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If you drop a throwing weapon from a height onto an enemy, does that incur range increment penalty, and if so, how much? I am asking, because a question in our group came up whether gravity or higher ground rules apply to "Throwing" a weapon downward, but we could not find anything.

For instance: My Paladin Sir Isaac, is standing on a bridge, and there is a goblin below him, 60 ft. He attempts to drops an alchemist flash on top of the Goblin's head.

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Range increment applies as normal. It's just vertical now.

The answer to this question does vary slightly depending on two things:

  1. whether you are dropping the weapon onto a target, or whether you are throwing the weapon aimed downward at a target. Your DM probably has some discretion to rule which scenario fits better, and you as a player would also be able to decide whether you are dropping or throwing.

  2. whether the item is found on the Weapon Table.

However, range increment is an indicator of how well your character can aim with a thrown or ranged weapon, and that would be the same regardless of whether you are aiming horizontally or vertically - you're still having to aim.

The range increment penalty is a cumulative -2 for every range increment beyond 10 feet.

According to Pathfinder 1e RAW, a weapon falling from height would be treated just the same as dropping any other object, whether that be a weapon or item. There are no special rules for specifically dropping weapons - as far as the rules are concerned, it is a dropped object from height. Range is treated as normal.

Range: Any attack at more than this distance is penalized for range... A thrown weapon has a maximum range of five range increments. A projectile weapon can shoot to 10 range increments.

So in your specific example with a goblin 60 ft. below you, every range increment beyond 10 ft. would incur a -2 penalty. You can imagine this as being because you're having to carefully aim your drop or throw downwards so that it hits the right target, and that's harder to do the farther down your target is.

If the item is "thrown" downward, it would be treated as a thrown weapon attack with range rules applied vertically.

If the item is just an item and not a weapon, it would be treated as an Improvised Weapon attack:

Improvised Weapons

Sometimes objects not crafted to be weapons nonetheless see use in combat. Because such objects are not designed for this use, any creature that uses an improvised weapon in combat is considered to be nonproficient with it and takes a –4 penalty on attack rolls made with that object. To determine the size category and appropriate damage for an improvised weapon, compare its relative size and damage potential to the weapon list to find a reasonable match. An improvised weapon scores a threat on a natural roll of 20 and deals double damage on a critical hit. An improvised thrown weapon has a range increment of 10 feet.

However, if it is a weapon, it is treated as a Thrown Weapon attack:

Thrown Weapons: The wielder applies his Strength modifier to damage dealt by thrown weapons (except for splash weapons). It is possible to throw a weapon that isn't designed to be thrown (that is, a melee weapon that doesn't have a numeric entry in the Range column on Table: Weapons), and a character who does so takes a –4 penalty on the attack roll. Throwing a light or one-handed weapon is a standard action, while throwing a two-handed weapon is a full-round action. Regardless of the type of weapon, such an attack scores a threat only on a natural 20 and deals double damage on a critical hit. Such a weapon has a range increment of 10 feet.

[Sources: https://rpg.stackexchange.com/questions/55203/throwing-things-and-people-as-weapons-how-would-this-work and https://paizo.com/threads/rzs2p7as?Dropping-an-object-from-height]

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