When is an ASI better than the Dual Wielder feat?

Many people ask questions about dual wielding (even though two-weapon fighting is subpar for everyone after level four). Most of them seemingly can't wait to pick up the Dual Wielder feat (PHB, p. 165).

Is the Dual Wielder feat really better than an ASI (Ability Score Improvement) for DPR?

Ability Score Improvements are almost always better for DPR

Calculation

On 4th level you could raise your attack stat from 16 to 18, or take Dual Wielder. I will assume you have the Two-Weapon Fighting style, while fighting against AC 10, 14 and 18. Criticals are also included in the final DPR.

Base DPR:
Damage 2 x (1d6+3) = 13
AC10: Hit chance 80%, 10.75 DPR
AC14: Hit chance 60%, 8.15 DPR
AC18: Hit chance 40%, 5.55 DPR

ASI:
Damage 2 x (1d6+4) = 15
AC10: Hit chance 85%, 13.10 DPR
AC14: Hit chance 65%, 10.10 DPR
AC18: Hit chance 45%, 7.10 DPR

Dual Wielder:
Damage 2 x (1d8+3) = 15
AC10: Hit chance 80%, 12.45 DPR
AC14: Hit chance 60%, 9.45 DPR
AC18: Hit chance 40%, 6.45 DPR

You can look at it this way, the damage is the same, as on average 1d6+4 = 1d8+3, but after the ASI you have higher hit chance.

Other considerations

Dual Wielder gives you +1 AC too, but if you are Dex primary, an ASI gives you the same, and +1 save, +1 skills, +1 initiative.
If you are Str primary the ASI is much less helpful in this regard. (But in this case you could just take Great Weapon Fighting, for significantly higher DPR)

Dual Wielder lets you draw two weapons without sacrificing an action. This can be important in cities, but in the wilderness and dungeons you can just run around with one of your weapons already drawn.

Exception

Take Dual Wielder if the only magic weapon you have is unusable without Dual Wielder (because it's not light).
+1 to attack and damage from a magic weapon plus the increased die size is better in itself, but if you consider all the monsters resistant or immune to mundane weapons, it is the highest priority.

Conclusion

You should only pick Dual Wielder if:

• the only magic weapon you have is unusable without Dual Wielder
• you can't keep at least one of your weapons in your hand when you expect a fight
• you cannot pick an ASI, because
• you are a Variant Human on 1st level
• Comments are not for extended discussion; this conversation has been moved to chat. – mxyzplk Oct 21 '17 at 2:43
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Two reasons to take the feat over a Dexterity boost:

1. You frequently use double throwing weapons and want to be able to "reload" both hands in one turn, or frequently start ranged and then close in for melee.

RAW does not allow for drawing two weapons in one turn (with a single "free object interaction"). Generally, this is only relevant for one turn, but it is an early turn which makes it important because (a) some combats are short and (b) because downing enemies at the beginning improves your side's advantage in the action economy.

2. You are bothered, from an RP perspective, that the only extensively developed real world forms of dual wielding (rapier with dagger fighting and the much rarer rapier with rapier fighting) can't be replicated in game without this feat.

This is something you may be able to work out with your DM without the feat since rapier(1d8) and dagger(1d4) is the damage equivalent of double short swords(2d6), and it really doesn't make sense that two hands can not draw two weapons when two-weapon fighting is generally available, and is also a fighting style for Fighters and Rangers.

• Downvoted: first point was already discussed in András' original answer and second point is out of the question's scope (RP perspective doesn't matter as question addresses only to DPR). – AntiDrondert Jan 18 '19 at 7:43
• Double throwing is bad for you, parting with your magical weapons twice faster. – András Jan 22 '19 at 20:26