Topple:

Here, the math gets more complicated. We can calculate the average damage for our first attack with relative ease - once again, the hit and crit damage is the same (though it's bludgeoning) but our second attack will have a variable chance to be made at advantage or not. We've made a pretty convenient assumption about how likely it is is for us to knock them prone.

Actually, our average damage per hit is easy to get thanks to the Greatsword calculation - we just remove the 1.6 we'd be getting on a miss. Thus, our average damage on our first attack is 6.95.

Then, we have to calculate our damage in the case we do get advantage on our attack. This has two factors at play: the first is whether we hit on our first attack, the second is whether our foe failed their saving throw.

So, our chance to provoke the saving throw is 60%. Then, within that 60% chance, we're assuming they fail 50% of the time. Thus, there's a 30% chance that we have advantage on our second attack, and a 70% chance we don't.

Thus, for our second attack's average damage, we can add 70% of the average damage of the first one to represent the scenario in which we didn't get advantage, which comes out to 4.865. Then, for the remaining 30% chance in which we do have advantage, we need to calculate what our average damage would be on that second hit.

With advantage, our miss chance drops to 16%. And our hit chance is thus 84%, but our crit chance is now 9.75% (again, we can just add that extra damage on top of our hit to make the math simpler.)

Thus, our advantage average damage per hit is 9.24 plus .6825 for crits, coming out to 9.9225.

This, then, is multiplied by our 30% chance to actually have advantage, giving us 2.97675. We add this to the 70% chance that we don't have advantage, getting 7.84175.

Finally, we add this to the much-easier-to-get average damage of our first attack, giving us 14.79175 average damage per turn.

Greataxe/Cleave:

This math should be simpler, but we will need to recalculated it given that Greataxes do slightly less damage than the other two weapons (note that if you're comparing Glaives, Lances, and Halberds instead, Halberds might fare slightly better thanks to the fact that all three of those Graze, Topple, and Cleave weapons use d10s).

Once again, we're looking at a 40% chance to miss, a 60% chance to hit, and the 5% crit damage bonus.

However, our average damage is 10.5 now, and our crit damage bonus is 6.5.

So, 60% times 10.5 is 6.3.

5% times 6.5 is .325

Thus, our average damage per hit (not counting our cleave attack) is 6.625. With two such attacks, we're going to deal 13.25.

Now, if either of those hit our target, and if there is another target within 5 feet, we get to make our Cleave attack. How likely is that to happen?

Well, we're first making the assumption that there's a secondary target half the time (which might be generous, but hey). Our chance to have landed a hit on one of our two attacks is similar to having advantage on one attack, so we already know that we've got an 84% chance to have hit at least once (thanks to our earlier Topple calculations). We can then multiply that by the 50% chance we expect to have an eligible target, giving us a 42% chance to even attempt a cleave in the first place. This is what we'll multiply the average damage per cleave attack by to find the overall contribution the mastery is making to our damage.

Our hit damage is lower here, as we won't be adding our +4 from Strength, so our damage is a simple 1d12, or 6.5. However, it's the same hit chance as always, or 60%, with a 5% chance to deal an additional 6.5. Actually, given that the extra damage on a crit is precisely the same as what we deal on a hit (magic +X weapons and Rage and other such damage bonuses would change this) we can simply treat this as if we have a 65% to hit and no crit. Thus, our average damage per cleave attack is just 6.5x65%, or 4.225.

As we said we would do before, we plug that number into our 42% of even making our cleave attack in the first place, getting 1.7745.

Now, we add that to our average damage of the normal attacks, which was 13.25, getting a total damage per turn of 15.0245

    So there we go:

I'm honestly a little surprised that Cleave wound up doing better than Topple, though again, we're making some big assumptions regarding the foe's chance to save against topple and the likelihood of a reliable target for cleave.

I think it's worth noting, of course, that Topple can have other benefits. Grappling a prone creature will keep them stuck in that position, and your party members will benefit from their being prone. It can also slow a target down if you want to keep them from going after one of your allies. Also, a flying creature that doesn't have the hover feature on their fly speed will plummet to the ground if you knock them prone. Giving Fly to your Fighter or Paladin with a Maul and knocking a Dragon out of the air will cause some extra fall damage depending on how high up you are (if you're very high up, a pretty significant amount).

Cleave only grants additional damage. I think that it could be very good in scenarios with a lot of low-HP monsters, like a bunch of kobolds who have 4 HP, I really think that Graze is going to be the go-to choice. It's going to be the most reliable and versatile of these heavy weapon masteries. (I will say, though, that Cleave might play nicely with Great Weapon Master - because the cleave attack is still part of your action, you should be able to add your proficiency bonus to the damage, which you won't be able to do on a Graze). The point is, Graze can be useful regardless of whether you're fighting minions or a big boss - only in situations where your chance to miss is utterly minuscule, like against Zombies or a Gelatinous Cube, will its value really feel redundant.

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