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In D&D 5e, the harpy has the Luring Song action option:

Luring Song. The harpy sings a magical melody. Every humanoid and giant within 300 feet of the harpy that can hear the song must succeed on a DC 11 Wisdom saving throw or be charmed until the song ends. [...]

Would changing one (or more) specific ability scores modify the DC for the saving throw against the harpy's Luring Song? Are monster spell-like abilities (such as this one) linked and/or attached to specific ability scores in the first place?

Reason for asking: A harpy + bard (VGtM, p. 211) would require changing basic harpy stats - does this even matter for her preexisting & innate song ability? Related questions obviously include examples like a Beholder (MM, p. 28) (and their eye-rays) finding the right ability-modifying tome. And so on with creatures like Medusas (gaze), Dryads (charms) and Angels (spell-like abilities) with ability score changes.

If this is addressed in the Monster Manual somewhere (or even in StackExchange already), my apologies in advance for failing to find it.

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You can make your monsters however you like

Originally, I was very into making consistent monsters where the hit points align with the size category and con modifier. Similarly, the calculation of save DCs. This is nice for published material. I do not do it anymore for my own games since it takes time but does not add any value. My players never get to see the nice alignment of numbers.

In the end the question is what you want to achieve. If you want to build the harpy bard like a player character, it seems reasonable to assume that the luring song is a race feature. In this case you could adopt a calculation like for a dragon born breath weapon, i.e. 8 + proficiency + ability, except you would use charisma instead of constitution. If you just want to be consistent with the MM, the same calculation method is also good.

The MM save DCs are consistent with spell save DCs

In my consistent monster days I disassembled all the DCs in the MM, and found that the vast majority is consistent with 8 + proficiency + ability.

The ability changes depending on the feature. Pushing, pulling and knocking prone uses str, charm and fright use charisma. Some abilities of spellcasters use their spellcasting ability. Almost everything else uses con, including breath weapons and poisons.

It is not explicitly stated in the MM and I cannot prove it, but it mostly works out.

There are some exceptions. The solar and the gas spore have DCs which seem to be set differently. Some, e.g. the dragon turtle and demilich seem miscalculated. But these are few and far between.

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    \$\begingroup\$ All three answers above are good. Still, really enjoyed your opener: DMs are aiming for Player Character experience - and not so much the making of 'nice alignment of numbers'. Bravo / thanks. \$\endgroup\$ – Tim of Time Aug 4 at 14:27
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Changing the DC is consistent with monster modifying guidelines

In the guidelines for how to create a full monster statblock the DMG gives two options for setting monster save DCs. The first is to set a DC based on the monsters CR. The other option is to calculate a DC by using 8 + prof + appropriate ability modifier. (DMG, 278)

Save DCs
A monster might have an attack or some other trait that requires a target to make a saving throw. The save DCs to resist such effects have a direct bearing on the monster's challenge rating, and vice versa. You can determine save DCs in one of two ways.
Use the Table.
You can start with the monster's expected challenge rating and use the Monster Statistics by Challenge Rating table to determine an appropriate save DC for any effect that requires a tar e· to make a saving throw.
Calculate the DCs.
Alternatively, you can calculate a monster's save DCs as follows: 8 + the monster's proficiency bonus + the monster's relevant ability modifier. You choose the ability that best applies. For example, if the effect is a poison, the relevant ability is probably the monster's Constitution. If the effect is similar to that of a spell, the relevant ability might be the monster's Intelligence, Wisdom, or Charisma.

It appears that the Harpy's Luring Song DC was calculated using the latter method considering 13 is the quick DC on the table for CR 1 monsters. A DC of 11 aligns with the harpy having a proficiency bonus of 2 (CR 1 monster) and a Charisma modifier of +1.

The section on creating a monster, however, gives guidelines to help DMs rather than rules that they must follow. The same section specifically allows for DMs to adjust stats and modifiers to complete their vision of the monster. (DMG, 274)

Raise or lower the monster's Armor Class, hit points, attack bonus, damage output per round, and save DC as you see fit, based on whatever concept you have in mind for the monster.

As such what is most important is how modifying the monster contributes to building the game you and your players want to play.

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Changing monsters' abilities doesn't change their other stats.

Monster stats are complete and self-contained, and monsters (and NPCs) aren't "backed by" the same complex rules machinery as player characters.

In general, a monster's stats are nothing more than what's printed. While the DC from the harpy's Luring Song may have been initially calculated based on the creature's Charisma bonus, there's no necessary connection between them.

The Monster Manual states that some traits are in part derived from ability score bonuses -- specifically hit points (from Constitution) and saving throws. But it doesn't say that changes in those abilities during play will affect the monster's traits. Some monsters do explicitly have spellcasting traits which define a spellcasting ability, so in those cases there is a "link" between the ability score and the monster's stats.

But: If you (as a DM) want to make a more charismatic harpy with a higher DC song (or a harpy with Bard abilities), go ahead. Just write down whatever stats you want the monster to have. The DMG has some guidelines in Chapter 9, which include deriving things like save DCs from ability scores.

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Monsters do not have to be backed by their stats, but 5e monsters in the monster manual are.

5e is a reaction to 4e, where monster stats and powers are a function of level. In 5e, monsters are simulated first then a level is determined (and then it may iterate); in 4e, a level and role is determined first then the monsters stats are determined.

The Harpy as a CR 1 monster has a proficiency bonus of +2. Save DCs are 8+proficiency+stat modifier; this using charisma bonus of +1 is would be plausible and explain the DC of 11.

The reason you might consider doing this is that it sometimes makes for a very small amount of additional verisimilitude. Often this comes from the iteration effects.

This monster is a CR 20 creature who hits people and knocks them flying. You want a DC of around 22. This means their strength will be 26-27, as 8+6+8 is 22.

The verisimilitude from this comes out when the players try to grapple or push or whatever this monster. Because of the scale of the monster and the target DC of an ability, you "accidentally" set its strength to a value that makes other interaction with the monster consistent.

Imagine you had just set all of its stats to 10, and gave it abilities like knockback (DC 22). Until the players interacted with its grapple, there was no difference. But when the grapple, they discover the creature is trivially easy to hold or push (or has a weak strength saving throw).

The connection between strength and save DC had no direct impact on the players, but if the connection exists then the monster smashing your PCs and knocking them flying provides a hint to the PCs that "this monster is super strong, might not want to grapple it or attack its strength".

In this case, it could show up when this harpy's save DC is noticeably higher than the other harpies. That little thing could give the players hints that this is a hardier harpy.

The effect is small in each instance that you do it, and it is work, so you can often neglect it and no harm is done.

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