How to calculate Savage Attacker damage?

[Thomar_of_Uointer]

I've been looking at the Savage Attacker feat and I'm not sure how to calculate its damage potential.

So if I'm a 1st-level variant human fighter, I can wield a battleaxe. Normally this does 1d12 (6.5) damage, the sum of its possible outcomes (1-12 / 12).

When I take the feat, If I roll a 6 or less on my single attack per round I'll reroll. This makes me replace the lower half of my outcomes with the result of a second roll, or 6.5, for a total average of (6x6.5/12 = 3.25 + average of a run of 7-12 = 6x9.5/12 = 8) 8 damage, or a 1.5 damage increase.

But that's at first level. As a fighter I get up to four attacks. I'm assuming I roll their damage in order, and only when they hit. What's the optimal damage threshold for a reroll? How does this improve my average damage boost from the feat?

[Sidmen]

Since you probably won't get to see all 4 attacks' damage rolls at the same time, it's probably best if you choose to reroll damage whenever you're at 1/3 or less of your maximum damage. (1-2 for a d6, 1-3 for a d8/d10, and a 1-4 for a d12/2d6).

Granted, there is still a chance you'll roll even lower on damage on a later attack, but the odds are in your favor that you won't.

[Cambrian]

I've been looking at the Savage Attacker feat and I'm not sure how to calculate its damage potential.

So if I'm a 1st-level variant human fighter, I can wield a battleaxe. Normally this does 1d12 (6.5) damage, the sum of its possible outcomes (1-12 / 12).

When I take the feat, If I roll a 6 or less on my single attack per round I'll reroll. This makes me replace the lower half of my outcomes with the result of a second roll, or 6.5, for a total average of (6x6.5/12 = 3.25 + average of a run of 7-12 = 6x9.5/12 = 8) 8 damage, or a 1.5 damage increase.

But that's at first level. As a fighter I get up to four attacks. I'm assuming I roll their damage in order, and only when they hit. What's the optimal damage threshold for a reroll? How does this improve my average damage boost from the feat?In general you will want to save your reroll for a lower value with more attacks. For example if you have 3 attacks, and your first attack yields a 6. With 2 rolls to go there is a 75% one of your next 2 attacks will yield the same or less. I'd save it until its a cointoss that you wont get better use out of it (intiutively that should give the best returns but statistics is often not intuitive...).

I believe this chart works for the Greataxe:
Attacks remaining 0 --- Always reroll
Attacks remaining 1 --- Reroll if die is 5 or less
Attacks remaining 2 --- Reroll if die is 4 or less
Attacks remaining 3 --- Reroll if die is 3 or less

Crits, action surges, etc... change all of this

Note: rerolling a 6 with one attack remaining is a coin toss. If you need lucky dice reroll the 6, if you need sustained damage keep it.

Now if only I could make sense of how 2d6 would work without hard calculating every possibility...

[Galen]

Assuming 4 attacks:
- 4th attack: reroll 6 or less
- 3rd attack: reroll 4 or less
- 2nd attack: reroll 4 or less
- 1st attack: reroll 3 or less

I took way too many statistics classes for my own good.