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Do monster special abilities default to CON if no ability stat is mentioned? And therefore increase when they are summoned with the augment summoning feat?
For example the Babau protective slime (Su) special ability does 1d8 damage and has a reflex DC 18. It doesn't mention an ability stat, though the DC number suggests it is con based (DC10 + HD/2 + con bonus).
It looks like the sort of ability that should be Constitution based. Is it? Is the fact it is a Supernatural ability relevant?
Does that become 2d6 damage and DC20 with the +4 con bonus from augment summoning?
What happens if the monster does not have a con score?
Unless noted otherwise saving throw DC default to Constitution score for most (but not all abilities) that produce physical effects and Charisma for magical ones (and some that magically produce physical effects).
When the monster does not have a Constitution score it either uses its Charisma modifier or +0, depending upon monster and ability.
For Undead Cha replaces con, for Constructs I believe you treat them as having a con of 10 (no bonus or penalty).
Oh, and strictly reading RAW Augment Summoning won't increase saving throw DCs - it's a temporary bonus to Constitution, which, according to ability score bonuses does not affect Constitution-based saving throws (but it also means that temporary reduction of Con won't decrease saving throw DC).
FAQ regarding temporary bonuses and ability DCs
FAQ regarding what "temporary" ability score bonuses affect
It'd affect the saving throw DCs.
While the temporary ability score system was supposed to simplify management of temporary bonuses, it only made things worse. I think Paizo realized this and relented on the distinction between temporary and permanent.
The only meaningful distinction remaining between temporary and permanent bonuses is in things like bonus spells/rounds of rage/uses of channel energy per day. Those require a permanent bonus--which, not coincidentally, requires having the bonus for at least a day.
Benefit: Choose one of the creature's special attacks. Add +2 to the DC for all saving throws against the special attack on which the creature focuses.
Ability Focus only increases DCs as well. (Of course, making opponents fail saves for half damage is an effective way to increase damage.) The only way I know to directly increase the damage of such an ability is to rebuild the monster--at least, unless the monster description or ability description states how to scale the damage.
No, they dont default but generally physical attacks are based off of con but magical attacks are charisma based. Every monster should tell you what to use. If not the statblock is in error.
Owner - D20 Hobbies
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Do monster special abilities default to CON ?
B1 p292 defaults to Con or Cha depending on "a relevant ability modifier", so yes physical depends on Con.
I think Paizo realized this and relented on the distinction between temporary and permanent.
The only meaningful distinction remaining between temporary and permanent bonuses is in things like bonus spells/rounds of rage/uses of channel energy per day.
I don't think so, I think the written list was "for example" and not "just these". The temp boost won't help anything that would have been "set" in the morning (like spell slots, blah/day etc.)
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Owner - D20 Hobbies
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Babau's specific ability, the text suggests that either modifier is "relevant". (it is a Su ability that produces a physical effect)
I don't know of a rule that says Su = Cha. I was speaking more along the lines of this:
Posion, Entangle, Negative Levels, etc = CONDomination, Insanity, Charm = CHA