When deflect arrows is used it says you take no damage from it. If a thrown AOE weapon (Such as a flask of acid or an Alchemist bomb) is thrown at a target with deflect arrows, what happens to the thrown weapon? Does it vanish and do nothing? Does it scatter and still perform AOE damage and ignore the deflecting target? Does it do something else?
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As Pathfinder has a basis largely in simulation, I rule in this case (I have a monk PC in my game and it's come up) that he can deflect the full effect of the weapon but still takes any splash damage.
For my game I rule that the player is allowed to deflect an AOE weapon. They get to role a reflex save against the attack role that was used to hit them. If they succeed they can choose which direction they deflected the attack to; if they fail it gets randomly deflected (d8 roll for direction).
I then have the attack hit the square that it was deflected too, and then figure out splash damage from there. If there's a creature in the deflected square I use the original attack roll to see if it hits that creature.
This can lead to some interesting strategies. One game saw our monk deflecting a flaming oil onto a summoned fire elemental in order to heal it from the fire damage.
By RAW, a character hit with a splash weapon also receives the splash damage.
The target is, in fact, a creature within 5 ft. of itself.
However, a character using the Deflect Arrows feat, explicitly receives no damage from the ranged attack. The feat does not force the attack to miss: it simply negates the damage. In fact, the splash weapon doesn't misfire and it still deal splash damage to adjacent creatures.
That said, what @mxyzplk wrote:
stands true, and I'd take no offense nor scandal from house ruling that a deflected alchemist's fire still deals splash damage to its target.