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Still exploring a few options to create an NPC in my Pathfinder campaign. To summarize : a half-orc with all mental ability scores as low as possible for a newly created character (he is supposed to be dumb as rocks, nearly devoid of common sense and socially inept) with pyromaniac tendencies and who has means to deal good amounts of fire damage.

At first, the kineticist class seemed to be a good choice for him, but I would like to try something different and less reliant on supernatural powers (and also less mechanically complicated), and the underground chemist rogue archetype looks to be a great choice.

However, this archetype adds the character's intelligence modifier to damage dealt with splash weapons, and that would be clearly detrimental to my NPC.

Then can the character choose to not add an ability score modifier from a class feature if it would penalize rather than help him ?

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Depends on the class feature. If a class feature says that you “can” or “may” do something, you have the choice not to.

If it doesn’t, however, as in the case of the underground chemist’s chemical weapons feature, and just says “you add your xyz modifier to...” then you have no choice, and must do so.

Do note that, especially for an NPC, it really would not be unreasonable to houserule this. That feature is generally considered a rather good one. An underground chemist variant without it is less good than with it, in general, so even though it’s better for this NPC, it isn’t overpowered (actually, it’s underpowered—I would worry, if this NPC is likely to see combat, that without adding something to those alchemical weapons they won’t be worth much).

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No.

If the text does not say you "can" or "may" do something, then you must do it. If you apply your "Intelligence modifier" (as opposed to Intelligence bonus) when the modifier is negative, then you must apply the modifier as a penalty.

Usually abilities like this say "bonus" instead of "modifier" specifically to avoid this corner case. I am not sure why it was designed this way. Game designer Sean K. Reynolds mentioned this issue in his Pathfinder game design book and remarked that sometimes game designers can make the mistake of creating this corner case by not using the proper language. Thus, there is a high likelihood that this was not an intentional quirk of the ability.

That being said, you are the GM. You have the power to simply house rule as you see fit.

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