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Does the save DC of a spell being concentrated on change if the caster's Int stat changes in the meantime due to polymorphing?
For instance, if a level 8 wizard with Int 16 casts Hold Person on someone, the save to stop being paralysed is 14.
If the target fails its first save, and then on the next turn, the wizard is polymorphed by another spellcaster into a T-Rex (with Int 2) that is still concentrating on the spell, is the save DC altered for the target's next save against Hold Person?
The spell DC is set at the time of the casting, it is not a dynamic feature of the spell. I would think of it like a poison - whose save DC would not change if the venomous creature were polymorphed after delivering the poison. The spell retains the potency it had at its application.
I can find no direct justification of this beyond the fact that changing DCs does not add to game balance and only complicates gameplay. 5e tends to be more streamlined, and tries to avoid dynamic changes mid-combat.
I don't think you can get a non-opinion based answer unless you ask Crawford of Mearls. I searched the PHB, Sage Advice, and the DMG. The various spell entries, combat rules and spell rules have nothing to say on this that I could find, unfortunately.
That said, it would not be the end of the world to do it the other way. Just a little more book keeping at the table.
There is no definitive answer. However, the general rule for calculating a spell save DC in the Spellcasting chapter of the PH/Player's Basic Rules/SRD is under the section called "Casting a Spell." This suggests that the DC is set at the time of casting. As there is a decided lack of any other evidence, this would seem to tip the scales in favor of the DC not changing.
The Wizard's save DC is stipulated as being calculated as:
8 + Int Mod + Prof. Bonus
The general save DC from the PHB is:
8 + Ability Mod + Prof. Bonus + Special Modifiers
The rules consistently do not indicate that this is static and indeed, are written algebraically to permit adjustments from increases to Int, leveling up that boosts proficiency (or finding a Mastery Ioun stone), or in this case being turned into a creature that would make a terrible Wizard.
The flip side of being turned into a T-Rex is a very high Con modifier, though. So while the victim of the Hold Person is likely to make their save on the next go around, the Wizard is unlikely to lose concentration due to being hit because of a likely increase to their Con. Bear in mind, this isn't all bad; the save happens at the end of their turn, so that's a chance to land some critical T-Rex damage!
There seems to be confusion on this as to whether or not this answer is an opinion. I will tell you that it's not intended to be. Though maybe providing some info on why I'm ruling that way would help.
A discussion on polymorph and the order of events that occurs during it is stipulated in this answer. Within the answer, it's stated that the Wizard's Constitution changes to match the creature they turned into and thus they make Concentration saves based upon that changed score. Order matters a great deal in that answer as there are discreet points wherein the Wizard is a Wizard and when a Wizard is a Giant Ape. Between those points, the ability scores are what they are.
The Polymorph spell clearly states that all of a creature's ability scores change to match the beast they turn into. This includes the bad with the good. One could use this to be all good by turning the weakened Fighter into a T-Rex and have him tear house by virtue of renewed HP and higher ability scores or have it be all bad by turning pretty much anything into a newt.
There is nothing in the rules, which stipulates that a Wizard maintaining concentration on a spell is permitted to negate one of the perks of polymorph, which is to alter your opponent's ability scores to something much more manageable. The benefits of using the spell in an offensive manner to reduce a raging Barbarian into a newt stem primarily from a drastic reduction in physical stats; the benefits are the same for turning a Wizard into a newt, except it's because of the reduction of mental stats.
To suggest that Wizards, or other casters, aren't subject to that penalty without something written into the rules gives those characters an advantage over martial characters as it relates to handling polymorph.
Because the RAW are silent on whether save DCs are static or not, we have to fallback on the formula that's provided in the PHB, which is written algebraically to permit adjustments as they become appropriate.
The parameters for a spell are determined at the casting of the spell. They do not change while the spell is active unless the spell description or another ability explicitly says so. This has been true for not only 5th Edition but also previous editions of D&D with Vancian spellcasting. Your casting ability modifier is a parameter for the spell's DC. Therefore, a spell's DC does not change if your ability score changes after the spell is cast.
