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If someone has a penalty to a save, does it automatically lower the matching DC?

Bon Mot for example gives a penalty to saves:

Critical Success: The target is distracted and takes a –3 status penalty to Perception and Will saves for 1 minute

If it is a critical success, and you try to Demoralize (Intimidation check against Will DC) the target, is the DC three lower?

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Yes

I believe it's stated explicitly somewhere but can't seem to find that at the moment. I'll update when I do, but until then we only have it implicitly in the various locations (here, Saving Throws) where modifier calculations are found.

Will saving throws measure how well you can resist attacks to your mind and spirit. They use your Wisdom modifier and are calculated as shown in the formula below.

Will save result = d20 roll + Wisdom modifier + proficiency bonus + other bonuses + penalties

Sometimes you'll need to know your DC for a given saving throw. The DC for a saving throw is 10 + the total modifier for that saving throw.

Note that the DC is 'the total modifier' added to 10, and the modifier calculation includes penalties.

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    \$\begingroup\$ Why does reducing a will save also reduce your DC? Your class DC is 10 + prof + ability mod. Decreasing your will save doesn't touch any of those values. Formula here: 2e.aonprd.com/Rules.aspx?ID=102 \$\endgroup\$
    – indigochild
    Commented May 30, 2021 at 22:12
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    \$\begingroup\$ @indigochild I'm speaking directly about (Will) Save DC, which has nothing (essentially) to do with Class DC \$\endgroup\$
    – Ifusaso 'he-him'
    Commented May 30, 2021 at 23:29

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