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Critical hits are introduced in the PHB under "Attack Rolls":

If the d20 roll for an attack is a 20, the attack hits regardless of any modifiers or the target's AC. This is called a critical hit, which is explained later in this section.

Then, later in this section under "Damage Rolls":

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.

The fact that the rules on critical hits are divided in this way makes it difficult for me to find a clear rule that says that critical hits can only happen on hits that follow after making an attack roll. Differentiating between a successful attack and a hit is not merely a theoretical nitpick, but actually relevant, as e.g. this question shows: Does the Piercing Arrow of a multiclassed Arcane Archer fighter/Assassin rogue crit against surprised creatures?

So my question is: Is there something in the rules that allows us to infer for certain that only hits resulting from an attack in the mechanical sense (i.e. something that involves an attack roll) can be critical hits?

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Sort Of

While there is no clear rule saying a critical hit can only happen after rolling an attack, we do find that there is enough in the rules to make that almost always be the case, so far with published materials. We start by looking at what an attack is, we get:

If there's ever any question whether something you're doing counts as an attack, the rule is simple: if you're making an attack roll, you're making an attack. (PHB 194)

So, to attack, we roll an attack - most of the time (see below). Some spells do damage without an attack, but those are "Cast a Spell actions" not attacks. Then, if we look at what you quoted, we find that it talks solely about attacks:

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.

Critical on Hit Cases

There are some situations where auto-critical happens if you hit. Like:

  • Attacking an object with an adamantine weapon
  • Attacking an unconscious creature within 5 feet
  • Rogue's assassinate feature. There doesn't seem to currently be a way to get a critical hit without attacking

Attack or Hit Without Rolling

However, like mentioned in other answers, D&D 5e is a game of exceptions, and at some point the published material, or a homebrew, might allow an "auto hit attack" under some circumstances, that could in turn cause an auto-critical under the above circumstances.

  • Arcane Shot option Piercing Arrow from XGtE (and the draft version in the Unearthed Arcana for the same) with the under the auto-critical on hit would cause an auto-critical on failed saving throw, which would always be the case for an unconscious creature. All because of this one line:

    you don't make an attack roll for the attack

  • Shove and Grapple also don't require a roll, but what a "critical shove" or "critical grapple" would mean in this context isn't clear except that the shove or grapple would auto-succeed in the case that the save was, for reasons like unconsciousness, auto-failed.

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    \$\begingroup\$ There're non-attack-roll attacks for the UA arcane archer as well, I believe. \$\endgroup\$ Aug 31, 2020 at 19:11
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Such a rule must certainly not be the case

5e is an exception-based rules system. It's founded on the idea that rules can define something as occurring in, even only in, certain circumstances, give that thing additional special properties, and then trust that despite that definition everything that calls itself that thing will in so doing acquire those properties without any consideration of the definition or the properties' effects. This is important because it makes the game modular, so a GM can throw out huge chunks of the game like what "an attack roll" is or the basic meaning and application of "an opportunity attack" and the game will have a good chance of remaining coherent across even third-party material.

Consequently, even if such a rule did exist, every feature granting automatic critical hits in the game would have to explicitly limit itself only to attack rolls in order to continue that restriction; "You can never critically hit without an attack roll" in the rules on attack rolls followed by "any attack you make with a trident is a critical hit" in a class, race, weapon description, spell effect, or any other content-level passage of rules would see the later bypassing the former (indeed, with such a wording you'd actually even crit on a miss).

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Yes, there must be an attack roll for the roll to be a critical hit.

To re-state the rules for a Critical Hit (emphasis mine):

If the d20 roll for an attack is a 20, the attack hits regardless of any modifiers or the target's AC. This is called a critical hit, which is explained later in this section.

From this, we can see that in order for an attack to be considered a crit, a 20 must come up on the die.

Now, of course, this is the general rule, and as we know, specific beats general. There are only two abilities that I can think of that modify how critical hits work, The first, is the Champion Fighters' abilities Improved Critical and Superior Critical, which state:

Beginning when you choose this archetype at 3rd Level, your weapon attacks score a critical hit on a roll of 19 or 20.

and

Starting at 15th level, your weapon attacks score a critical hit on a roll of 18–20.

Neither of these change very much, they just expand on what numbers count as a crit when you make an attack roll, and are fairly clear cut.

The second ability that changes how critical hits are scored, on the other hand, is much less clear cut. The Assassin Rogues' ability Assassinate:

Starting at 3rd level, you are at your deadliest when you get the drop on your enemies. You have advantage on attack rolls against any creature that hasn't taken a turn in the combat yet. In addition, any hit you score against a creature that is surprised is a critical hit.

This is where it gets sticky though, since it doesn't explicitly say "You need to make an attack roll to score a critical hit". But if we look into it a bit, we see something. You see, it requires that we score a hit against the target in order for us to automatically crit, and you can't score a hit without an attack roll.

But wait, if you need to make an attack roll, why can Assassinate crit with Piercing Arrow?

Well, that's because of one tiny clause in the rules for Piercing Arrow.

On a failed save, a creature takes damage as if it were hit by the arrow, plus an extra 1d6 piercing damage. On a successful save, a target takes half as much damage.

In other words, it is treated as though an attack roll had been made, even though one was not actually rolled. AFAIK, this is pretty much the only way to crit without an attack roll.

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Not explicitly but other features that grant a critical hit require an attack

the Unconscious condition, for example, says (PHB, 292)

Any attack that hits the creature is a critical hit if the attacker is within 5 feet of the creature.

the Assassin Rogue's Assassinate feature reads (PHB, 97)

In addition, any hit you score against a creature that is surprised is a critical hit.

"a hit" in the PHB is only ever used to refer to attacks1

In addition the Savage Attacks and Brutal Critical feature are both limited to criticals with a melee attack.

It seems clear from how features that grant and effect critical hits that critical hits were only intended to apply to attacks. That being said, if a feature were created that allowed a critical hit without an attack, it would not violate any specific rule. If I saw such a feature in a homebrew, however, I would recommend just saying "roll the damage dice a second time and use the sum of the two rolls" rather than introduce a new mechanic to critical hits.

1: Specifically "a hit" as a noun is used to refer to a successful attack whereas "hit" as a verb is also used in the case of Magic Missile.

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  • \$\begingroup\$ I think it may be helpful for you to link the concepts of "attack" and "attack roll" for this answer to be truly helpful in answering the question seeing as the "roll" part is specifically what is being asked here. But preemptive caution here too: there's no rule that says all attacks must have an attack roll source and some explicitly don't. \$\endgroup\$ Aug 31, 2020 at 22:07

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