There is no info on the hydra traits "multiple heads", so i'm trying to reverse engineer it, here are my thoughs.
Effective attack CR 8:
- Five attacks (1 per head), 10 damage each for an average of 50 damage.
- +8 bonus to hit
- Average damage is CR 7, but the bonus to hit scale it to CR 8
Effective defense CR 10:
Keeping in mind that regeneration effects are calculated for 3 rounds, I'm guessing that the game expects a 3 round combat, so the hydra is expected to take, at least, 1/3 of its life each round: 57 (172/3)
Multiple heads
Whenever the hydra takes 25 or more damage in a single turn, one of its heads dies. If all its heads die, the hydra dies. At the end of its turn, it grows two heads for each of its heads that died since its last turn, unless it has taken fire damage since its last turn. The hydra regains 10 hit points for each head regrown in this way.
My interpretation of this is that each time the hydra receives 25 damage it lose a head, because we're assuming that the hydra lose 57 health each round, 2 heads dies and 2 heads grows back. Therefor the hydra is regenerating 20 hp each round.
- 20 hp each round per 3 rounds = 60 hp. 172+60 = 232 effective hp
- AC 15
- Average hp is CR 11, AC reduces this to CR 10
This ends with an average CR 9, not a CR 8.
Things to keep in mind:
- Maybe its CR is a result of playtest.
- The multiple heads traits is ignored.
- My calculations of how much hp it loses each round doesn't include the hp regeneration. That would be 77 (232/3), or 3-4 heads dead each round.
My bet is that the hydra is expected to lose more than 2 heads each round, therefor the hydra lose attack power each round, so the Multiple heads is ignored, to some degree.
Are my calculations correct? How the trait "Multiple heads" is calculated?
Best Answer
In general the developers don't follow the CR calculation mechanics in the Dungeon Masters Guide. There were several articles that lead to the thought that they kind of just went with 'what felt right' and until the DMG came out we were expected to do the same.
In fact the DMG only has you calculate in HP, AC, save DC, and damage to figure out a challenge rating. So if the developers used this it ignores any special attacks or features that don't fall into one of those categories.
Its why ghouls are only CR 1 and Ghasts are CR 2, but in a small group can take down characters that are level 4+.
Also note that the DMG says after setting a CR you should play test the monster and adjust up or down from there. So again, they go with what it feels like it should be.
In other words the real answer is that there is not a set CR adjustment for the Hydra's heads. They simply went with what they felt like after play testing.