So my level 3 Alchemist has an INT of 16. This makes his bomb damage on a direct hit 2d6+3. He also has point-blank shot (+1 to hit/damage within 30') and the Tiefling FCB of +1/2 bomb damage per level (+1 at 3rd level). But he also has a strength of 12. Does he add the +1 from Strength to damage from a direct hit, as with other thrown weapons? That would give him 2d6+6 damage (8 splash damage, REF save for half). Is this correct?
The damage from an Alchemist bomb is from the explosion, not the strength of the throw. So no, you do not get to add your STR modifier to damage done.
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Does he add the +1 from Strength to damage from a direct hit, as with other thrown weapons?
Daggers, clubs, shortspears, spears, darts, javelins, throwing axes, light hammers, tridents, shuriken, and nets are thrown weapons. The wielder applies his Strength modifier to damage dealt by thrown weapons (except for splash weapons).
You add your INT bonus to the damage, so strength is by passed and made irrelevant