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Wizard is currently concentrating on a spell. Wimpling has a -1 Strength modifier, and makes a melee attack on Wizard. The attack hits, but Wimpling rolls a 1 on the damage roll, meaning that after applying his Strength modifier, he deals 0 damage.

Per the SRD, Damage Rolls (and in more recent Player's Handbook printings):

With a penalty, it is possible to deal 0 damage, but never negative damage.

From the Spellcasting chapter, Concentration:

The following factors can break concentration:

Taking damage. Whenever you take damage while you are concentrating on a spell, you must make a Constitution saving throw to maintain your concentration. The DC equals 10 or half the damage you take, whichever number is higher. If you take damage from multiple sources, such as an arrow and a dragon’s breath, you make a separate saving throw for each source of damage.

But I'm not sure if "dealing 0 damage" means that the target "takes damage". Does Wizard need to make a Constitution saving throw to continue concentrating on the spell?

I'd prefer official sources or references if available. If there aren't any, then I would accept any semi-official or well-informed well-reasoned arguments, preferably backed up by whatever evidence is available.

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No saving throw is triggered

I found two relevant Q&A twitter posts from Jeremy Crawford (the Lead Designer and Managing Editor for DnD 5e) that shed some light on this. Per the Sage Advice Compendium, Jeremy can make official rulings on Twitter.

Question:

if a raging barbarian makes no attack, but takes one damage that is reduced to zero, does rage drop?

Answer:

Taking 0 damage is the same as taking no damage.

If you took no damage, you didn't take any damage.

Taking 0 damage does not count as taking damage, therefore it shouldn't trigger any effect conditioned upon taking damage.

I also found a specific example of a different effect that triggers on damage (in this case, drow poison from the DMG):

Question:

If the Battlemaster maneuver parry, reduce the weapon Drow damage to zero, the poison damage still work ?

Answer:

Drow poison in the DMG is delivered by piercing/slashing damage (0 dmg = 0 poison).

To me, this lays out a clear line of logic. Dealing damage applies drow poison. If you deal 0 damage, it does not apply the poison according to Jeremy Crawford. Therefore, dealing 0 damage does not count as dealing damage for effects that trigger on dealing/taking damage. This would logically include concentration checks.

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    \$\begingroup\$ It's also an be important distinction between activating on a hit or on damage. If no damage was supposed to be a trigger, they'd just use on a hit. \$\endgroup\$ – NautArch Dec 15 '17 at 20:01
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    \$\begingroup\$ Note that JC's rulings on twitter are not official and that the SAC is official - they should not be used interchangeably. \$\endgroup\$ – Akixkisu Mar 18 at 17:52
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    \$\begingroup\$ @Akixkisu: As of this answer's writings, Crawford's tweets were official per the 2017 Sage Advice Compendium, which is why it says what it does. The phrasing should be updated since Crawford's tweets are no longer official rulings as of the 2019 SAC, as you point out. \$\endgroup\$ – V2Blast Mar 18 at 21:33
  • \$\begingroup\$ @V2Blast exactly. \$\endgroup\$ – Akixkisu Mar 18 at 21:37
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No concentration saving throw is required.

Fifth Edition strives to use natural language whenever possible. This was a stated design philosophy from the writers of the game. From the D&D Podcast, Jan. 2017 at approximately the 11:39 mark, Lead Designer Jeremy Crawford says:

"This is a general principal in our rules. If the rules do not specifically add meaning to an English word, or take meaning away, or completely change the meaning it simply means what it means in idiomatic English"

Web searches on "5e" "design philosophy" and "natural language" will turn up many other hits, and Crawford and Mearls will often use similar language when answering rules questions.

In this case, "0 damage" is the functional equivalent of "no damage". The saving throw is not contingent on being hit, but upon taking damage. Since "no damage" was taken, no saving throw is required.

Keep in mind that the rules allow a DM to impose saving throws for other circumstances. From the same section:

The DM might also decide that certain environmental phenomena, such as a wave crashing over you while you’re on a storm—tossed ship. require you to succeed on a DC 10 Constitution saving throw to maintain concentration on a spell

It is unlikely that Wimpling is sufficiently distracting, but a DM could require a saving throw whenever he feels it appropriate to the circumstance. In the case of straight out damage though, Wizard is safe.

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    \$\begingroup\$ Do you have a citation, even a citation for a similar case where 0 becomes not at all, or is this an example of "ought"? \$\endgroup\$ – Yakk Dec 15 '17 at 18:35
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    \$\begingroup\$ @Yakk, There are other answers on this page now that give examples. I won't add them to mine since the other answerer is answering the question in a slightly different way, and I don't see the need to inflate this one. \$\endgroup\$ – keithcurtis Dec 15 '17 at 19:28
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A saving throw is triggered

Damage Rolls [..] You roll the damage die or dice, add any modifiers, and apply the damage to your target.

Hit Points [..] Whenever a creature takes damage, that damage is subtracted from its hit points. (PHB 196)

The case of damageValue=0 is not called out as an exception anywhere and produces no contradiction. Thus RAW you can take 0 damage, and it should trigger any effect that depends on taking damage.

In the scenario you mention, it could be described as the weakling waving his arms in the wizard's face quite annoyingly, thus distracting him.

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    \$\begingroup\$ If I take 0 apples from you have I taken any apples? Similarly, if I take 0 damage from you, have I taken any damage? I don't think it needs a specific call out. 0 is NULL. \$\endgroup\$ – LegendaryDude Dec 15 '17 at 17:09
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    \$\begingroup\$ @LegendaryDude That is the competing interpretation, yes. I urge you to write a competing answer :) \$\endgroup\$ – Szega Dec 15 '17 at 17:28
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    \$\begingroup\$ @LegendaryDude to be super-pedantic, I think the relevant construction would be "if I take 0 apples from you have I taken apples?" It's the distinction (possibly without a difference) between taking no apples and not taking apples that seems (to me) to be at play. \$\endgroup\$ – nitsua60 Dec 15 '17 at 19:58
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Taking 0 damage is still taking damage: the saving throw is triggered.

The Sage Advice Compendium clears up that taking 0 damage still counts as taking damage and thus interrupts your concentration.

It is possible to deal 0 damage - which is dealing damage as opposed to not dealing damage. Damage requires a target that receives it, so dealing 0 damages means that someone has to receive 0 damage which is still receiving damage.

Sage Advice Compendium V.2.3 (11):

Can damage be reduced to 0 by resistance or another form of damage reduction? There is no damage minimum in the rules, so it is possible to deal 0 damage with an attack, a spell, or another effect.

Dealing 0 damage might sound strange because the outcome is that you are at the same Hit Points (PHB 196) that you have had before:

Whenever a creature takes damage, that damage is subtracted from its hit points.

But this is merely from a mathematical mindset, from a plain English standpoint you still take damage (and subtract it). That your hit point total doesn't have to change is emphasised by looking at receiving damage to temporary hit points Sage Advice Compendium V.2.3 (13):

If I have 10 temporary hit points and I take 30 damage from an attack while concentrating on a spell, what is the DC of the Constitution save to maintain my concentration? The DC is 15 in that case. When temporary hit points absorb damage for you, you’re still taking damage, just not to your real hit points. In contrast, a feature like the wizard’s Arcane Ward can take damage for you, potentially eliminating the need to make a Constitution saving throw or, at least, lowering the DC of that save.

So unless a game effect specifically calls out that it absorbs damage like the Arcane Ward does (PHB 115) or changes the recipient like the Aura of the Guardian (XGtE 39) et cetera eliminating the need to make a saving throw, then you still need to make a saving throw even when the damage does not change your actual hit points.

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  • \$\begingroup\$ @Medix2 this is a raw answer, not guessing at intentions. The THP supports the argument that there is no need of change in your actual hp required for you to take damage while also addressing absorbing damage and showcasing that those kinds of effects are always explicit which targets arguments that would go against that reasoning. The 0 damage quote is necessary to define whether all damage that is 0 is not taking damage or taking damage (it is the latter). Taking damage is by tautology taking damage. \$\endgroup\$ – Akixkisu Apr 7 at 11:38
  • \$\begingroup\$ Why is that relevant? Because the point of contention is whether taking 0 damage is taking damage or not - as that is the relevant information required for triggering the DC 10 saveing throw. My argument is: taking any damage, even 0 damage = taking damage. But I'm open to be convinced, if you may tell me what about this you think is incorrect. \$\endgroup\$ – Akixkisu Apr 7 at 12:03
  • \$\begingroup\$ Okay that males more sense now. Still seems like a rather strange argument to suddenly be making and I don't really see the support because if I receive zero apples I simply did not receive apples. The rules use standard English and if somebody told me "I received zero dollars, thus I received money" I would be bewildered. I honestly disagree with the claimed tautology that taking zero damage means you took damage at all. I can eat zero apples without eating apples, and so forth \$\endgroup\$ – Medix2 Apr 7 at 13:02
  • \$\begingroup\$ @Medix2 that is a faulty analogy. Taking damage is a binary state, you either take damage or you don't take damage; It is possible to take 0 damage by raw. The amount of damage merely doesn't change your life total. While you either eat or don't eat apples, you can also eat 0 apples, for instance, two bites. If you don't eat apples, then you don't. There is no 0$ banknote, but if there was one you could easily receive that banknote. \$\endgroup\$ – Akixkisu Apr 7 at 13:22
  • \$\begingroup\$ @Medix2 A better analogy would be someone hits you on the head, but lucky you wear a helmet, and they are pretty weak - there is no arguing that they hit you, but usually, you care little about that, but damn is it annoying. \$\endgroup\$ – Akixkisu Apr 7 at 13:22

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