The importance of being a 20

sageadvice said:

http://www.sageadvice.eu/2016/01/26/does-the-savage-attacker-feat-apply-to-sneak-attack-or-divine-smite/

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yeah apparently not, my bad

mellored said:

When comparing savage attacker to +2 str you need to factor in to-hit. You do 0 on a miss.

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I see this argument a lot, but I get the feeling most people haven't actually run the numbers. Let's see what we get.

If we assume 20 attacks (roll a d20), then we can get the average damage over those 20 attacks by multiplying the hit chance by the average damage per attack. Average damage is pretty easy, just see my previous table. Hit chance is a rolling target, though.

In this case, let's assume this is a 4th level character looking at their first ASI. That would give them a proficiency bonus of +2. Let's also assume that they have 16 in their relative attack stat, giving them a +3 bonus. If they are attacking with a weapon they have proficiency with (which they should be), then they have +5 to hit.

Now for the AC of the monster they will be attacking. Let's assume a low end AC of 7. With a +5 to hit, anything lower will still have the same result (a natural 1 always misses). Same idea for the top end AC, giving us 26 (again a natural 20 always hits).

Two quick examples to illustrate the edge cases:
6AC; Rolls 1 +5 = 6; Rolling a 1 auto-misses
27AC; Rolls 20 +5 +1(ASI Str) = 26; Rolling 20 auto-hits

It's also worth nothing that even a Tarrasque only has 25AC, so 26AC and higher is not likely to be seen.

Now to the math:
Assuming a 10AC and +5 base to hit, Savage Attacker will hit 15/20 attacks; with an average damage of 11.4861 per attack (1d12+3) and 18.7861 per crit (2d12+3), attacking a target with 10AC has an average result of 9.5539 damage.
Assuming a 10AC and +5 base to hit, +2 Str will hit 16/20 attacks (+1 bonus to hit); with an average damage of 10.5 per attack (1d12+4) and 17 per crit (2d12+4), attacking a target with 10AC has an average result of 9.25 damage.
This means that +2 STR does 96.82% of the damage Savage Attacker does when the target has 10AC. See the below table for the numbers at each range.

+2 Str doesn't actually catch up in damage until the target has 17AC. For each +1 to hit beyond 5, take one step up the ladder (i.e +6 base to hit on 10AC would equate to the same as 9AC on the table). Interestingly enough, the reverse is (roughly) true for +1 to damage when calculating which gives a bigger increase. This means that every Proficiency increase will move the break point down one notch, so at lvl 17, Savage attacker would give you more damage when attacking anything with 20AC or less than +2 Str would. Of course, that also assumes that you still have the option to take +2 Str by then.

Now, admittedly I am using 1d12 to make this comparison, but that's because 1d12 is where Savage Attacker has the most impact. If you're planning on using a 2d6 weapon, then Savage Attacker probably isn't the way to go. In the above example, the break even point falls all the way down to 7AC. You run into a similar issue with Great Weapon Fighting Style.

<edited to account for critical damage>

I see this argument a lot, but I get the feeling most people haven't actually run the numbers. Let's see what we get.

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I've run some of the numbers 2d6, but not d12. Nice to see the full chart.

So yes, savage attacker does more damage on a d12 against low-mid AC targets.

Though, i think the non-attack benefits of +2 Str, still make it the better first choice. Take SA after you get 20.

mellored said:

I've run some of the numbers 2d6, but not d12. Nice to see the full chart.

So yes, savage attacker does more damage on a d12 against low-mid AC targets.

Though, i think the non-attack benefits of +2 Str, still make it the better first choice. Take SA after you get 20.

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%100 per correct. But the fun factor of getting out of horrible damage roll might shift it. I do think SA is limited though, if it applied to all dice it would be much better and more thematic, especially if you took the choice away i.e. you had to use the second roll. I will try it out this weekend using the choice rule and all dice reroll and see how it plays. I have a half-orc rogue that it might work well on.

So, I have to admit that I was being a bit lazy with my previous calculations in that I didn't include the value of crit damage into the average damage. This is in no small part because they can be a pain to calculate (square the number of possible results for a standard attack), but it needed to be said. Of course, having that sit in my mind overnight meant that I needed to fix it today.

The gist of the result is that the break point shifted down the chart, meaning Savage Attacker does more average damage on targets with 16AC or less at lvl1-4 with 16 Str. The rest of the conclusions remain the same (+1 damage, move up {roughly} one space; +1 to hit, move down one space). This also means that at +6 prof bonus, the break point moves to 20AC or less. I'll go back and update the previous table to reflect.

Also, I made some quick adjustments to look at how it compared when the Champion's Improved Critical range was through in. The break point moved to 17AC or less at +2 proficiency bonus and 21AC or less at +6 proficiency bonus. If you want, I can try posting those numbers as well. If I get really motivated, I might even try testing for the Half-Orc racial crit bonus, but seeing as there are almost 3 million possible permutaions (12^6), I may just end up being too lazy. We'll see...

*sigh* OK, so I'm probably a bit obsessed at this point.

I decided to check the numbers for crit on 18+ and the result is 22AC or less gets more damage out of Savage Attacker. This is the case if you're 16 Str or 18 Str (20 Str can't make the choice). I also did the calculations factoring in the Half-Orc racial:
For crit on 20 - 16AC or less (+2 proficiency)
For crit on 19 - 17AC or less (+2 proficiency)
For crit on 18 - 22AC or less (+5 proficiency)
For crit on 20 - 16AC or less (+2 proficiency, Half-Orc racial)
For crit on 19 - 19AC or less (+2 proficiency, Half-Orc racial)
For crit on 18 - 24AC or less (+5 proficiency, Half-Orc racial)

smbakeresq said:

... if it applied to all dice it would be much better and more thematic...

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Hold on, does SA apply to only one weapon die? Not both as in the 2d6 example?

Savage Attacker applies only to the weapon dice. If you use something like the rogue's Sneak Attack or the Paladin's Smite, you don't get to re-roll the values on those specific dice.

A common suggestion for "fixing" Savage Attacker is to let you re-roll all the dice for the ATTACK instead of just the dice for the weapon. However, from the calculations I've been doing, I don't think it would have nearly the effect most people believe. The more dice you roll, the closer you get to average for each. A good example of this is with the percentage increase calculations from my first table wrt 1d12 vs 2d6. Savage Attacker has a much larger impact on the d12 than the d6s. Frankly, it would lower the effectiveness of the feat to have it apply to more and more dice.

If you're really interested in making it better, the superior option would be to say that you may re-roll "any or all" of the dice. That way if you roll a 1 and a 6, you can choose just to re-roll the 1 and keep the 6.

Ah, now that makes more sense. I thought i had misread the feat. Thanks

Every class that would consider savage attackers gets multiple attacks. ASI is better if attacks > 1.

Also please note that smart use of savage attacker may actually make it better when considering multiple attacks than the chart would indicate.