Wednesday, November 17, 2021

Napkin Math: Do Subclass-Granted Weapons Need a Buff?

 D&D classes aren't and don't need to be balanced quite to the razor's edge that video game classes generally need to. The sample size of D&D combat is way smaller, and there are many non-damage-based utilities that can provide value without necessarily being quantifiable in the same way. A Fighter will generally need to pump out a lot of single-target damage, because that's what it's built to do. But a Wizard would still be welcome in a party if it could do things like create battlefield-controlling barriers (Wall of Force, Wall of Fire, etc.) or buff party members (Haste, Stoneskin) or focus less on dealing with single monsters, but instead blasting away swaths of minions (Fireball, Cone of Cold).

But I still think that, in an ideal world, each published subclass would have some degree of equity.

So, I want to talk about subclass-based weapons.

For martial classes (and I'm counting Rogues and half of Artificers here) your damage mostly comes through the Attack action. And that means using weapons to attack your foes.

There's a moment in every campaign where the martial classes find a magical weapon for the first time. In most cases, it's the simplest of magic weapons - the +1 weapon. This generally comes around level 5, and becomes necessary if you find yourself fighting monsters that have resistance or even immunity to nonmagical weapon attacks. (There are some common magical weapons found in Xanathar's Guide to Everything with a pretty small effect, their biggest upside simply being the fact that they are magical.)

While WotC's official position is that a D&D game doesn't actually need magical items to work, you're going to find a lot of casters' concentration dedicated to Magic Weapon or similar spells if your Fighter, Barbarian, Paladin, etc. is going to actually be able to hurt, say, the demon lord that is your final boss.

However, there are a few classes and subclasses in which the focus is not on weapons you have acquired, but weapons you have innately. The Soulknife Rogue conjures Psychic Blades that they can just manifest while they attack, and which have all the properties a Rogue wants - they're light, finesse, and have the thrown property so you can use them from 60 feet away.

The Path of the Beast Barbarian undergoes a partial transformation to get bestial claws, a muzzle, or a tail with which they can attack.

I'd argue that the Armorer Artificer kinda sorta also has this, in that they're primarily going to be using their armor's weapons (these, however, can be infused, so it's slightly different.)

The issue I want to explore, though, is if this becomes a problem when it comes to scaling.

The Monk has always had to deal with this - in theory, once your martial arts die becomes a d8 at level 11, the Monk can truly throw out all their material possessions and fight at full capacity naked. Still, if they have a +2 Quarterstaff or any magical weapon that buffs their hit or damage rolls, or really has any other beneficial effect, they're going to want to hold on to it. Their unarmed strikes won't get this bonus, but you could argue that, given that they still get their two regular attacks with whatever magical weapon they might have, the unarmed strikes can be balanced separately.

But a Beast Barbarian that has the option to use a nice magical greataxe or what-have-you is going to have to weigh abandoning one of the core concepts of their subclass against using a superior weapon.

I don't know, off the top of my head, if WotC accounted for this issue in the design of these subclasses. And that is a tricky balance to pull off: different DMs and different campaigns are going to act differently when it comes to giving out magical items. If you have an extremely item-poor game, having your own natural weapons (that overcome damage resistances as part of the subclass) would be a huge advantage, but if your Beast Barbarian gets some crazy thing like Akmon, Hammer of Purphoros (a warhammer artifact weapon from Theros that deals an extra 3d10 fire damage on every hit, and I think is probably the best melee weapon in all of 5th Edition - though an Ascendant Dragon's Wrath weapon of any sort is not far behind) their Claw attack is going to look pretty darn pathetic.

This is not a game like World of Warcraft, where classes are balanced with an expected "item level" of magical gear (with basically all gear after the earliest levels having at least some magical bonus) and so this might be a fool's errand.

My instinct is that Rogues care slightly less about their weapons as long as they can overcome resistance to nonmagical damage. A Soulknife's blades dealing psychic damage means that in most situations, they'll be fine - though the class is at a disadvantage against mindless things like Golems or some psychic-resistant or -immune aberrations. But given how much of a rogue's damage comes from Sneak Attack compared to how much comes from weapon damage, it's really just the bonus to hit that is the primary concern.

To an extent, the same is true for Barbarians, as they're going to get a more significant portion of their damage from their Rage bonus and their Strength modifier (at level 20, it can be up to +7).

So, I think we're mainly talking about the Beast Barbarian, and specifically its Claw attack, which seems to obviously be its highest damage-dealing option for its melee attacks.

As a note, the way that the Claws are worded, there's a weird kludge here - you get the extra attack as long as you make at least one Claw attack as part of your Attack action. This means that by level 5, you could make one attack with a super-magical weapon and then the second with your claw, which would open you up for a third attack also with the claw.

Ok, we're almost done with the preliminary ideas here, but we have two other notes to think about:

First is that what makes the Claws seemingly so good is that they aren't actually dual-wielding. While the implication is that you're slashing with both hands, technically all three of your attacks could just be your dominant hand, leaving your off-hand to hold something else like a shield. They are not light, though, so you can't actually turn it into four attacks with a traditional off-hand bonus action strike (fun fact, if for some reason you want to use two different weapons, you can actually make a normal attack with your off-hand with all the usual benefits if it's one of your attacks in the Attack Action.)

The second is a note that Barbarian damage math gets stupidly complicated because of Brutal Critical. While the higher potential Strength and, more importantly, your Rage bonus relatively de-value your weapon dice, this turns around and adds value to them, but also in a weird way, making a Greataxe's 1d12 eventually (though only at very high levels) outstrip a Maul or Greatsword's 2d6 simply. On top of that, the AC of a target then shifts the relative values. Somewhat non-intuitively, a monster with higher AC raises the value of Brutal Critical, because critical hits get a higher share of the attack rolls that actually result in your dealing damage.

Ok, one more thing: we need to choose which subclass to compare Beast to when it comes to relative damage output. Though I haven't crunched the number on all of them, my instinct is that the Zealot Barbarian might have the best boost to output.

Again, there are a lot of factors that can be tweaked here, so consider this a rough sketch rather than a comprehensive analysis. I'm also not, like, a mathematician, so there could be some huge errors in either my calculations or my methodology.

Characters also scale as they level, so I'm going to make a few assumptions and select a few slices of the leveling pie to compare.

I'm going to look at things at the last level of each tier of play. So this will be level 4, level 10, level 16, and level 20. I'm going to assume that we've got a character who started off with a 16 in Strength at level 1, and is not going to have any feats (Barbarians do have a lot of stat dependencies, so I think it's not unreasonable that someone would go for maxing out Strength and Con and doing as much Dex as they can).

Now, regarding AC: for max-level play, I usually use 22 AC as a standard (25 could work, though that tends to be for only the super-high CR creatures). But that's pretty high for level 4. I think I'm just going to have the AC rise by 2 each tier - 16 for tier 1, 18 for tier 2, 20 for tier 3, and 22 for tier 4.

Phew, another preliminary: what kind of weapons are we talking about? I think that I'm going to keep things simple: at tier 1, the Barbarian has no magical weapons. At tier 2, they have a +1. At tier 3, they have a +2, and at tier 4, they have a +3.

I'm also going to be having the "standard" for Barbarians be a Greataxe, and have the Beast just use its claws. I actually did some non-blog napkin math that suggested that every Barbarian should actually dual-wield thanks to the Rage damage and the additional magical weapon damage, but for now I'm going to stick with the Greataxe model, which I think is quite common.

Finally: What do we hope to learn from this? As I see it, if the Beast can do up to 90% of what the Zealot can with its magical weapon, that's still pretty balanced, and could be off-set by other factors (though the Zealot has some insanely powerful features, like being able to simply not die if they're raging - I think it's still one of if not the most powerful high-level Barbarian.)

Let's begin!

At level 4, both of our Barbarians have taken a +2 ASI to Strength, raising it to 18 in both cases. Both should have a +6 to hit, +2 rage bonuses, and +4 strength modifiers. Facing an AC 16 monster, they need to roll a 10 or higher to hit. Thus, they both have the following array:

1-9 (45%): Miss. 10-19 (50%): Hit. 20 (5%): Crit

The Beast's Claw attacks each do

Hit: 1d6+4+2 slashing damage, for an average of 9.5 damage on a hit

Crit: 2d6+4+2 damage, for an average of 13 damage on a crit

We multiply the damage of the hit by its chance, and the damage of the crit by its chance, and then we add those together to find the damage per attack. (We don't need to bother finding 45% of 0 for misses).

Level 4 Claw: 4.75 + 0.65 = 5.4 damage per attack.

The Beast is doing two Claw attacks per round at this level, so that comes to:

10.8 damage per round.

Zealot's Greataxe and Divine Fury.

Ok, before we start, Divine Fury makes things complicated. It always goes off on the first hit per turn. At tier 1, that's not a problem because it's part of the single attack. But when we get Extra Attack, it gets two chances to go off. We'll cross that bridge when we get to it.

So, the Zealot's Greataxe does

Hit: 1d12+4+2 damage, for an average of 12.5 damage her hit.

Crit: 2d12+4+2 damage, for an average of 19 damage per hit.

Using the same methodology, we get:

Level 4 Greataxe: 6.25 + .95 = 7.2 damage per attack.

But, we also need to add Divine Fury. The damage here is 1d6 + half your Barbarian level. I believe, like Divine Smites, that the d6 is doubled on a crit, so we'll calculate that:

Hit: 1d6+2: 5.5 damage

Crit: 2d6+2: 9 damage

Level 4 Divine Fury: 2.75 + 0.45 = 3.2 damage per attack.

So, we add those two together (perhaps we should have simply added that damage to the single attack - again, this gets more complicated down the line) and so we have a total of 10.4 damage per turn.

Ok, the Beast is ahead, but only slightly with .4 damage per round. Now, we jump to level 10.

Level 10:

At this level, our Zealot has gotten a +1 Greataxe. Our Beast is sticking with the Claws. Both now have Extra Attack. Given the marginal lead the Beast had already, I'm thinking the Zealot is going to overtake it. A couple other things to note: we now have Brutal Critical, which means that crits are going to do 3 dice rather than 2. More complicated is that we're going to see Divine Fury have an increased chance to occur given that there are two chances for it. I'll be calculating it separately from the attacks to account for this.

Also of note, both subclasses have new features that can change the math here - Beasts can use Infectious Fury to effectively "smite" a limited number of times per day while Zealots can give the party advantage for a round. These are limited-use, however, and are beyond the complexity I'm willing to explore here, so I'll set it aside.

By this point, the Barbarians should both have maxed out their Strength to 20/+5. Proficiency bonuses are up to +4 at this point, and Rage damage is up to +3. We are also going to see a disparity in hit chance because of the magic weapon the Zealot is using.

Level 10 Beast:

At this level, the Beast has a +9 to hit. Its Claw now does 1d6+5+3 damage. And it can now make three Claw attacks per round. The AC we're using is now 18. And again, Brutal Critical. So, we get the following:

Miss: 1-8 (40%) Hit 9-19 (55%) Crit 20 (5%)

Claw Hit: 1d6+5+3, or 11.5 damage

Claw Crit: 3d6+5+3, or 18.5 damage

Damage per Attack: 6.325 + 0.925, or 7.25

With three attacks per round, this comes to 21.75 damage per round.

Level 10 Zealot:

Again, what complicates this is going to be Divine Fury. We'll cover that after the greataxe damage. The bonus to hit, thanks to the magical axe, is one higher, for a +10. So, we get this array:

Miss: 1-7 (35%) Hit 8-19 (60%) Crit 20 (5%)

Greataxe Hit: 1d12+5+3+1 = 15.5 damage

Greataxe Crit: 3d12+5+3+1 = 28.5 damage

Damage per Attack: 9.3 + 1.425, which comes to 10.725.

With two attacks per round, this comes to 21.45 damage - from the axe. But now we need to add in Divine Fury.

What we now need to do is treat the 35% miss chance as its own microcosm of an array. If we miss both attacks, we don't get any Divine Fury. But if we miss the first one, there's still a chance that we'll get a crit on the second. There's no choice in the matter here, which might actually make the math simpler. I think the way I'll handle this is to first calculate the damage per first attack in the round. The divine fury will only proc on the second attack if the first one misses, so we'll basically take that value and multiply it by 135%, with that extra 35% representing the situations where the first attack misses (essentially, it's less likely the divine fury will activate on the second attack because it might have already gone off on the first). So, same array, but now:

Divine Fury Hit: 1d6+5, or 8.5 damage

Divine Fury Crit: 2d6+5, or 12 damage (your Brutal Critical is going to your weapon damage, not this.)

Damage per first attack: 5.1 + .6, or 5.7 damage.

Now, in that 35% chance where the first attack misses, we get the same array. 5.7 x 0.35 = 1.995

Giving us an average Divine Fury damage per round of 7.695.

Add the Divine Fury to the Greataxe damage per round and we get:

Level 10 Zealot damage per Round: 29.145

Already, the Zealot is cruising ahead of the Beast by a fair amount - while the damage from the weapon attacks still favors the Beast, Divine Fury is more than making up for it. Again, we're ignoring Infectious Fury, which might be a bad call, as it could be considered a pretty important part of a Beast's damage output. I might revisit that at the end of this. (That said, the target gets to save against this feature for zero damage even after the hit, and it's limited to at most 6 times a day, so I'm a little hesitant to consider it a reliable part of the package.)

I'm actually tempted to stop here. The Zealot will continue to scale up faster than the Beast. Yes, having one extra attack will mean 1d6+11 by level 20 (+7 strength, +4 rage) but that's already basically countered by the Divine Fury hitting 1d6+10, and then you're also hitting more often and doing an extra 3 damage with each greataxe hit thanks to the weapon bonus.

So, let's actually get to the hypothesis of what I think might solve the scaling issue for classes that rely on built-in weapons. I think we need some sort of item that can be picked up like a weapon that will buff any natural or conjured weapons. Call it a +X Amulet of the Sharpened Claw.

+1 Amulet of the Sharpened Claw: While wearing this amulet, your natural weapons, and any weapons you conjure or summon as part of a class feature, get a +1 bonus to attack and damage rolls, and count as magical for the purposes of overcoming resistance to nonmagical weapons.

What would happen in, say, that level 10 scenario, if the Beast Barbarian had such an item.

A lot of the math is already waiting there for us:

We use the array the Zealot had:

Miss 35% Hit 60% Crit 5%

Claw Hit Damage: 1d6+5+3+1, or 12.5

Claw Crit Damage: 3d6+5+3+1, or 19.5

Damage Per Attack: 7.5 + 0.975, or 8.475

With three attacks per round, we get 25.425.

It's still below the Zealot, but it's caught up significantly.

Ok, I'm going to just go for broke and imagine this all at level 20:

Level 20 Beast with Homebrew +3 Amulet:

Our attack bonus here is +16, thanks to +7 from Strength, +6 proficiency bonus, and +3 from the amulet. With AC 22, we need to roll a 6 or higher.

Miss: 1-5 (25%) Hit 6-19 (70%) Crit 20 (5%)

Claw Hit: 1d6 + 7 + 4 + 3: 17.5 damage

Claw Crit: 5d6 + 7 + 4 + 3: 31.5 damage

Damage per Attack: 12.25 + 1.575, or 13.825 damage per attack.

Which then gives us 41.475 damage per round.

Level 20 Zealot with perfectly normal +3 Greataxe:

All the hit chance stuff remains the same.

Greataxe Hit: 1d12 + 7 + 4 + 3: 20.5 damage

Greataxe Crit: 5d12 + 7 + 4 + 3: 46.5 damage

Damage per Attack: 14.35 + 2.325, or 16.675

With two attacks, that gives us 33.35 damage. Now for Divine Fury:

Divine Fury Hit: 1d6 + 10: 13.5 damage

Divine Fury Crit: 2d6 + 10: 17 damage

Divine Fury Damage on First Hit: 9.45 + 0.85, or 10.3

And then 25% of that in case the first attack misses: 2.575

So, total Divine Fury per Round: 12.875

Adding that to the Greataxe damage per round, we get: 46.225.

So!

As it turns out, again ignoring the extra damage of Infectious Fury (perhaps at our folly) we have the Beast with this hypothetical item still underperforming compared to the Zealot, but keeping up a lot closer, with 41.475 damage per round compared to the Zealot's 46.225. That is, actually, about 90%.

If you've followed me this whole time, and you haven't found some massive error in my premises or calculations, then I think this is a point in favor of the idea of making an item like the Amulet of the Sharpened Claw.

Now, there are a few other subclasses for other classes that I might consider. And I also wonder if making this amulet apply to unarmed strikes would make Monks far too powerful, or maybe just allow them to keep pace with other martial classes.

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