Think I finally understand how and why confusion re: max settlement population exists, with stated formula 10 + Charisma seemingly to not always apply.
The simple answer is it doesn't because the formula works only as additive, never subtractive.
e.g. you only ever GAIN settlers this formula, never LOSE them - and all temp charisma buffs are permanent far as formula checking, then adding new settlers.
For example, say you have base Charisma 10 and beacon on at one or more settlements. At various intervals through game day, game checks your charisma score - whatever it is at the time - to see if new settlers can be added.
- If you have NEVER, ever worn any Charisma closing even for 1 second, or taken any Char boosting drug like mentats - then your max pop at all settlements truly will be 10 + Charisma - in this example 20 max per settlement
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- But If you HAVE worn any item that adds Charisma boost temporarily, or taken graqe mentats when selling loot, etc - this is how and why the confusion exists.
- Far as game is concerned, moment it checks your charisma score is what is used for 10+Charisma formula
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- If you took a graqe mental for example which boosts char another +5, and also wore +4 clothing, you now have a temp charisma of 19. Which now means your max settler limit during this temp boost period = 10 + charisma = 10 + 19 = 29 settler maximum
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- If the game just happens to check for new settler addition at this time, it will believe you are under you max settler cap and allow the addition of beacon attracted settler, one you manually move, etc. Once your charisma drops back to normal though, the formula is never checked to reapply new limit and you never lose those extra settlers.
- you can't attract more settlers or manually move them to settlements at or beyond your 'base' charisma cap, but once those settlers are there, they don't disappear even if charisma drops lower than the formula used at time of adding new settler
So there you have it - the formula technically is correct. But the reason people far exceed 20 setters max is because any boost to charisma for even one nanosecond will allow the high probability that new settlers will be added when game checks and sees your boosted charisma allows for more settlers.
Couple side benefits - want to move a companion somewhere but can't because settlement you want them to go to is maxed out? Pop a graqe mentat - unless you are already at your graqe mental boosted max, this will make game think settlement is now under max cap and you can now send your companion or other settler manually to that location.
Offhand from vanilla, non-modded game, I can only think of +4 from clothing and +5 from graqe mentats, which makes effective max 29 settlers per settlement. There may be other char boosts you can take but don't recall offhand other than these two.