Improving the Savage Attacker Feat

[Snownine]

I was thinking of making the Savage Attacker feat apply to every attack a character makes or, perhaps, all of those made with the attack action instead of only once per turn. Do you think that this would make the feat worthwhile enough to be worth the ASI? It does not need to be the best feat of all time, just good enough to where it is not a total trap option. What are your guy's feelings?

[Kane0]

Rerolling each attack rather than one is a good step forward, but what i’m currently doing is:

Savage Attacker:
- Once per turn when you roll damage for a melee weapon attack, you can reroll the weapon's damage die and use either total
- When you have advantage on a melee weapon attack and both rolls would hit you can roll one additional weapon damage die

[OldTrees1]

Allowing advantage on each weapon dice roll is going to have the biggest impact on 2d6 and 1d12. If I did my math right that is an average of +1.94 or +1.99 damage per attack. Basically +1d3 damage.

I expect a feat to be worth a level's worth of features. An ASI grants +1 to ability checks, saves, attack, and damage.

Since having advantage on a weapon die is such a small advantage, even assuming the right weapon and it applying all the time, I suggest improving the feat further by asking the Player what they want. For example Kane0 must like rolling a handful of dice, so they added an extra +1d12 if they have advantage. Another player might be looking for something else.

[Edea]

"Whenever you roll damage for a weapon attack made with advantage, you can reroll the weapon's damage dice and use either total."

[Snownine]

Allowing advantage on each weapon dice roll is going to have the biggest impact on 2d6 and 1d12. If I did my math right that is an average of +1.94 or +1.99 damage per attack. Basically +1d3 damage.

I expect a feat to be worth a level's worth of features. An ASI grants +1 to ability checks, saves, attack, and damage.

Since having advantage on a weapon die is such a small advantage, even assuming the right weapon and it applying all the time, I suggest improving the feat further by asking the Player what they want. For example Kane0 must like rolling a handful of dice, so they added an extra +1d12 if they have advantage. Another player might be looking for something else.

Could I possibly ask you to explain how you arrived at the +1.94 and +1.99 figures? I was trying to figure out the expected damage increase myself before I asked on here but did not know how to go about it. That kind of stuff is, sadly, not my forte.

[OldTrees1]

Could I possibly ask you to explain how you arrived at the +1.94 and +1.99 figures? I was trying to figure out the expected damage increase myself before I asked on here but did not know how to go about it. That kind of stuff is, sadly, not my forte.

Well initially I did the math for if you had to accept the 2nd roll. That worked out to be +X/8 on a 1dX*. However Savage Attacker is advantage on the weapon damage. So I just plugged that into anydice and copied the averages.


ADVANTAGE: [highest 1 of 2d12]
output 1dADVANTAGE - 1d12


ADVANTAGE: [highest 1 of 2d6]
output 2dADVANTAGE - 2d6

Edit: However we can do the real math quickly to double check.
Advantage on a 1d4 changes it from
1, 1, 1, 1
2, 2, 2, 2
3, 3, 3, 3
4, 4, 4, 4
to
1, 2, 3, 4
2, 2, 3, 4
3, 3, 3, 4
4, 4, 4, 4

So we can see an average for a 1d4 with advantage is (1*1 + 3*2 + 5*2 + 7*4)/(4^2)
(1x1 + 3x2 ... (2(X-1)-1)*(X-1) + (2X-1)*X)/(X^2)
(1/X2) * Sum from 1 to X of (2N-1)N
(1/X2) * Sum from 1 to X of 2N^2 - N
(1/X2) * ( 2(Sum from 1 to X of N^2) - (Sum from 1 to X of N) )
(Sum from 1 to X of N) = (X)(X+1)/2
(Sum from 1 to X of N^2) = (X)(X+1)(2X+1)/6
(1/X2) * ( 2(X)(X+1)(2X+1)/6 - (X)(X+1)/2 )
(1/X2) * (X) * (X+1)* ( 2(2X+1)/6 - 1/2 )
(1/X) * (X+1) * ( (4X+2)/6 - 3/6 )
1dX with advantage has an average of (1/X) * (X+1) * (1/6) * (4X-1)
1dX has an average of (X+1)/2
The difference is (X+1)(X-1)/(6X)
2d6 has a gain of 2 * (7*5)/36 = 70/36 =1.9444...
1d12 has a gain of (13*11)/(6*12) = 143/72 =1.986111...


* Math for the wrong effect = +X/8 on a 1dX (when X=2N. Does not work on 1d3)

I did the math with average of 1dX where X=2N.
But the arithmetic is clearer with an example of a 1d6.
Average of 1d6 = (1 + 2 + 3 + 4 + 5 + 6) / 6
Average of reroll 1d6 = (1d6 + 1d6 + 1d6 + 4 + 5 + 6)/6
~= (3.5 + 3.5 + 3.5 + 4 + 5 + 6)/6
= (1+2.5 + 2+1.5 + 3+0.5 + 4 + 5 + 6)/6
= Average of 1d6 + (0.5 + 1.5 + 2.5)/6
Gain = (0.5 + 1.5 + 2.5)/6 = (1 + 3 + 5)/(3*4)
= (3^2)/(3*4) = 3/4 = 6/8 = X/8
I actually did the math with average of 1dX where X=2N.

[clash]

I have changed it to "if you roll less than half of the maximum on a weapon die it counts instead as half the maximum."

[OldTrees1]

I have changed it to "if you roll less than half of the maximum on a weapon die it counts instead as half the maximum."

Average of new 1d6 = (3+3+3+4+5+6)/6 = (2+1+0)/6 + Average of old 1d6
Average of new 1dX (where X=2N) = Average of old 1dX + (1/X)(N-1)(N)/2
= Average of old 1dX + (X-2)/8
Gain on a 2d6 = +1 damage
Gain on a 1d12 = +1.25 damage

An ASI is probably quite a bit stronger unless the player strongly prefers consistency.

[Frogreaver]

Why not just let it add +1d6 damage to an attack once per turn?

[Snownine]

Well initially I did the math for if you had to accept the 2nd roll. That worked out to be +X/8 on a 1dX*. However Savage Attacker is advantage on the weapon damage. So I just plugged that into anydice and copied the averages.





Edit: However we can do the real math quickly to double check.
Advantage on a 1d4 changes it from
1, 1, 1, 1
2, 2, 2, 2
3, 3, 3, 3
4, 4, 4, 4
to
1, 2, 3, 4
2, 2, 3, 4
3, 3, 3, 4
4, 4, 4, 4

So we can see an average for a 1d4 with advantage is (1*1 + 3*2 + 5*2 + 7*4)/(4^2)
(1x1 + 3x2 ... (2(X-1)-1)*(X-1) + (2X-1)*X)/(X^2)
(1/X2) * Sum from 1 to X of (2N-1)N
(1/X2) * Sum from 1 to X of 2N^2 - N
(1/X2) * ( 2(Sum from 1 to X of N^2) - (Sum from 1 to X of N) )
(Sum from 1 to X of N) = (X)(X+1)/2
(Sum from 1 to X of N^2) = (X)(X+1)(2X+1)/6
(1/X2) * ( 2(X)(X+1)(2X+1)/6 - (X)(X+1)/2 )
(1/X2) * (X) * (X+1)* ( 2(2X+1)/6 - 1/2 )
(1/X) * (X+1) * ( (4X+2)/6 - 3/6 )
1dX with advantage has an average of (1/X) * (X+1) * (1/6) * (4X-1)
1dX has an average of (X+1)/2
The difference is (X+1)(X-1)/(6X)
2d6 has a gain of 2 * (7*5)/36 = 70/36 =1.9444...
1d12 has a gain of (13*11)/(6*12) = 143/72 =1.986111...


* Math for the wrong effect = +X/8 on a 1dX (when X=2N. Does not work on 1d3)

I did the math with average of 1dX where X=2N.
But the arithmetic is clearer with an example of a 1d6.
Average of 1d6 = (1 + 2 + 3 + 4 + 5 + 6) / 6
Average of reroll 1d6 = (1d6 + 1d6 + 1d6 + 4 + 5 + 6)/6
~= (3.5 + 3.5 + 3.5 + 4 + 5 + 6)/6
= (1+2.5 + 2+1.5 + 3+0.5 + 4 + 5 + 6)/6
= Average of 1d6 + (0.5 + 1.5 + 2.5)/6
Gain = (0.5 + 1.5 + 2.5)/6 = (1 + 3 + 5)/(3*4)
= (3^2)/(3*4) = 3/4 = 6/8 = X/8
I actually did the math with average of 1dX where X=2N.


Thanks a lot for taking the time to break that down for me, I really appreciate it. Sorry for the late reply, I have not had much opportunity to get on here for awhile. I think I am just going to let a player that decides to take it get advantage on every attack role, I think that is the only way to make it competitive enough with an ASI or another feat to really feel worth it.

[Mjolnirbear]

Here were my changes:


1x per attack
If you bring an enemy to 0, you may make an additional attack as a bonus action.
Once per short rest if you are at less than half your maximum health, you may take an additional action, which may only be used to attack (a kind of limited action surge or Haste action).


The changes were partly to increase the strength of the feat and partly to make the feat live up to the word 'savage'.

Right now I'm testing it on the moon druid in the party. They just reached level 5. Until this point it has felt very strong, but I know that it's at least due to the fact that moon druid at this level is very strong. And the third point has happened only a couple of times, because of moon druid 'temp hit point' deal. I have to focus the druid down to accomplish it, so in the interests of not being unfair I space these attempts out a great deal and spread them among my other players too.

[Kane0]

Thanks a lot for taking the time to break that down for me, I really appreciate it. Sorry for the late reply, I have not had much opportunity to get on here for awhile. I think I am just going to let a player that decides to take it get advantage on every attack role, I think that is the only way to make it competitive enough with an ASI or another feat to really feel worth it.

Do note that this helps fighters the most and rogues the least, just to keep in mind.

[bid]

So we can see an average for a 1d4 with advantage is (1*1 + 3*2 + 5*2 + 7*4)/(4^2)
FYI, the average for the lowest dice of 2d4 is (1^2 + 2^2 + 3^2 + 4^2) / 4^2
{It becomes obvious if you invert your pyramid in the spoiler.}

For the same reason, lowest of 4d6 is (1^4 + 2^4 + 3^4 + 4^4 + 5^4 + 6^4) / 6^4

In case you need that in the future.:smallbiggrin:

[OldTrees1]

FYI, the average for the lowest dice of 2d4 is (1^2 + 2^2 + 3^2 + 4^2) / 4^2
{It becomes obvious if you invert your pyramid in the spoiler.}

For the same reason, lowest of 4d6 is (1^4 + 2^4 + 3^4 + 4^4 + 5^4 + 6^4) / 6^4

In case you need that in the future.:smallbiggrin:

:smallbiggrin: That is correct and does make it easier. Cutting each layer of the pyramid instead of each radius of the square.