AD&D 1E XP Value for Monsters?

There. Done!
Hmm… I’m actually not liking all of this at all.

For one, all of it is based on at least two arbitrary decisions.

Many more than that. Regardless of which edition of D&D we are talking about, assigning a "challenge rating" and thus a reward to defeating a monster always involves a ton of arbitrary decisions starting in the 1e AD&D case with the numbers assigned to each line in the table. What you are going for is never objectively true numbers, but rather "good enough" estimates relative to other monsters that exist or you might design. That is, for whatever process you come up with, the only real test is: "If this monster X is by a reasonable standard harder/tougher than this monster Y, does X also yield a suitably larger reward than Y?" And you are never going to get there perfectly. All you can manage is to try to get close enough that any problems are not obvious.

I do appreciate though your attempt at rigor. I'd be interested to see if you could reverse engineer where I'm getting my revised dragons. Speaking of...

For two, calculating dragon xp is gonna be an even bigger headache that it already is, and not only because of the “special defense” mentioned in the red dragon example in the DMG (p. 85).

It's worse than that because dragons break all the rules normally applying to other monsters because of the rule about hit points/hit die. The basis of giving an award for a monster of a particular HD has baked into it an assumption that those hit points probably come in some reasonable range. Normally the hit points of the monster contribute only a relatively small portion of the reward because normally there isn't huge extreme differences in the amount of hit points needed to kill a monster, and the amount of hit points needed to kill a monster don't also determine many of its abilities. But neither of those things is true of 1e AD&D dragons with their special exceptions to all other rules. I would contend that an 10 h.p. monster is a lot easier to kill than an 80 h.p. monster; so much so that the table of rewards don't reflect the difference in this extreme of a case.

Because how many “major breath weapons” do dragons with multiple “major breath weapons” (e.g., gold dragon, silver dragon) have?

In general, because they can only use one at a time, I would tend to say that they only have one.

I can see why Appendix E says that Tiamat has 5 breath weapons, for they all inflict damage and they come from five different heads.

I would say that Tiamat has 5 breath weapons, but it might be a mistake to quintuple count them if you are also already giving her a multi-attack extraordinary ability since attacks are not useable with bites and employing multiple breath weapons might be seen as a parallel to multiple attacks. But then again, though I LOATHE the design of 1e AD&D Tiamat with a burning hatred and strongly suggest no one ever use it; if I were to use it, I might make an exception for Tiamat in that each of her breath weapons hits the rule for single attacks doing at least X damage and thus makes it worthy of an EAXPA x 5.

But then why doesn’t the pyrohydra have “breath weapons”? Because all of them generate the same effect?

No, but rather the same logic I just applied to Tiamat. Breath weapons are an alternative to bites, and the hydra is already getting the power of making multiple attacks counted. "Can make multiple attacks" and "Can do minor breath weapons" are here counting separate things, and recounting each breath weapon would be excessive.

Hydra though is unlike the dragons a really good case because the hydra's reward is intrinsically tied to hit dice so that there is no need to quadruple count a 16HD hydra's multi-attacks (4 instances of 4 or more attacks or 8 instances of a breath weapon or whatever) because the table itself has a built in assumption that most of the difficulty of a monster is intrinsically in its HD and that higher HD monsters generally bring along with them more extreme and powerful abilities and so the rewards of their extraordinary abilities and special abilities and base rewards are all also higher leading to no need to double count a 16HD breath weapon as twice that of a 8HD breath weapon. If the hydras number of heads weren't attached to its HD, then yes, we'd need extra counting to potentially differentiate 4 attacks from 8 or 12 or 16.

So, should they count for the amount of damage a monster can deliver in a single round?

I generally didn't. I saw this as double counting since a major breath weapon to me implied it met that rule or something similarly lethal. But again, this is all going to be subjective at some level. What's not important really is the rules you set, but rather that once you apply your judgment to each monster, you end up with a ranking of rewards that very closely matches a ranking of difficulty.
 
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Back to the table.... you have
Trying to avoid the “splitting” effects territory—and failing miserably

Breath weapon or major breath weapon?
DMG, p. 227: “Breath Weapon — Special attack of certain creatures like dragons, chimerae, etc. causing any of several different effects. For saving throw purposes the “Breath Weapon” category excludes petrification and polymorph results, which have their own category.
So what is a “major breath weapon”? Many things have been said about this, but there’s nothing conclusive in the MM, DMG, and PHB that I can find, with (possibly) two exceptions.

You are overthinking this.

The table (table 32 in the DMG) gives +2 dice equivalence to a breath weapon. Do that.
The table gives +1 dice to any singular attack doing more than 20 points damage. I'd argue that includes the breath weapon.
The table gives +2 dice equivalence to a being able to cause more than 30 points damage/round. I'd argue that includes the breath weapon.
 

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