Saturday, February 19, 2022

Napkin Math: Another Crack at Firearms - Dropped Modifiers

 In Starfinder, there are plenty of ranged weapons - you can have various kinds of laser guns, sonic weapons, conventional firearms, etc. Damage scaling in that game works very differently than in D&D, but while melee weapons do include your Strength modifier in the damage (even if that damage is something like fire from what is essentially an axe whose blade is made of burning plasma) you don't add your Dexterity modifier to ranged weapon attacks - it's just the flat roll of the dice (admittedly, everyone also gets a feat that allows them to add their level to the damage of weapons they're supposed to be using - again, the damage scaling is very different in that game).

Anyway, in my ongoing quest to make Firearms in D&D balanced, I wondered a bit about exploring this as an option.

I found that introducing Misfires was a reasonable balance for Renaissance-era weapons (even making a Musket less powerful overall than a Heavy Crossbow) but that even if you make the weapon misfire on any natural roll equal to the number of dice your roll, Modern and Futuristic weapons still pull ahead because the damage potential is so high (this might be why Matt Mercer's Gunslinger doesn't just prevent you from firing more that round, but forces you to attempt a repair mid-battle).

But what I want to explore here is whether you could remove the Dexterity bonus to damage and make these weapons more balanced.

Here, I think Renaissance weapons will naturally fall behind - if Misfire was making Muskets less powerful than a Heavy Crossbow, the lack of any Dex modifier to damage would be an obvious problem - 1d8 (a longbow) + 3 is 7.5 on average, which is more than 1d12's average of 6.5 (a musket,) and the floor on that longbow is 4, as opposed to 1.

When we get up to modern weapons, though, the math begins to change a bit.

An automatic pistol hits for 2d6. If we compare that to a Hand Crossbow (another pretty standard one-handed ranged weapon,) that does 1d6+Dex. Depending on your Dexterity modifier, the average damage will be different. At +5, of course, the Hand Crossbow is averaging 8.5, compared to the Automatic Pistol's flat 7. Granted, the Hand Crossbow's crit is 12, while an Automatic Pistol's crit is 14.

If we move up to two-handed weapons, a Heavy Crossbow is doing 1d10+Dex, so with maxed Dex we get about 10.5 damage on average. A Hunting Rifle? 2d10, or about 11. That's pretty close, actually. The Hunting Rifle will do a lot more on a crit (4d10, or 22, versus 2d10+5, or 16) but the floor on the Heavy Crossbow is 6, compared to the Hunting Rifle's floor of 2.

So, how's this for a proposal? First, let's just get rid of Renaissance Firearms, as they don't really fit into this paradigm. We're going to look at Modern weapons only (which includes some Western-appropriate options like Shotguns and Revolvers). Essentially, the price you're paying for getting a gun is that you're not adding your Dex modifier, giving you swingier weapons with still fairly comparable overall damage output (you can think of the second die as replacing the Dex modifier).

I'm going to be a little masochistic and do this for all the options (though weapons the same damage die will be identical).

Without Misfire altering the chance to hit multiple times, we're only now looking at damage per attack - not per round. Because critting is important here, we're going to use a "target dummy" with an AC of 18, and we're going to assume a +9 to hit, as someone who has a +5 to Dexterity and a PB of 4 - around the mid levels. (This of course doesn't account for the Archery fighting style, but with Rogues, Artificers, and potentially others, I'm ok with that).

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

    1d6 (Shortbows, Hand Crossbows)

Hit Damage: 1d6+5, or 8.5

Crit Damage: 2d6+5, or 12

Damage Per Attack: 4.675 + 0.6, or 5.275

    2d6 Firearms (Automatic Pistol)

Hit Damage: 2d6, or 7

Crit Damage: 4d6, or 14

Damage Per Attack: 3.85 + 0.7, or 4.55

So, here things do favor the traditional weapons a bit, but the average difference is less than 1 point of damage, which I think is close to the margin of error. Let's look at bigger weapons.

    1d8 Traditional Weapons (Light Crossbows, Longbows)

Hit Damage: 1d8+5, or 9.5

Crit Damage: 2d8+5, or 14

Damage Per Attack: 5.225 + 0.7, or 5.925

    2d8 Firearms (Revolvers, Automatic Rifles, Shotguns)

Hit Damage: 2d8, or 9

Crit Damage: 4d8, or 18

Damage Per Attack: 4.95 + 0.9, or 5.85

Here, the gap has closed to less than .1 damage per round, and still favors traditional weapons.

    1d10 Traditional Weapons (Heavy Crossbow)

Hit Damage: 1d10+5, or 10.5

Crit Damage: 2d10+5, or 16

Damage Per Attack: 5.775 + 0.8, or 6.575

    2d10 Firearms (Hunting Rifle)

Hit Damage: 2d10, or 11

Crit Damage: 4d10, or 22

Damage Per Attack: 6.05 + 1.1, or 7.15

    At this point, the firearm has pulled ahead. But again, it's less than 1 average point higher.

    Is this it? Have we cracked it? One thing to note is that against higher AC monsters, the firearms fare better given the greater relevance of critical hits, but that's actually quite historically accurate (firearms were popularized because they punched through armor).

I think this system might create a sense of balance - players willing to tolerate more swing in their damage numbers can go for firearms while those who want more consistency will go for traditional ranged weapons. Neither becomes that much more powerful than the other. Ostensibly, a character with lower Dexterity might prefer a firearm, as while the chance to hit will be the same, they won't be penalized as much for low Dex - but that also reflects the historical fact that guns became more popular as weapons because they required less skill to use (especially post-industrial-revolution ones).

I have to say, I'm really happy with this solution, and might implement it in future games (not my current campaign given that I'm keeping MTG's gun ban - except for cannons on Ixalan, but no hand-carried guns). Was it really this simple?

Naturally, as I said before, AC is going to factor in, but a 55% hit chance feels like a fairly reasonable average. Magical weapons will naturally provide firearms with more stable floors, too, but still not quite as much as traditional ranged weapons.

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