Assuming 4th level, a Striking rune and no property runes, an Arquebus does 2d8 + 1 + 1 damage (11, base + singular expertise + kickback) on a hit, and 5d12 + 2 + 2 (36.5, fatal 12 + singular expertise + kickback) on a crit.

If you have the right feat, and there is only one enemy, a Dwarven Scattergun does 2d8 + 1 + 1 + 2 damage (13, base + singular expertise + kickback + scatter) on a hit, and 4d8 + 2 + 2 + 2 (24, scatter is not doubled) on a crit.

Clearly, a Scattergun does better damage normally, while an Arquebus does better on a crit. From what hit chance am I better off with an Arquebus on average?


2 Answers 2


The Arquebus wins at to hit chance of 60% and up

The average rate to hit on level 4 is 65%. That means on average you hit with a 8 or higher. The critical hit rule is:

When you make a Strike with a weapon or unarmed attack and succeed with a natural 20 (the number on the die is 20), or if the result of your attack exceeds the target’s AC by 10, you achieve a critical success (also known as a critical hit). If you critically succeed at a Strike (page 418), your attack deals double damage.

You hit when the number you roll equals or exceeds the target AC, so an 8 needed to hit plus your modifiers is equaling the AC, the lowest you can roll to still hit. That means when you roll an 18 or higher, you exceed the AC by 10 on average, so you will crit when the dice show an 18, 19, or 20 on average, or 15% of the rolls. To generalize this, the percentage that your hit chance exceeds 50% is the percentage you will crit, on average.1

With that we can calculate the expected damage. That damage consists of the chance to non-crit times the damage for that, plus the chance to crit times the damage for that. Taking the numbers you provided this gets us (bolded is the better expected damage)

Percentage to hit Percentage to crit Non-Crit Arquebus Scattergun Arquebus wins?
5% 5% 0% 1.825 1.2 TRUE
10% 5% 5% 2.375 1.85 TRUE
15% 5% 15% 3.475 3.15 TRUE
20% 5% 20% 4.025 3.8 TRUE
25% 5% 25% 4.575 4.45 TRUE
30% 5% 30% 5.125 5.1 TRUE
35% 5% 35% 5.675 5.75 FALSE
40% 5% 40% 6.225 6.4 FALSE
45% 5% 45% 6.775 7.05 FALSE
50% 5% 50% 7.325 7.7 FALSE
55% 5% 50% 7.325 7.7 FALSE
60% 10% 50% 9.15 8.9 TRUE
65% 15% 50% 10.975 10.1 TRUE
70% 20% 50% 12.8 11.3 TRUE
75% 25% 50% 14.625 12.5 TRUE
80% 30% 50% 16.45 13.7 TRUE
85% 35% 50% 18.275 14.9 TRUE
90% 40% 50% 20.1 16.1 TRUE
95% 45% 50% 21.925 17.3 TRUE

That is, from the expected to hit chance of 60% onward and better, the Arquebus is superior against a single target.

Liekwise, if you have miserable to-hit chances, 30% or below, then, the higher critical damage from the arquebus also gets to be more and more important (as you crit more and more of the few cases you hit), and the arquebus wins. [Thank you to @Greebo for catching a mistake in the math for the table.]

1 Of course you always crit on a nat 20, so the chance never falls below 5%.

@Brandon also notes that at the arquebus has a much better range — this will matter in practice, at least outside of dungeons with relatively more restricted environments, and also benefit the arquebus' damage.

  • \$\begingroup\$ How did you compute those numbers? I tried to do the same math, and found that Scattergun only out-damages the Arquebus at the 5% crit mark (so hitting on 10+). Interestingly enough, I also found that the Arquebus is better again once you need 14 to hit, as the hit rate goes down but the crit rate stays the same. \$\endgroup\$
    – Greebo
    Commented Jul 2 at 11:47
  • \$\begingroup\$ @Greebo "That damage consists of the chance to non-crit times the damage for that, plus the chance to crit times the damage for that." based on the damage numbers provided by Andras \$\endgroup\$ Commented Jul 2 at 11:49
  • 1
    \$\begingroup\$ Yeah but if we take, as an example, the 15% chance to hit, you have a 50% normal hit chance (8-17 on the die), and a 15% crit rate (18-20 on the die), so arquebus damage should be 0.5*11 + 0.15*36.5 = 10.975, but you got 14.825. Edit: It looks like your calculation ignores miss rate, where you would do 0 damage. \$\endgroup\$
    – Greebo
    Commented Jul 2 at 11:51
  • \$\begingroup\$ @Greebo You are right,, thanks for catching this. It shifts a little down, now the arquebus is better over 60%. I also did take a look at the bottom end of the distribution, and becasue there a large share of the hits are crits, the higher crit damage of the arquebus also wins. - I updated the table to reflect this. \$\endgroup\$ Commented Jul 2 at 12:51
  • \$\begingroup\$ Also possibly worth mentioning, the average-rate-to-hit you reference at the top is the probability of creatures hitting players, not the other way around. In this case it gives the same answer, as a gunslinger would also typically have a 65% hit rate against High AC lvl 4 enemies. \$\endgroup\$
    – Greebo
    Commented Jul 2 at 12:54

(Nobody the Hobgoblin's numbers are accurate, so I will just use them)

Optimize for non-critical damage

I guess the underlying question is which one you should pick. If you had unlimited money, carrying capacity and knowledge, you could have two weapons with all the runes, and pick the one that fits the encounter better. Usually, you do not have these.

Encounters are varied

If an encounter is easy, what weapon you have does not matter. If not, either there is one high level enemy, where the hit chance is lot less than 65%, or many smaller ones, and there will be more than one enemy in the scatter area, and the crit might be overkill.

So pick the Dwarven Scattergun

  • \$\begingroup\$ Party composition will also play a role in this - if you have significant buffers (Inspire Courage/Courageous Anthem or Inspiring Marshal Stance, etc) or debuffers (grapplers, Dread Marshal Stance, demoralizers, etc), then percentages to hit can skyrocket. My party (before the Bard left) could easily get +15% to hit on enemies (and I've played in a party that could get +25%), strongly favoring the crit build here. Your analysis is correct in a vacuum - if your party doesn't debuff or buff, don't bother with the crit build. \$\endgroup\$
    – ESCE
    Commented Jun 26 at 18:07
  • \$\begingroup\$ How do you get +25%? \$\endgroup\$ Commented Jun 27 at 8:24
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    \$\begingroup\$ Frightened 2 from Lizardfolk's Threatening Approach, flat-footed/off-guard (Snagging Strike in our case, could just flank), Inspire Courage/Courageous Anthem. Obviously requires a couple successful rolls, but would be a great combo starter for any crit build. \$\endgroup\$
    – ESCE
    Commented Jun 27 at 20:48

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