In a mathematical comparison of the Half-Orc Savage Attacks trait and the Elf/Half-Elf feat Elven Accuracy (XGtE, p. 74), which one increases average damage more at level 10 for a Fighter-Champion 5 / Warlock 5?

The Monster Manual (p.245) has a specific section about Orc Crossbreeds. It states that:

. . . they readily crossbreed with other races. When an orc procreates with a non-orc humanoid of similar size and stature . . . the resulting child is either an orc or a half-orc.

As a result it is forbidden to have a character that is half-orc/half-elf, as such a child would simply be a half-orc and use those rules as written. Therefore only one of the following benefits would be achievable via race (RAW).

The description of Savage Attacks says:

When you score a critical hit with a melee weapon attack, you can roll one of the weapon’s damage dice one additional time and add it to the extra damage of the critical hit.

The description of Elven Accuracy says:

  • Increase your Dexterity, Intelligence, Wisdom, or Charisma score by 1, to a maximum of 20.
  • Whenever you have advantage on an attack roll using Dexterity, Intelligence, Wisdom, or Charisma, you can reroll one of the dice once.

I would like a mathematical comparison of these two situations at level 10:

A Half-Orc Champion 5 / Warlock 5 using a Greataxe +1 (1d12 Slashing +1) as a weapon with a +4 bonus from Str. This character benefits from Savage Attacks and the Great Weapon Fighting fighting style from Fighter level 2.

A Half-Elf Champion 5 / Warlock 5 using a Rapier +1 (1d8 Piercing +1) as a weapon with a +4 bonus from Dex. This character received the Elven Accuracy feat at level 4 and the Dueling fighting style from Fighter level 2.

In both cases:

  • The character can Critical Hit on a 19-20 due to the archetype ability for Champion at 3rd level.
  • The character can attack twice per Attack Action from Extra Attack at fighter level 5.
  • The character has advantage (on average) for 50% of their attacks. (If you need a reason, they are within 5' of their prone target, or they are attacking a target their Barbarian/Path of the Totem Warrior - Wolf at level 3 - ally is within 5' of, or they have Darkvision 60' as per their race and they are attacking a target in non-magical darkness who is Blinded due to a lack of Darkvision - take your pick.)
  • The target is subject to the Warlock Spell Hex which causes an extra 1d6 necrotic damage on hit.
  • The target is Challenge 10 and has 16 AC.

My preliminary analysis is that the former hits much harder on Critical hits, with the ability to re-roll damage dice due to both Savage Attacks and Great Weapon Fighting. They also do a lot more damage on non-crits due to having larger damage dice.

With the latter scenario they do less damage and are unable to re-roll damage dice but crit much more often, because they can roll three d20s on advantage instead of two.

I am also curious about two similar situations: a critical range of 18-20, or a 1d10 finesse weapon (as mentioned in comments).

I would really enjoy an analysis similar to what was provided here: Does the Resilient (Con) feat or the War Caster feat most improve the chances of maintaining concentration?

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    – V2Blast
    May 8 '20 at 7:29

Fighter/Champion level 3 (critical on 19-20)

Savage Attacker is better because elves/half-elves can't take a feat until they get an Ability Score Improvement at 4th level.

Fighter/Champion level 15 (critical on 18-20)

As described using a Heavy weapon, Savage Attacker is better because Heavy weapons do not use Dexterity, Intelligence, Wisdom, or Charisma and cannot benefit from Elven Accuracy.

However, if you want to compare the best GWF weapon (1d12) with the best finesse or ranged weapon (1d8) then Savage Attacker is clearly better unless the attack has advantage because Elvan Accuracy doesn't work unless it has advantage. It's also better when there is advantage. How much better? Assuming an AC of 18 (normal for a CR15 creature) and a +10 to hit (+5 proficiency, +5 stat bonus):

\$ \begin{array}{c|c|c} \text {Expected Damage}& \text{Disadvantage} & \text{Normal} & \text{Advantage} \\ \hline \text{Savage Attacker} & 3.50 & 7.11 & 10.72\\ \text{Elvan Accuracy} & 2.00 & 3.60 & 6.04\\ \end{array} \$

Fighter/Champion level 15 (critical on 18-20)/ Warlock 5 (Hexblade w/- Pact of the Blade)

Now we can benefit from GWF and Elvan Accuracy at the same time. We can use the same program because even though the proficiency is now +6, CR20 monsters have 19 AC.

\$ \begin{array}{c|c|c} \text {Expected Damage}& \text{Disadvantage} & \text{Normal} & \text{Advantage} \\ \hline \text{Savage Attacker} & 5.13 & 10.43 & 15.73\\ \text{Elvan Accuracy} & 4.89 & 8.79 & 14.75\\ \end{array} \$

Savage Attacker is still better.


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