Would the Savage Attacker feat deal more expected damage than an ASI?

Question

An ASI to Strength has many additional benefits above just increasing your chance to hit by and damage: it increases your carrying capacity, it helps you with Strength saving throws, it makes all your Strength based skill checks better, including Athlethics which is used for grappling or for climibing to avoid possibly deadly falls.

The feat Savage Attacker has only one function:

Once per turn when you roll damage for a melee weapon attack, you can reroll the weapon’s damage dice and use either total.

So for it to make sense to pick this feat at any time before you have maximized your Strength score already, I think it would need to clearly deliver more expected damage than a straight-up increase in Strength.

Does Savage Attacker reliably deal more damage than an ASI, and if so, under which circumstances?

Answer 1

Savage Attacker Outperforms an ASI In Certain Special Circumstances

Quick Note

Savage Attacker may not "reliably deal more damage than an ASI" in most cases, but Savage Attackers can make you "deal damage more reliably than an ASI" assuming you have a good chance to hit.

I am working on a program to calculate other statistics besides mean/median damage (such as 1st/5th/10th percentile damage) as part of a pet project comparing the reliability of different builds. Savage Attacker is actually much better at improving your (practical) damage floor than your average damage. The reroll raises these metrics by much more than it improves the mean.

As you can see on the chart below, it can be up to a 200% increase in 5th percentile damage for 1d10 and 1d12 (the damage equivalent of rolling a 1 on a d20, frequent enough to come up once per session or so), and the increase remains a sizable fraction of overall weapon damage even for very large dice rolls (7d10, from a Goristro's Gore attack)

5th Percentile Outcome

Weapon	Normal	Savage	Difference
1d4	1.0	1.0	0.0
1d6	1.0	2.0	1.0
1d8	1.0	2.0	1.0
1d10	1.0	3.0	2.0
1d12	1.0	3.0	2.0
2d4	2.0	4.0	2.0
2d6	3.0	5.0	2.0
2d8	4.0	6.0	2.0
2d10	4.0	8.0	4.0
2d12	5.0	9.0	4.0
3d6	6.0	8.0	2.0
3d8	7.0	10.0	3.0
3d10	8.0	13.0	5.0
3d12	10.0	15.0	5.0
4d6	8.0	11.0	3.0
4d8	10.0	14.0	4.0
5d8	14.0	19.0	5.0
7d10	26.0	33.0	7.0

I'd argue one major reason you might choose to take this on a martial character early is because your accuracy/average weapon damage is already good enough for the challenges you're facing, and you want to mitigate the impact of bad damage rolls, especially with high variance weapons. This is especially the case with Gish builds that don't exclusively rely on weapon attacks: they can cast spells or cantrips vs high AC enemies, so they're unlikely to attack enemies that are hard to hit in the first place. They just want to make sure when they do hit something it actually hurts.

Looking only at Average Damage undersells the impact of this feat where its impact is highest. That said, the question is about average damage, so lets look at the cases where Savage Attacker actually does win by that metric.

Savage Attacker Average Damage can be Higher in Certain Cases

ASIs are better than Savage Attacker in most cases, however here are some example characters who do more damage with Savage Attacker vs increasing their Strength (or Dex):

1. Any character with abundant accuracy and Flametongue. The 2d6 from Flametongue are weapon damage dice, and increases the gap between "reroll weapon damage 1x per turn" and "+1 damage per attack". With very high accuracy and/or crit chance, this gap can outweigh +1 to hit.
2. Melee Rogue with Elven Accuracy: Elven Accuracy significantly increases the likelihood of a critical hit and diminishes the value of base accuracy boosts. Rogues only attack 1x per turn anyways, but try their best to guarantee it is with advantage.
3. War Domain Cleric: War domain are incentivised to use weapon attacks between casting levelled spells via Divine Strike class feature, although they never get Extra Attack. With plenty of spell options to use against high AC enemies and Guided Strike available to save misses against creatures they do think it's worth attacking, the value of additional accuracy is negligible, and damage reroll 1x per turn beats +1 damage 1x per turn.
4. Any class supported by Peace Cleric. With 2d4 (average 5) added to accuracy between Bless and Emboldening Bond, the value of additional accuracy is greatly diminished, and the difference between Savage Attacker's damage boost vs a flat 1 damage is magnified.
5. Druids who wild shape. (ASIs for physical stats don't matter in wild shape, Savage Attacker is certainly better than nothing)
6. Wizards or Druids who use the Shapechange spell to deliver beatdowns in melee (ASIs for physical stats don't matter in wild shape, Savage Attacker is certainly better than nothing)
7. Bladesinging Wizards who use Shadow Blade (4d8-5d8 base weapon damage by the time they've maxed INT and are deciding whether to go for DEX or Savage Attacker) and can reliably use it in dim light for advantage. Advantage minimizes the benefit of accuracy, while high base weapon damage maximizes Savage Attacker's potential.

The Impact of Savage Attacker

Some PCs can get access to weapons well beyond their starting equipment quite early in their career, certainly before attack stats are typically maxed at level 8 (or later if multiclassing delays ASIs)

Below is the numerical benefit to raw average damage, extended to include things like oversized weapons (2d12, Large Greataxe, available to Rune Knight or any PC that can cast Enlarge/Reduce), (3d12, Huge Greataxe, available to Rune Knight w/Enlarge/Reduce cast on them), Giant Elk Hooves attack (4d8, accessible to druid at level 6), shadow blade (2d8 at Wizard level 3, 3d8 by level 5, 4d8 by level 9), etc.

Single Attack

Weapon	Normal	Savage	Difference
1d4	2.5	3.13	0.62
1d6	3.5	4.47	0.97
1d8	4.5	5.81	1.31
1d10	5.5	7.15	1.65
1d12	6.49	8.49	1.99
2d4	5.0	5.89	0.89
2d6	6.99	8.37	1.38
2d8	9.01	10.85	1.84
2d10	11.02	13.32	2.3
2d12	12.99	15.79	2.79
3d6	10.5	12.17	1.68
3d8	13.51	15.75	2.25
3d10	16.5	19.34	2.83
3d12	19.51	22.91	3.4
4d6	14.0	15.93	1.93
4d8	18.0	20.6	2.6
5d8	22.5	25.4	2.9
7d10	38.49	42.8	4.31

If you use it intelligently, Savage Attacker does scale (somewhat) with extra attacks. The following chart was made using the following strategy: If the first attack's damage roll <= the expected damage for the attack, use the reroll immediately. Otherwise, use the reroll on the second attack. This can be especially relevant for Bladesinging wizards, who are likely to get high level spells before they're thinking about using an ASI for anything except INT, and who use Shadow Blade for very high base weapon damage.

Two Attacks

Weapon	Normal	Savage	Difference
1d4	5.0	5.87	0.88
1d6	7.0	8.35	1.35
1d8	9.0	10.82	1.82
1d10	11.01	13.28	2.27
1d12	13.0	15.74	2.74
2d4	10.0	11.17	1.17
2d6	14.0	15.83	1.83
2d8	18.0	20.47	2.47
2d10	22.01	25.11	3.1
2d12	26.01	29.75	3.74
3d6	20.99	23.28	2.29
3d8	27.0	30.06	3.05
3d10	33.0	36.84	3.84
3d12	39.0	43.61	4.61
4d6	27.99	30.58	2.59
4d8	36.0	39.48	3.48
5d8	45.01	48.94	3.94
7d10	77.01	82.84	5.83

The Trivial Cases: ASI doesn't improve damage

This is a somewhat trivial case, but it can come up even if your primary attack stat isn't maxed yet.

Gauntlets of Ogre Power

If you encounter the uncommon magic item Gauntlets of Ogre Power in tier 1 play, taking Savage Attacker represents an immediate damage boost at level 4. Taking an ASI to make your raw Strength from 16-18 makes no immediate impact, and will only improve your damage if you invest a second ASI into Strength at level 8.

The same logic applies if you took a different feat at level 4 (such as Polearm Master or Great Weapon Master): taking Savage Attacker at 8 would be sensible if you have Gauntlets, rather than taking the 16->18 ASI at that point, or if you got both Polearm Master and Great Weapon master then taking Savage Attacker at 12 is probably better than an ASI that won't benefit you until 16.

Similarly, if you find the rare/very rare/legendary Belt's of Giant's Strength, all STR ASIs do is free up an attunement slot if you take enough of them. The value of that attunement slot may or may not be worth more than Savage Attacker, but many games won't have 4+ "must attune" items.

Wild Shape

Circle of the Moon druids use the statistics of the beast they Wild Shape into. ASIs cannot improve the damage of their Wild Shape form, and neither can go-to damage feats like Crossbow Expert, Great Weapon Master, or Polearm Master. Several Wild Shape forms have attacks that greatly exceed 2d6. Even as early as CR 2, Giant Elk has a 4d8 attack against prone targets, several dinosaurs have 3d6 or 2d10 attacks, and 2d8 is common not unusual (Giant Constrictor Snake, Rhinoceros, etc.).

Shapechange

Any druid or wizard who has already maxed their casting stat and is thinking it might be fun to use ShapeChange and mix it up in melee occasionally could benefit from Savage Attacker. Savage Attacker would apply to many valid Shapechange forms where an ASI would be useless. Other damage feats are more restrictive in what Shapechange targets they work with (creature must be capable of wielding weapons).

A Bladesinging Wizard should probably dedicate ASIs at 4 and 8 to INT (16->18->20), 12 to DEX (16->18). At level 16 though, there's a compelling argument for a feat that works with both Bladesinging as well as Shapechange forms (which become available only 1 level later at 17, and also have sweet synergy with Extra attack), instead of an ASI that only affects their normal form.

As one example, Goristro has a massive 7d10 (with 7d10 bonus damage) single attack if you choose to charge + Gore. Assuming all attacks hit, Savage Attacker increases your damage per turn by 4.3, or 5.8 if you are a Bladesinging Wizard with Extra Attack and gore twice.

High Accuracy/Big Weapon Dice/No Extra Attack

Outside of the trivial cases, there are multiple builds that involve weapon attacks which could benefit from damage rerolls more than an ASI. Typically these are NOT straight fighters/rangers/barbarians though. Savage attacker does scale with # of attacks (although typically worse than an ASI, see table above). However ASIs scale better with those extra attacks, so Savage Attacker is at its relative best when only a single (relevant) attack is made per turn.

Races with High Accuracy

Elves w/Elven Accuracy

Classes and Subclasses

• Cleric subclasses with Divine Strike (War Domain, Forge Domain, etc.)
• (Any) Rogue, but especially Assassins (auto criticals on surprised enemies makes the reroll much bigger) and Arcane Tricksters (Shadow Blade)
• Wizards under the influence of: Shadow Blade (big weapon damage + advantage), Tenser's Transformation (gives advantage), Shapechange (big weapon damage), etc.

Magic Items

• Flametongue
• Dragon's Wrath Weapons
• Frost Brand
• Gauntlet of Ogre Power
• Belt of Giant Strength (any)

Gishes

Characters who have good combat options outside of attacking don't mind that Savage Attacker is primarily good against low ACs. Against high AC targets, they are going to be targeting saving throws anyways. Since they will only attack when the enemy has low AC or they have advantage anyways, Savage Attacker becomes much better relative to an ASI.

In addition to Blessed Warrior Paladin builds fall into this category despite having Extra Attack. With cantrips as a reliable attack option, such Paladins can attack only when they have a very good chance of hitting and may take Savage Attacker over a STR increase after maxing CHA.

I've mostly tried to stick to single class builds here, as the possibilities when multiclassing can become ridiculous, but many multiclass builds could also fall into this category.

Conclusion

If you have sizeable accuracy boost, advantage, no extra attack, bigger than usual weapon dice, and alternative combat options for enemies with high AC, Savage Attacker will outperform an ASI for maximizing melee weapon damage. Actually doing the math for a specific character is the only way to know for certain which is better for them, but the more of these boxes you tick the more likely it is Savage Attacker wins out. The default assumption should always be "ASI is better" however, especially since ASIs do have benefits outside of damage.

One example would be a level 8 elven arcane trickster Rogue with Elven Accuracy (taken at level 4) using Shadow Blade who is supported by a Peace Cleric. 1 attack, ridiculous accuracy (easy triple advantage from shadow blade), ineligible to use GWM or Crossbow Expert, and base weapon damage of 2d8.

The easiest way to think about accuracy boosts is to consider them directly modifying enemy AC. If your accuracy goes up by 6 (+2d4 from Peace Cleric and +1 from a magic weapon), that's equivalent to reducing enemy AC by 6, and as @Nobody the Hobgoblin's answer shows, lower ACs are where Savage Attacker outperforms ASIs to begin with.

Answer 2

No, an ASI outperforms Savage Attacker on most levels

The numerical benefit to raw average damage from the feat is:

Weapon	Normal	Savage	Difference
1d4	2.5	3.13	0.63
1d6	3.5	4.47	0.97
1d8	4.5	5.81	1.31
1d10	5.5	7.15	1.65
1d12	6.5	8.49	1.99
2d6	7	8.37	1.37

The expected damage is that, times the to-hit probablity against AC plus the contribution from critical hits. The higher the AC, the lower the expected additional damage will be.

For the contribution from a critical hit (as crit damage works with Savage Attacker, while Sneak Attack damage does not.) I use a critical chance of 5% to simplify. The contribution is minor with at most 0.1 points of damage; if you had additional features that increase the crit chance, like a Champion fighter, it could increase to 0.2 or 0.3 points.

The damage contribution from an ASI also depends on the hit chance. Your normal expected damage is:

n * h * (D+M) + c * D

where n is the number of attacks, h is your chance to hit in %, D is the average damage from the dice (replaced with D' in case of savage attacker), M is the fixed damage modifier from your stat bonus, and c is the chance to crit. With an ASI this changes to n * (h+1/20) * (D+M+1) + c * D. Advantage and Disadvantage influence h and c, respectively, depending on the number you need to roll.

Monsters with an AC of worse than 8 are exceedingly rare (many of them are monsters that want to be hit, like Oozes that split, or Gas Spores that explode). Likewise, monsers with an AC above 20 are extremly rare (mostly a few ancient dragons and demon lords), so we will focus on that range of ACs.

For this answer we'll assume a character starts with a maxed starting Strength or Dexterity of 16, which typcially is the case for melee builds, for a +3 inital ability bonus. They also will have a proficiency bonus of +2, for a total of to hit of +5. That means, a roll of 3 or better to hits AC 8, up to a roll of 15 to hit AC 20 is of interest. At the tier where AC 20 foes are common, your proficiency bonus will be higher, as the average expected to hit remains around 65% throughout play.

We calcluate the expected damage for a single attack, once with the improvement from the ASI, and once with the improved D' from Savage Attacker, and then measure the difference at each target number to hit.

Here is how the damage contributions break down in comparison, for a d12 weapon, the one that is most favourable for Savage Attacker. Positive numbers are additional expected damage in favor of Savage attacker. Bold is the number you need to roll for 65% hit chance, that is, for your typical or average level-adequate opponent.

Target to Roll	Normal	Advantage	Disadvantage
3	0.5	1.1	-0.2
4	0.4	1.0	-0.2
5	0.4	1.0	-0.2
6	0.3	0.9	-0.3
7	0.3	0.8	-0.3
8	0.2	0.7	-0.3
9	0.2	0.6	-0.3
10	0.1	0.5	-0.3
11	0.1	0.4	-0.3
12	0.0	0.3	-0.3
13	0.0	0.2	-0.3
14	-0.1	0.1	-0.3
15	-0.1	0.0	-0.2

For a single attack, Savage Attacker is of advantage for low-AC opponents. At the initial +5 to hit contributing a bit under half a point of damage for Zombies and the like, dwindling to no benefit around AC 17 and turning negative at very high ACs. The benefit for a typical opponent is only 0.2 points over an ASI. If you had a reliable way to gain advantage (for example, from being a mounted combatant against foes smaller than your mount) it would do a little better, ranging from a full point to no benefit.

If we instead switch the weapon to a d8 weapon, then Savage Attacker would be worse across the entire range under normal conditions. With a d10 weapon, it would be slightly positive (0.2 to 0.1 points) at low ACs up to 11, and worse from AC 16 on up.

However, Savage Attacker only works once per turn. As soon as you get multiattack at level five, the beneficial effect from ASI gets added to two attacks per turn, doubling the contribution (which in absolute terms is larger than one half point of damage on each attack). When that happens, Savage Attacker's damage output will be worse even under the most beneficial setup with a d12 weapon, unless all you do all day is fight AC8 Zombies with Advantage.

As you normally only get the feat at fourth level, that means you may be doing ever so slightly better for exactly one level, and be behind the rest of your career. The exception is when you pick variant human and can pick one feat at first level, then you would have that benefit for four levels.

So, I think it is save to say that in general Savage Attacker is not better than an ASI for damage, and way worse overall. The damage advantage, even in the best case scenario, is trivially small and short-lived, too. The only possible use I see for it is to take it either after you have maximized your ability score already, or maybe if you know your campaign is only tier one, and you are playing a variant human. In that case, if you are looking for damge, one of the combat feats that give you bonus action attacks, such as Crossbow Expert or Polearm Master, will do more for you.

Obviously, if you are not looking to optimize, and are looking to pick thematic feats for your character, then based on the name it can be a flavorful choice for a wild barbarian, orc or other "savage" fighter.