How would giving Hydra a Breath Weapon affect game balance and CR?

Question

I wanted to spice up a fight I'm planning for my party by giving a Hydra a Breath Weapon. I'm flexible on the specifics, but the change would effectively be described as such:

Actions

Multiattack. The hydra makes as many bite attacks or frost breaths as it has heads, but only one per head.

Frost Breath (Recharge 5–6 each head). The hydra exhales an icy blast in a 30-foot cone. Each creature in that area must make a DC 12 Constitution saving throw, taking 14 (4d6) cold damage on a failed save, or half as much damage on a successful one.

I took the breath weapon statistics from the Young White Dragon, but I significantly lowered the DC and damage dice to accommodate for the Hydra being able to use it multiple times during a turn.

I am open to suggestions to make this more balanced, but as is, how would this modification affect the Hydra's CR?

Answer 1

Erik's answer gives a very good breakdown of CR for your hydra, but here's an alternative version of the ability:

Frost Breath (Recharge 5–6). The hydra exhales an icy blast from each head in a 30-foot cone.

Because, if nothing else, keeping track of the recharge for each head will be annoying for you as a DM. As the Dragon's Breath spell is a 15-foot cone, while the Young White Dragon is 30-foot (but can't multi-attack with it), you may need to consider reducing the cone for balance

Each cone may be aimed individually. Each creature affected must make a DC 15 Constitution saving throw, taking 3 (1d6) damage per cone that affects them on a failed save, or half as much on a successful one

This is a massive reduction in damage from what you suggested. However, here's an example of why I suggest it:

Ability as listed in Question
Your party is facing a 5-headed hydra. Unfortunately, they have just come through a doorway, and are all bunched together. Your hydra attacks! All 5 heads use their Frost Breath on the clustered party.
Every party member now has to make 5 different saving throws, and 20d6 (5 * 4d6) for damage - for every failed save, they take 4d6 damage (average 14), for every successful save they take half that (average 6)
This would then typically be anywhere from 30 (all 5 saved) to 60 (all 5 failed) damage.
(With all damage rolls 1, and all 5 saves made, this can be reduced to an absolute minimum of 10 damage to a character in 1 turn)
(With all damage rolls 6, and all 5 saves failed, this can be as high as an absolute maximum of 120 damage to a character in 1 turn)

versus

Ability as listed in Answer
Your party is facing a 5-headed hydra. Unfortunately, they have just come through a doorway, and are all bunched together. Your hydra attacks! All 5 heads use their Frost Breath on the clustered party.
Every party member now has to make 1 saving throw, and 5d6 (5 * 1d6) for damage - if they fail the save then they take 5d6 damage (average 17), for every successful save they take half that (average 8)
This would then typically be anywhere from 8 (saved) to 17 (failed) damage.
(With all damage rolls 1, and the save made, this can be reduced to an absolute minimum of 2 damage to a character in 1 turn)
(With all damage rolls 6, and the save failed, this can be as high as an absolute maximum of 30 damage to a character in 1 turn)

Your hydra can also split or focus the damage asymmetrically - dealing 5d6 damage to 1 cone, or 1d6 each to 5 different cones, or one cone of 2d6 and a second cone of 3d6, et cetera.

Answer 2

Probably between CR 9 and 14 depending on how clever your Hydra is - assuming you bring the save DC to 16, more in line with expectations.

The Hydra is a tricky beast to figure out balance for, due to its unreliable number of heads. However, if we look at the stats compared to the table, it seems that at least the base stats (ignoring the Multiple Heads mechanic) line up decently with a normal creature for its CR-1.

That is; you'd expect a balanced offense/defense CR 7 creature to have about AC 15, slightly under 175hp and deal about 50 points of damage with a +6 attack bonus. The attack bonus on a Hydra is slightly higher, but everything else lines up; so by that reasoning you can reasonably ignore its Multiple Heads mechanic when determining base CR and then bump its CR by 1 for having it.

Based on that logic, it's still hard to factor in your new attack, mostly because of the very low save DC. A DC 12 is lower than even the recommended DC for a CR 0 creature, which is so far below what the CR 8 of a regular Hydra that it's hard to compensate for.

If we bump the DC to the more reasonable DC 16 (which happens to line up nicely with 8 + prof + con mod for the Hydra) that matches roughly with its normal +8 attack bonus (both being the expected level for CR 8; or slightly above the CR 7 the other stats seem to line up with) then we can run some calculations.

Your attack deals 14 damage compared to the Hydra's normal 10, a clear increase. It's also a Cone, meaning you could potentially hit multiple characters with it; a 30ft Cone is pretty big.

The true challenge will depend heavily on how many characters you'll hit on average when using a breath weapon.

If this Hydra is smart or cunning (most aren't, but I don't know yours) then it could expect to easily hit 2 characters with each breath; that means it'll be able to bump its damage to 140 in the first round (5 breaths x 2 targets x 14 damage) and then be able to add extra breath attacks and bites for 106 damage over the next 2 rounds (roughly 2 breaths recharging x 2 targets x 14 damage + 3 bites x 10 damage).

That means an average of about 117 damage; bumping its offensive CR up to 19. If we average this with its defensive CR of 7, you'll end up with a CR 13 creature, or a CR 14 one if we add +1 CR for the Multiple Heads ability.

This will be one mean monstrosity, but also a major glass cannon compared to the original.

If you play the creature really dumb, and only target 1 character in each breath, your CR will come out closer to 70 (5x14) on the first round and around 58 (2x14+3x10) on the other rounds, which averages to 62. That's closer to CR 9, which averages to CR 8, which if we add +1 CR for the Multiple Heads ability means we'll end up at total CR 9.

That's nasty, but not a lot stronger. Keep in mind this is with bumping the save DC to a more respectable 16. I'm not sure how to account for a really low save DC here, it will probably prevent a lot of damage and make it quite a bit weaker, but I'm not sure by how much.

So if your Hydra spams breath weapons around in a way that each hits about one person, it'll be slightly tougher than a normal one, but not much so. If it is clever about targeting as many people as it can, it will probably wipe the floor with a party challenged by a normal Hydra.