How many hit points does the UA Battle Smith Artificer's Iron Defender have?

Question

The Iron Defender's stat block for the Battle Smith Artificer (from Unearthed Arcana: The Artificer Returns), under "hit points" says the following:

equal to five times your level in this class + your Intelligence modifier + the Iron Defender’s Constitution modifier

I could read this two ways:

Way 1:

equal to five times (your level in this class) + your Intelligence modifier + the Iron Defender’s Constitution modifier

Or way 2:

equal to five times (your level in this class + your Intelligence modifier + the Iron Defender’s Constitution modifier)

Which of these readings is correct?

Answer 1

(5 × Level) + your Int + defenders Con

Interpreting equations like this isn't defined by the game rules and so we use the english meaning. Unfortunately, english (and most other languages AFAIK) isn't very good at it, which is a big reason for using mathematical symbolics. As a good rule; take the simplest reading as you scan through. This gives:

$$ 5 \times \text{Level} + \text{Your Int} + \text{Defender's Con} $$

which for anyone not fully comfortable with order of operations equals

$$ (5 \times \text{Level}) + \text{Your Int} + \text{Defender's Con} $$

If it were to mean

$$ 5 \times ( \text{Level} + \text{Your Int} + \text{Defender's Con} )$$

it should (in my opinion) been worded as (italics to emphasise change):

equal to five times the sum of your level in this class + your Intelligence modifier + the Iron Defender’s Constitution modifier

As additional support, the same problem of having such equations in D&D rules have appeared for Arcane Ward where lead designer Jeremy Crawford has chimed in on twitter (not official ruling, but gives what the intended meaning is) with the statement that

The ward has hit points equal to twice your wizard level + your Intelligence modifier.

should be read as:

its hit point maximum equals your Intelligence modifier plus twice your wizard level.

Meaning to be read as

$$ (2 \times \text{Level}) + \text{Int} $$

similar to that above.

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As an addendum: the final version of the subclass clarifies the calculation as:

equal the steel defender’s Constitution modifier + your Intelligence modifier + five times your level in this class

and this is how the feature is implemented in D&D Beyond. (Thanks to @Garret Rooney and @V2Blast)

Answer 2

It is likely interpretation 1, due to the initial HP difference between the two interpretations.

Assuming you go to level 20, here is the range of HP the defender could have under the 2 interpretations, with your Intelligence score assumed to be 18 (+4 modifier).

Interpretation 1: (5× Artificer level) + Intelligence modifier (4) + Iron Defender Constitution modifier (2) = 21 (5×3 + 4 +2) HP at level 3, to 106 (5×20 + 4 + 2) HP by level 20.

Interpretation 2: (5× Artificer level + Intelligence modifier [4] + Iron Defender Constitution modifier [2]) = 45 (5×[3+4+2]) HP at level 3, to 130 (5×[20+4+2]) HP by level 20.

As seen by interpretation 2, its HP would likely be higher than the Artificer themselves at first, and would be equal to an average of 2d10 + 4 HP per level, higher than any class.

Answer 3

The way it is printed, it's HP are calculated by (lvl×5) + 2(CON bonus) + (players INT bonus). As to whether the Steel Defender should have more HP then the Artificer, it's a guardian - it darn well should have more HP than what it's protecting. The fact that it might not seems off.

The formula looks off because it gets its CON bonus to HP only once, not per level like every other creature in the game. The only explanation I can come up with is that its hit dice are not equal to the Artificers level, like it seems it should be. It's a zero hit dice creature, but that just doesn't feel right.

Answer 4

When the Artificer was officially released, they reworded the formula for the Iron Defender's Hit Points as follows:

2 + your Intelligence modifier + 5 times your artificer level (the defender has a number of Hit Dice [d8s] equal to your artificer level)

The Iron Defender has a Constitution stat of 2, so this is equivalent to "way 1" as stated in the question.

Answer 5

The wording makes me say it is equal to your level times x 5 + your Intelligence modifier + the Iron Defender's Constitution modifier.
If it were the second option, it would have been worded more like this:

equal to your level times and your Intelligence modifier x 5 + the Iron Defender's Constitution modifier.