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Barding Inspiration has this rule (PHB page 33, emphasis mine):

...you use a bonus action on your turn to choose one creature other than yourself within 60 feet of you who can hear you. That creature gains one Bardic Inspiration die, a d6. [...] the creature can roll the die and add the number rolled to one ability check, attack roll, or saving throw it makes.

If I roll an 18 and get a 2 or more on my Bardic Inspiration die, do I get a critical hit?

Note: This question was inspired by a ruling made by Jeremy Crawford that Cutting words can cancel a critical hit. He then later changed his mind, as explained in a different question. The answer to this question is still accurate, however (though it might require rewording), so I decided to keep everything here for posterity.

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No, Bardic Inspiration can't cause a critical hit

Cutting Words states, "...subtract the number rolled from the creature's roll.", so the number is being applied to actually change what you rolled on the d20.

Bardic Inspiration states, "add the number rolled to one ability check, attack roll, or saving throw", so the number is just another bonus on the attack roll.

The difference in phrasing is very small but important here. Terms like, "attack roll", "saving throw", "ability check", are common phrases in 5e used throughout the book. PHB, p.195, explains that you make an attack roll by rolling a d20 and adding appropriate modifiers. If it weren't for the Jeremy Crawford tweet it would be sensible to assume that the, "roll", in Cutting Words refers to the, "attack roll", but that tweet exists so instead it refers to the actual roll of the d20. Bardic Inspiration specifically says, "attack roll", so we can be relatively certain that it is just another modifier added to the roll.

The spell Bless uses the same phrasing as Bardic Inspiration, "...and add the number rolled to the attack roll or saving throw", and there is no reason to believe that it grants (or bizarrely prevents) critical hits.

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    \$\begingroup\$ Fun fact: what you said would be "sensible to assume" was actually the main argument of my answer to the related question. Considering it garnered 17 upvotes before Derek found that tweet (at which point I deleted my answer), most people probably assumed the same thing. Hopefully your clarification puts that issue to rest :) \$\endgroup\$ – DaFluid Dec 11 '15 at 8:18
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    \$\begingroup\$ @DaFluid I still think your reading of Bardic Inspiration makes more sense. The JC interpretation with, "roll", meaning the actual d20 roll is quiet a strange way of reading the rules. I'm curious what other shenanigans you could get up to by applying it universally. Alas, our gods are still with us. \$\endgroup\$ – Ceribia Dec 11 '15 at 8:35
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    \$\begingroup\$ Note: Crawford deleted the tweet the question is referencing and made a followup tweet stating that Cutting Words can't nullify a critical hit (as the answer that the question links to was then edited to clarify). \$\endgroup\$ – V2Blast Sep 3 at 6:07
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    \$\begingroup\$ @Akixkisu: If you mean the original ruling, I agree - it was pretty obviously wrong. and I'm not sure what Crawford was thinking when he made it. If you mean the corrected ruling... The corrected ruling matches how every other modifier to attack rolls in the game works, so there's nothing to errata; that's already how it works. \$\endgroup\$ – V2Blast Sep 3 at 13:07
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    \$\begingroup\$ @V2Blast ah yes, that sounded ambigious, I agree with you. \$\endgroup\$ – Akixkisu Sep 3 at 16:39
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Option 1 - Yes

If I roll an 18 and get a 2 or more on my Bardic Inspiration die, do I get a critical hit?

No. If you roll 2 you get a critical hit: your roll is 20. If you roll 1, 3, 4, 5 or 6 you don't: your roll is 19, 21, 22, 23 or 24 respectively and critical hits only happen on a 20 (barring Superior Critical in which case the 19 is one too).

If the d20 roll for an attack is a 20, the attack hits regardless of any modifiers or the target’s AC. In addition, the attack is a critical hit, as explained later in this chapter.

Note that this does change your chance of a critical, if you roll lower than 20 but within range, the Bardic Inspiration can get you there. An interesting effect, however, is that as the Bardic Inspiration die increases in size your chance of getting a critical decrease with this method.

If it helps, for both Cutting Words and Bardic Inspiration, think of the roll as the two dice together. Just like rolling 2d8 or 3d6 is a single roll.

Option 2 - No

Upon further consideration I am not at all happy with option 1.

Going back to the really, really fundamental rules about the d20 onp.7 of the PHB:

2. Apply circumstantial bonuses and penalties. A class feature, a spell, a particular circumstance, or some other effect might give a bonus or penalty to the check.

Well, Bardic Inspiration is a class feature; its effect is therefore a circumstantial bonus, therefore it simply adds to the original roll without actually changing it.

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  • \$\begingroup\$ So if you roll a 18 and expend an inspiration die, you have 1/6 chance of seeing your roll turned into a critical hit, right? Once your BI die becomes a d8, that probability becomes 1/8 (12,5%) and later, with the d10, 10%... If we accept your reading, we accept the fact that bards get a weaker class feature (in terms of critical hit chances anyway) each time they upgrade their BI die. \$\endgroup\$ – Meta4ic Dec 11 '15 at 4:13
  • \$\begingroup\$ @Meta4ic Not really, if you copy+paste the anydice program to include d10 to d12s, it'll still yield 5% \$\endgroup\$ – daze413 Dec 11 '15 at 4:30
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    \$\begingroup\$ @daze413 If you roll both dice at the same time, yes. But since the use of the inspiration die is chosen after the result of the attack die is known, the BI has to be added afterwards, thus changing the odds of a crit. See : anydice.com/program/733f \$\endgroup\$ – Meta4ic Dec 11 '15 at 4:40
  • \$\begingroup\$ @Meta4ic you're using only 18s as the example when a bigger BI die would allow you to crit even when you rolled a 12, 10, and finally an given its progression \$\endgroup\$ – daze413 Dec 11 '15 at 4:45
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    \$\begingroup\$ The further case for this (is this question an included case or not?) is how a Champion Fighter might get 18, 19, or 20 roll thanks to a Bardic Inspiration. He'd get more critical hits when his Bard is around and able to use his Bardic Inspiration. At higher levels (15+), if he rolls a 14, the Bardic inspiration can get him to 18, 19, or 20 (Superior Critical) or a 19 or 20 (Improved Critical at level 3). \$\endgroup\$ – KorvinStarmast Dec 11 '15 at 13:59

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