Mathing Out Graze and Cleave

 That warlock post bummed me out. So let's look at two of the many very cool Weapon Masteries.

Graze comes on Greatswords and Glaives, while Cleave comes on Greataxes and Halberds.

How much will these boost your damage? Let's break it down.

Let's star with Graze. Graze can be put on heavy melee weapons by Fighters. When you miss with a Graze weapon, you can deal damage equal to the ability score modifier you used to make the attack. This damage does not get increased in any way, and doesn't take the benefit of, say, a +1 weapon or damage from class features or spells. It's just that raw amount.

But, it's guaranteed, which is pretty damn good.

For the sake of sanity, let's imagine two level 5 characters - one Fighter, one Barbarian, and ignore subclass features. We'll assume each has an 18 in Strength.

Now, Graze of course gains value the harder a target is to hit, so scenarios with a tough enemy are going to favor this mastery. At level 5, we'll say that a lot of foes we face have an AC of, say, 14.

So, if we have a mundane Greatsword, we're attacking with a +7 to hit and dealing 2d6+4 when we hit, or 4d6+4 on a crit.

We now use my usual hit array, but we actually have a damage value for missing.

Miss Damage: 4

Hit Damage: 11

Crit Damage: 18

We hit on a roll of 7 or higher, and we crit on a 20.

Miss (1-6) 30%, Hit (7-19) 65%, Crit (20) 5%

Average Total Before Graze: 7.15 + 0.9, or 8.05

Average After Graze: 8.05 + 1.2, or 9.25

This then becomes 16.1 before Graze and 18.5 with Graze when we use our second attack. In both cases I believe it's approximately a 15% increase in damage.

Now, let's do this as a Barbarian.

The only real distinction is that the hit and crit will now get 2 extra damage, from raging.

So, our hit damage is now 13 and our crit damage is 20.

Average Total Before Graze: 8.45 + 1, or 9.45 average damage.

Average Total With Graze: 9.45 + 1.2, or 10.65

With two attacks, we get 18.9 versus 21.25, with an average boost in damage by about 12%

    Now, let's look at Cleave. We'll assume that there are now two creatures with 14 AC here, standing near one another.

The damage of the cleave attack is more or less the opposite - the secondary creature takes all aspects of your damage except the ability modifier. In this case, that means we'll be rolling the die and adding our rage bonus for our Barbarian.

The cleave attack does not take a bonus action, but it can still only happen once a turn (somehow this feels like it pairs really well thematically with Great Weapon Master, even if it kind of means the same thing flavor-wise, but in two different expressions).

We've also got a different weapon die, but the hit array will at least be the same.

Fighter:

Average Main Hit Damage: 10.5

Average Main Crit Damage: 17

Average Cleave Hit Damage: 6.5

Average Cleave Crit Damage: 13

Average Main Damage Per Attack: 6.825 + 0.85, or 7.675

Average Cleave Damage Per Attack: 4.225 + 0.65, or 4.875

    So, our average total damage per turn without Cleave is 15.35. With Cleave it becomes 20.225. That's a 31% increase in damage.

Barbarian:

Average Main Hit Damage: 12.5

Average Main Crit Damage: 19

Average Cleave Hit Damage: 8.5

Average Cleave Crit Damage: 15

Average Main Damage Per Attack: 8.125 + 0.95 or 9.075

Average Cleave Damage Per Attack: 5.525 + .75, or 6.275.

    So, our average total damage per turn without Cleave is 18.15, and our average with Cleave becomes 24.425, which gives us a 34% increase in damage.

Ok, so that seems to reinforce my initial guesses. The Barbarian, getting to add its Rage bonus to the cleave, winds up getting a little more bang for its buck out of it, while losing that bonus on Graze makes it less of an increase for them (even if, at this level, they're outdamaging the Fighter - again we're ignoring lots of factors).

I think it's also appropriate that in both cases, the damage boost of Cleave is significantly higher. The reason for this is simple: any time you're attacking something on its own or in groups, Graze will have some relevance. But if a monster is either encountered alone or just happens not to be next to one of their monster allies, Cleave isn't going to do anything for you.

Cleave definitely increases martials' ability to help clear out large groups of enemies. And especially at early levels, you will be able to take down a lot of kobolds.

    OH! I MISSED SOMETHING!

Cleave only triggers if you hit a target with the main hit.

Our chance to not hit at all during our turn is our miss chance times our miss chance (unless we action surge as a fighter, in which case it's our miss chance to the fourth power... er, tesseracted?) That then means that the... not inverse, but the, um... the "1 minus that amount" value becomes our chance to attempt our cleave. So in our scenario, with two attacks, we have a 9% chance to not hit at all, which means that 91% of the time we're going to hit at least once, and so we need to multiply our cleave values by .91.

I'm too lazy to do this now, but it does mean that we're getting slightly less value out of Cleave than I calculated above.

Still, I think this shows that if you want something that will absolutely always be useful at least a bit, Graze is great. And if you're a high-enough level fighter, consider getting both of them on a single weapon!