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I'm a bit confused on how extra damage works for critical hits. Let's take the following example:

A thief with sneak attack rolls a crit. I'm under the impression he rolls double his normal attack dice AND double his sneak attack dice. Is this accurate?

Another example, I finished DM-ing my first campaign recently. The Giant Spider enemy monster has an melee attack that causes a constitution saving throw. If the player fails, the enemy rolls an additional 2D8 of damage. In this situation, if there was a critical hit, and the player failed their saving throw, would I also roll double dice on the additional damage? Or is that considered a separate attack?

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    \$\begingroup\$ @Vylix I've refunded the bounty. Its text was "Need to explicitly include how it works for Booming Blade, Greenflame Blade, extra damage from spells and feats, like Hex, Colossus Slayer, etc". Bounties aren't for major scope additions to a question — the "improve detail" reason is about getting answers to answer the question more fully on the question's own terms. If you want explicit explanation of these mechanics, please ask about that separately. \$\endgroup\$ – doppelgreener Jul 5 '18 at 17:35
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From the Player's Basic Rules:

Critical Hits

When you score a critical hit, you get to roll extra dice for the attack’s damage against the target. Roll all of the attack’s damage dice twice and add them together. Then add any relevant modifiers as normal. To speed up play, you can roll all the damage dice at once.

For example, if you score a critical hit with a dagger, roll 2d4 for the damage, rather than 1d4, and then add your relevant ability modifier. If the attack involves other damage dice, such as from the rogue’s Sneak Attack feature, you roll those dice twice as well. (PHB, p. 196; BR, p. 75)

The example given answers your first question perfectly.

For the spider, the secondary damage is from poison, so is not inherently part of the attack. This can be seen by the fact that the damage doesn't depend on the attack roll, but a separate saving throw.
Critical hits represent hitting a vulnerable area. With poison, it doesn't really matter where you are hit.

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    \$\begingroup\$ I would add that some people double the damage rather than rolling extra dice. The very nice analysis here suggests why one should roll the extra dice. \$\endgroup\$ – KevinO Apr 27 '16 at 23:52
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    \$\begingroup\$ Ah, my apologies. I did not mean to suggest you should update your answer; I can see where the language would suggest that. I was merely attempting to note that the extra damage from a critical hit should be rolled, and not merely doubled. I apologize for any confusion in my word choice. \$\endgroup\$ – KevinO Apr 28 '16 at 14:25
  • \$\begingroup\$ Yes, saving throw. I'll see if I can find a specific quote (unless someone else beats me to it) \$\endgroup\$ – Adeptus Jan 3 '18 at 22:03
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You only roll extra dice for effects that explicitly add the damage to the attack.

I have not found an definitive statement in the PHB that addresses this question. However, I think that we can draw reasonable conclusions by interpreting the text that we do have.

We know that sneak attack damage is doubled on crits, so let's look at the wording: (PHB 96)

Once per turn, you can deal an extra 1d6 damage to one creature you hit with an attack if you have advantage on the attack roll.

So the wording there is "extra" damage.

Looking at divine smite (PHB 85):

...when you hit a creature with a melee weapon attack, you can expend one paladin spell slot to deal radiant damage to the target, in addition to the weapon’s damage.

The key wording here is "in addition to the weapon's damage". Similar wording appears in the various smite spells, such as thunderous smite (PHB 282):

...and the attack deals an extra 2d6 thunder damage to the target.

Likewise, monsters use similar wording. The Revenant, for example (MM 259):

If the target is a creature against which the revenant has sworn vengeance, the target takes an extra 14 (4d6) bludgeoning damage.

Therefore, we can conclude that we double any dice that are "added to the attack" or any "extra damage," and not any secondary effects.

Any damage resulting from a failed saving throw is not doubled.

There's a Jeremy Crawford tweet that addresses this issue as well: any damage from a saving throw is not doubled:

Any damage dice delivered by a critical hit—as opposed to a saving throw—are rolled twice.

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    \$\begingroup\$ This doesn't answer the question. This is your interpretation of the given phrases. The OP is looking for a particular line in the rules that explains the correct interpretation, not looking for the correct interpretation. So when you say "we can conclude," you're offering conjecture (which is almost definitely correct), rather than evidence (quotes from the rules). The quote you do provide is about saving throws, not attacks. Saving throws do not get critical hits, so they're not what the OP is asking about. \$\endgroup\$ – Bloodcinder Sep 7 '17 at 21:40
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    \$\begingroup\$ I find this to be an effective minor frame challenge, in that it can be understood from the rules and doesn't need a meta-source to actually solve the problem, despite the question assuming so. \$\endgroup\$ – SevenSidedDie Sep 7 '17 at 21:45
  • \$\begingroup\$ the question is not assuming the need for a meta source but will accept them. I was hoping for something I missed in the actual rules. much how "origin" is defined for the purpose of spells in the magic section, I was hoping there was somewhere that what is and is not part of the attack is defined. I appreciate this answer and I find it to be far more insightful than most. but the purpose of the question is still to find a definitive source if any is available. \$\endgroup\$ – Daniel Sep 8 '17 at 0:41
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    \$\begingroup\$ @Daniel but the purpose of the question is still to find a definitive source if any is available And if one is not, then what? That tweet comes from an official WoTC source, though I did check and noted that that particular tweet was not folded into the Sage Advice Compendium. Have you considered sending a tweet to Crawford yourself? Plenty of people do. \$\endgroup\$ – KorvinStarmast Sep 8 '17 at 1:26
  • \$\begingroup\$ @KorvinStarmast I understand that there may not be a definitive source. but I seriously hoped that there was. I do not have twitter. so sending a tweet directly isn't an option from my end. thank you for your help keeping this question clear. \$\endgroup\$ – Daniel Sep 8 '17 at 1:33
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In general, this is messy and is left to the DM to adjudicate. There have been rulings for some of these, and others they refused to answer because they aren't sure if the RAW needs to be changed or not and are still examining the question themselves. So, the overall answer, the "What counts as part of the attack" here is as clear as mud. And additions to the Errata are rare on purpose, so don't expect it getting cleared up anytime soon.

They have stated in tweets that they don't fear or mind large spikes in dealing damage, but frown on large sustained gains to dealing damage.

Sneak Attack

Yes, it is part of the attack.

Any dice that are part of an attack's damage are rolled again on a crit.

https://twitter.com/JeremyECrawford/status/530139178869075968

Divine Smite

Can a Paladin hit with a crit, and then choose to use smite and double all his dice? Yes, it is part of the attack.

Yep!

https://twitter.com/JeremyECrawford/status/664986819830767617

Poisons

Here we get into the weeds. It isn't clear because what they intended and what made it into the books differs.

The intent is no. The saving throw, not the attack, determines whether the poison takes effect after a hit.

https://twitter.com/JeremyECrawford/status/536683487517224961

The intent is no, but what is the ruling? Well, there isn't one:

I'm not ready to give the official answer, since this is part of my potential-errata analysis.

https://twitter.com/calebrus44/status/569938380428939264

Perhaps because that was in 2015, and no poison additions were made, we are to expect that poison RAW is doubled, even though RAI it is not.

Saving Throws

See poison's messy situation in my section on Poison. I think the same is true there: RAW yes, RAI no.

Other Smites

I've not seen this one answered, and looking at it I don't see how it would be different from a normal smite, but it COULD be looked at in the same light as poison.

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  • \$\begingroup\$ There is also the spell Ice Knife, from the Elemental Evil supplement, that involves both a to-hit roll that can crit and a saving throw for half-damage against its secondary effect (but the secondary damage is contingent on a successful hit); Same situation as monsters with poison attacks. \$\endgroup\$ – eyecosahedron Jan 3 '18 at 16:04
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The authors have repeatedly stressed that the words mean what the words mean in natural language.

So, what does "involves" mean? The first answer at dictionary.com is,

1. to include as a necessary circumstance, condition, or consequence; imply; entail:

So, is the attack a necessary condition for rolling the dice? Is rolling the dice a consequence of the attack? If so, then roll the dice twice on a critical hit. If not, then don't.

A paladin can't smite a target unless they hit, so the attack is a condition of the smite. A giant spider cannot poison a target unless they hit, so the poison damage is a consequence of the attack. A saving throw is made to reduce the poison damage, but that damage is still a consequence of the attack.

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