Of all the Origin Feats in the new Player's Handbook, there's only one that really directly increases the damage of a weapon-based character. Sure, Lucky could arguably count as well, giving you advantage on a few attacks per day, but I'd generally prefer to save that for big Saving Throws or story-crucial ability checks.
Savage Attacker comes with the Soldier background, a pretty common choice for many martial classes (in my original campaign, two of my initial three PCs took this background, though that was in 5.0).
Still, my instinct was that, while this does technically boost one's damage a bit, that it wasn't actually all that good. That being said, I wonder if I lumped this in too much with the Great Weapon Fighting Style feat, which itself wasn't that great in 5.0 and got even worse in 5.5. Might Savage Attacker be better?
First, let's remind ourselves what it does:
Once per turn, when you hit with a weapon attack, you can roll the damage dice twice and pick which roll to use against the target.
As it turns out, this is a little more complicated than something like Great Weapon Fighting - in that case, whether it's the new or the old version, you first roll and then can re-roll, or just take the flat result. For example, with the 5.5 version, you count rolls of 1s and 2s on appropriate weapons as 3s. Thus, the way you'd calculate damage on a d10 weapon, for example, would go from adding up the results, 1 through 10, and dividing it by 10 (which would normally get us a 5.5) and instead just add 3 three times and then 4 through 10, and divide the result by 10, giving us 5.8.
But in the case of Savage Attacker, it's more like Advantage, which is a bit more complex.
Let's start simplest: say we're attacking with a d4 weapon like a dagger.
First off, we'll use this on our first hit of the turn - it's best on a crit, when the potential difference is higher, but we probably aren't going to count on getting a crit, so we should just use it on that first hit.
Normally, we have a 25% chance of getting a 4 on a single roll of a d4. But if we are rolling two, the chance that one of them rolls a 4 is now 43.75% (the way we get this is by calculating that there's a 75% chance that we don't roll a 4 on one die, and so that 75% is squared because we need that to happen twice, which comes to 56.25%, and the remaining chances become 43.75%).
I think the next step would be to see how likely it is we get a 3 or higher - not just 3 specifically, which would also be 43.75%. But what we do is get the 3 or higher and then subtract the chance that we get a 4 instead, as we'd prefer that. This winds up being pretty simple, because it's just a 50% chance here normally, which means it's a 75% chance one of the dice come up on the upper half of their range. However, we then subtract the chance that we get a 4, because we'd prefer to keep that if we get it. Thus, our chance that, rolling twice, 3 is our highest result winds up being 31.25%
Next, we find the chance that we roll a 2 or higher. This winds up being pretty simple as well, because it's just the chance we don't roll a 1 on both dice. That's a 25% chance on a single die, and thus just a 6.25% chance on two dice (25% squared) meaning it's a 93.75% chance we get a two or higher. Now, though, we're going to find those cases where the 2 is our highest result, and so we subtract that 75% chance that it's higher than two, giving us 18.75%.
And then, we have that 6.25% chance that we've rolled double-ones.
Finally, we take each value and multiply it by its likelihood. 4x43.75% is 1.75, 3x31.25% is .9375, 2x18.75% is .375, and of course 1x6.25% is .0625. Then, we sum them all up and get 3.125, which would be our average roll with a d4 on Savage Attacker.
Once per turn, thus, with a dagger, we're effectively doing .625 more damage.
But what about a harder-hitting weapon? I'm going to set aside 2d6 weapons because there are essentially 36 permutations of how the dice could go, but we'll do a d12.
So, once again, we do basically the same thing, but it takes longer:
There's a (and we're going to round off here, because the decimal places are going to go long) 16% chance on two dice to roll a 12.
Then, there's a 31% chance to roll an 11 or higher, meaning that we've got a 15% chance that the 11 is the higher of the two values.
For 10, there's a 44% chance to roll a 10 or higher, so subtracting 31% gives us 13%
For 9, the chance is 56%, so subtracting 44 gets us 12%
For 8, we're at 66%, so that means a 10% chance that the higher is 8.
For 7, it's 75%, and thus we get 9%.
For 6, it's 83%, so we get 8%
For 5, it's 89%, with a difference of 6%
For 4, it's 94%, with a difference of 5%
For 3, it's 97%, so we're at a difference of 4%
For 2, it's 99%, so a difference of 3%.
And then 1 happens about 1% of the time (actually a little less).
So, then, we take these and again multiply each by their frequency:
12x16% is 1.92, 11x15% is 1.65, 10x13% is 1.3, 9x12% is 1.08, 8x10% is .8, 7x9% is .63, 6x8% is .48, 5x6% is .3, 4x5% is .2, 3x4% is .12, 2x3% is .06, and then 1x1% is .01 (obviously).
Adding these together, we get 8.55 as our average roll on a d12.
That is 2.05 damage higher than we'd previously rolled.
So, comparing the low and high ends of damage dice, our d4 went from 2.5 to 3.125, which is a 25% jump. Our d12 went from 6.5 to 8.55, which is about a 32% jump.
But that's just the raw dice damage. When we take modifiers into account, this bonus is diluted: if our Battle Smith Artificer with a Repeating Musket and +5 to Intelligence is rolling our d12, and thus adding 6 to the damage rolls, we're talking 12.5 versus 14.55, which means an increase of damage by about 16% instead.
And, let's also remember that this is only once per turn. So, if we think of this as two attacks, either both doing 12.5 on hits or one doing 14.55 and another doing 12.5, we're talking 25 versus 27.05, which means that our average damage has only gone up by 8%.
Again, this feat does increase your damage done. But I'd argue that the effect is marginal enough that I'm not sure it's really worth taking compared with something like Alert or Tough or most other Origin Feats.
Now, what if we were to redesign it?
I believe the old version (and maybe I'm confusing this with Great Weapon Fighting) allowed you to first roll and then decide to reroll an attack's damage once per turn.
Here, the math becomes far simpler, because I think there's a clearly optimal way to use this: if you roll below average damage, you reroll.
Thus, on a d4, we reroll if we roll a 1 or 2. Thus, when calculating the average damage of the die, we treat the 1 and 2 places as if they were actually the same as a d4's average damage roll, which is 2.5. So, it's 2.5+2.5+3+4, and then divide that by 4. That gives us a 3 on average. Interestingly, that's actually worse than this. What about for a d12? Again, any roll of 6 or lower is below average, so we're replacing each with 6.5. The average winds up being 8, which, again, is lower than what we get with this version.
So, ok, credit where credit's due: this is a little bit better than getting to reroll when you want, which honestly surprised me (if anyone cares to check my math, please let me know if I got something wrong).
Still, once again, my conclusion is that I don't know that this feat would feel all impactful. I think there are cooler Origin Feats, and even something as simple as Tough might be better (the math would require far too many assumptions to really nail down how effective Tough is at keeping your character up, and I think it's possible that it's not as impactful as it might first appear, but whatever.)
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