# 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 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. 

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](https://www.dndbeyond.com/sources/dmg/dungeon-masters-workshop#Step11Damage) (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. They're probably using shadow Blade

### 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](https://www.dndbeyond.com/magic-items/4641-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](https://www.dndbeyond.com/monsters/17156-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
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

## Conclusion
If you have a sizeable accuracy boost, advantage, no extra attack, and bigger than usual weapon dice, 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.

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.