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Does this help?
To cast a spell, you must concentrate. If something interrupts your concentration while you're casting, you must make a concentration check or lose the spell. When you make a concentration check, you roll d20 and add your caster level and the ability score modifier used to determine bonus spells of the same type. Clerics, druids, and rangers add their Wisdom modifier. Bards, paladins, and sorcerers add their Charisma modifier. Finally, wizards add their Intelligence modifier. The more distracting the interruption and the higher the level of the spell you are trying to cast, the higher the DC (see Table: Concentration Check DCs). If you fail the check, you lose the spell just as if you had cast it to no effect.
I might be missing an aspect of the question, but I'd say it's a Charisma-based check.

Rathendar |

I don't see room for interpretation. Intent is what it is, but if it's a charisma-based check, it's very clear by RAW. That's why I'd like to get an official word on it.
I'd suggest you are reading it wrong, it's a Level-Based Check with the key casting stat as an additional modifier.
=)

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Looks to me like it's a Caster level check, modified by Charisma (for sorcerers, bards, etc.), not a Charisma check, so the Circlet wouldn't technically work here.
(Nor would one of those Varisian tattoos from the Faction Guide that gives a +1 to checks based on a specific ability, since the Concentration check isn't an ability check, it's a CL check, modified by casting attribute.)

Oliver McShade |

Concentration checks are based off of: Prime Stat for Said Caster Class, as listed on PF phb page 206 = Concentration.
Int for Wizards/Witches/Alchemist
Wis for Cleric/Druid/Paladin/Rangers/Inquisitor
Cha for Bards/Sorcerers/Oracle/Summoner
Note: You only add the modifier when listed. Some checks are just DC # + spell level, some are DC # + effect + spell level. Not all concentration checks use the modifier depending on how the concentration check is being used for.

Oliver McShade |

Circlet of Persuasion
"This silver headband grants a +3 competence bonus on the wearer's Charisma-Based Check".
Strangle enough you use "Eagle's Splendor" to crate the circlet, but the spell version gives a +4 enhancement bonus.
So one could stack Circlet of Persuasion + Eagle Splendor spell bonus together.
So the bonus could be used on Skill based checks, checks that represent attempts to influence others, channel energy DC for cleric and paladins attempting to harm undead foes,
I would think it could be used for Concentration checks (provide said concentration check said it used "caster ability score").
~~~It would NOT grant any extra spells, due to Circlet of Persuasion, saying this is a bonus to Charisma-Based checks... Not to Charisma itself~~~

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The reason I said it was debatable, is because it's not a "charisma-based check" it's a "variable stat-based check, with charisma being one possible variable."
That's a reasonable point.
The only issue I have with it working is the lack of a similar option for non-charisma based casters, which is easily solved by introducing circlets for intelligence and wisdom based checks... and possibly belts for the physical stats.

Tendrin |
Yeah, we're *specifically* wondering whether or not the Circlet of Persuasion works, which seems debatable, for some of the reasons mentioned in this thread. :)
It strikes me as odd that all charisma based casters could get a +3 to all their caster checks and ONLY charisma based casters could get this.
Just to clarify, this is *specfically* about the Circlet of Persuasion, giving its bonus to concentration checks. :)

Ruggs |

Yeah, we're *specifically* wondering whether or not the Circlet of Persuasion works, which seems debatable, for some of the reasons mentioned in this thread. :)
It strikes me as odd that all charisma based casters could get a +3 to all their caster checks and ONLY charisma based casters could get this.
Just to clarify, this is *specfically* about the Circlet of Persuasion.
The price for the item is only 4500 as well, and it gives a bonus equivalent to a +6 attribute item to concentration checks. This seemed somewhat odd in terms of intent, and hence some of the question.

Oliver McShade |

Tendrin wrote:Yeah, we're *specifically* wondering whether or not the Circlet of Persuasion works, which seems debatable, for some of the reasons mentioned in this thread. :)
It strikes me as odd that all charisma based casters could get a +3 to all their caster checks and ONLY charisma based casters could get this.
Just to clarify, this is *specfically* about the Circlet of Persuasion.
The price for the item is only 4500 as well, and it gives a bonus equivalent to a +6 attribute item to concentration checks. This seemed somewhat odd in terms of intent, and hence some of the question.
"This silver headband grants a +3 competence bonus on the wearer's Charisma-Based Check".
Please note that this is all that it says. While i can see it giving a +3 bonus to concentration checks.... not all concentration checks get or use the caster ability bonus.
Also, This item does not increase ones Charisma... So even if you were to wear it for 24 hours.... it still would only effect those concentration checks ... that allow a ability bonus.
The reason why i think they did it this way, was so that it would not let Charisma caster get a magic item, that 24 hour latter, would let them gain bonus spells slots.
A nice little item, but for neck slot items... There are much better, and i would never bother with this item.

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Oliver McShade wrote:Why would you wear a circlet around your neck? It's a head slot item.
A nice little item, but for neck slot items... There are much better, and i would never bother with this item.
"I knew there was a reason I wouldn't wear it around my neck... Because it wouldn't work."
:)

Dire Mongoose |
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It strikes me as odd that all charisma based casters could get a +3 to all their caster checks and ONLY charisma based casters could get this.
To me this seemed fair just because... INT and WIS are good for something besides casting spells.
CHR just doesn't do enough to justify having it high unless you have class features and/or spellcasting tied to it, so in a sense having it as your casting stat is already a little bit of punishment.

Dire Mongoose |

So, Diplomacy, Intmidate, or Use Magic Device are nothing worth talking about, I guess.
Relative to the benefits of a high INT or WIS? No. Not even close. (To add insult to injury, if you really want those skills, a high INT is a great way to keep more of them maxed!)
In the Mental Stat Olympics, CHR wouldn't even earn the bronze.

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Note: You only add the modifier when listed. Some checks are just DC # + spell level, some are DC # + effect + spell level. Not all concentration checks use the modifier depending on how the concentration check is being used for.
I am not sure where you are getting this from. All concentrations checks are (Caster Level)+(Casting stat Modifier)+(D20) vs. some DC where the DC is pulled from the table titled "Table: Concentration Check DCs".
Can you please point me to one of the concentration checks where you would not add the casting stat mod?

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Raven did not state what he would use the answer to this question for...
...but I do think that the Concentration Check most likely is an Ability Check.
As for whether the Circlet of Persuasion would help out with a sorcerer's Concentration Check, I would say YES since the spell used to create the circlet is eagle's splendor.

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My 2 copper
So I accidentally posted this in the other thread on this because I don't pay enough attention it seems.
Check: A check is a d20 roll which may or may not be modified by another value. The most common types are attack rolls, ability checks, skill checks, and saving throws.
Plus:
What kinds of d20 rolls does the game have you make that (1) are called "checks" rather than saves or attacks, and (2) involve your Charisma modifier?
Equals the following:
1) Did I roll a d20? (Per definition of a check). If Yes, move on to 2. If No, Circlet of Persuasion has no effect.
2) Did I add my Charisma Modifier (re: SKR comment)? If Yes, move on to 3. If No, Circlet of Persuasion has no effect.
3) Was the d20 roll the specific form of check (per the definition of Check) known as an Attack roll (re: SKR comment)? If No, move on to 4. If Yes, Circlet of Persuasion has no effect.
4) Was the d20 roll the specific form of a check (per the definition of Check) known as a Saving Throw (re: SKR comment)? If No, move on to 5. If Yes, Circlet of Persuasion has no effect.
5) Circlet of Persuasion +3 Bonus applies.