Heroism and Negative Temporary Hit Points.

[AdAstra]

An interesting thing I found with the Heroism spell: Unlike most rules that have caveats like (minimum of 1) or some such, Heroism has no such restriction. Thus, if your spellcasting ability modifier is -1, you would "gain" -1 temporary hitpoints. Theoretically speaking, if you rolled a 3 in Charisma (since only Bards and Paladins can get it) you could give a creature -4 temporary hit points at the start of every one of their turns.

Now, this is a pretty niche situation, but the question would be, what does it mean to have negative temporary hit points? In a particularly tortured reading, you could say that since damage cannot bring the THP to 0, you can never lose it, making you totally immune to damage. Perhaps you lose x hit points at the start of each of your turns?

What do you all think? Mostly I just think this is a funny interaction/area not covered by RAW.

EDIT: This site https://dnd5e.fandom.com/wiki/Heroism seems to have the (minimum of 1) restriction, but I've looked everywhere else and none of those places have this version, including the Player's Handbook and online Errata list. Considering how the site's version of the spell only gives advantage on saves against being frightened rather than immunity, I think it's safe to say that it's not actually what anyone's book says.

[Anymage]

"Minimum 1" sounds like a reasonable errata, that only hasn't been pushed because it hasn't been noticed and/or there isn't enough stuff to make an errata document worth putting out.

Strict RAW? Temp HP doesn't say anything about reaching 0, just that they absorb damage first as long as you have any left. -3 THP doesn't have any left to give, any more than someone with -$3 has any money left to give. As such, it's functionally identical to 0.

[Greywander]

Give yourself -1 temp HP.
Realize that temp HP is an unsigned 32-bit integer.
Temp HP overflows to 4,294,967,295 temp HP.
???
Profit!

[Lord Haart]

If it came up in an actual game, i'd rule that you get unconscious at 1 HP (or however many you have negative temps) instead of 0.

As a theoretical interaction, i don't think it's defined.

[ezekielraiden]

I would need to be convinced that negative temporary hit points are actually possible before considering what they would be capable of. They don't meet several of the descriptions given for THP (you cannot "lose" negative HP by taking damage, you cannot heal THP, etc.)

So yeah. I'd call it a pretty obvious minor oversight that leads to an obviously nonsensical result, hence, not actually a real thing. Like asking what the properties of a negatively charged proton (not an antiproton--a legit normal-matter proton, that has a negative charge) would be. Even though you can string that set of words together, it doesn't mean anything.

[Chronos]

It'd have a mass of 1232 MeV/c^2 (https://en.wikipedia.org/wiki/Delta_baryon), and a spin and isospin of 3/2.

So, about them negative temp HP...

[ezekielraiden]

It'd have a mass of 1232 MeV/c^2 (https://en.wikipedia.org/wiki/Delta_baryon), and a spin and isospin of 3/2.

So, about them negative temp HP...

That's...not a negatively-charged proton. Either it's not negatively charged (Δ+ is...clearly positively charged), and is a higher excitation state of a proton, or it is negatively charged (Δ-) but isn't a proton, as the Δ- and Δ++ particles have no nucleonic analogue. (Plus, a Δ- particle is made of different things than a proton--protons are uud, Δ- is ddd.)

But fine. You found an obscure way that my analogy fails if you squint hard enough and ignore enough. Congratulations, you win one whole Internet for a flippant, unhelpful answer only loosely correlated with reality, which doesn't detract from any of my other points--like how "negative THP" cannot be "lost first."

If you prefer a better example: vectors of negative magnitude. (Though I'll be honest, if you manage to find even one actual, legit scientific or mathematical paper/discussion that takes negative-magnitude vectors seriously, I will be impressed. I won't concede the point though.)

[AdAstra]

I would need to be convinced that negative temporary hit points are actually possible before considering what they would be capable of. They don't meet several of the descriptions given for THP (you cannot "lose" negative HP by taking damage, you cannot heal THP, etc.)

So yeah. I'd call it a pretty obvious minor oversight that leads to an obviously nonsensical result, hence, not actually a real thing. Like asking what the properties of a negatively charged proton (not an antiproton--a legit normal-matter proton, that has a negative charge) would be. Even though you can string that set of words together, it doesn't mean anything.

There is, at the minimum, precedent for the existence of negative numbers in 5e. Ability modifiers are the obvious examples. Addition and subtraction in the game can be assumed to work as they do in real life (barring order of operations which is explicitly different, addition/subtraction happening before multiplication/division). Abilities that explicitly add a modifier can indeed add a negative number.

HP is specified as being able to be any number between a creature's max HP and 0, so no negatives allowed there. Of course, Temp HP are treated as something different by the game.

Plus, there is the fact that most other abilities in the game designed to not allow negative numbers do so explicitly with things like (minimum of 1). Healing does not, but still is generally interpreted as not allowing negative healing, so I sincerely doubt the designers intended for Heroism to be left out, but from a RAW perspective the game just doesn't cover this.