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I'm reading the Gunslinger page and the Deadeye deed says:

the gunslinger can resolve an attack against touch AC instead of normal AC when firing beyond her firearm’s first range increment.

I've always heard the term "range increment", usually in reference to siege weaponry or the such. I've never really understood what determines how many range increments it's off of, when the target is out of the initial weapon's range. Is it the full range as the first, and then another full range as the second? Or is it only like 10 feet per increment?

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The listed range in the weapon table is the range per increment. You get 5 increments for thrown weapons and 10 for projectile weapons:

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.

Firearms, however, work different:

Range and Penetration: Armor, whether manufactured or natural, provides little protection against the force of a bullet at short range.

Early Firearms: When firing an early firearm, the attack resolves against the target’s touch AC when the target is within the first range increment of the weapon, but this type of attack is not considered a touch attack for the purposes of feats and abilities such as Deadly Aim. At higher range increments, the attack resolves normally, including taking the normal cumulative –2 penalty for each full range increment. Unlike other projectile weapons, early firearms have a maximum range of five range increments. [emphasis added]

Advanced Firearms: Advanced firearms resolve their attacks against touch AC when the target is within the first five range increments, but this type of attack is not considered a touch attack for the purposes of feats such as Deadly Aim. At higher range increments, the attack resolves normally, including taking the normal cumulative –2 penalty for each full-range increment. Advanced firearms have a maximum range of 10 range increments.

In addition, Modern and Technological firearms have their own rules sections.

Modern firearms don't clearly state whether they are Early or Advanced firearms for the purpose of range increments (except the Nagant M1895 Revolver), but are obviously supposed to follow the rules for Advanced Firearms since they are advanced firearms in the colloquial sense.

Technological Firearms benefit from the following rule:

Range: This lists the weapon’s range increment; no listing is given for melee weapons that cannot be thrown. Unless otherwise noted, all firearms in this chapter are treated as projectile weapons for the purpose of determining their maximum range.

Notable when discussing firearms, range increments, and Deadeye are the scope (25 gp, 1 lb), which reduces the range penalty by 1 per range increment, and the 'touch' weapon property found on several technological firearms like the laser rifle or gravity pistol, which lets the firearm target touch AC up to its maximum range instead of just within the first 1-or-5 increments.

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There are many range increments.

The following comes from about 2/3 of the way down in weapons.

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.

Range: Any attack at more than this distance is penalized for range. Beyond this range, the attack takes a cumulative –2 penalty for each full range increment (or fraction thereof) of distance to the target. For example, a dagger (with a range of 10 feet) thrown at a target that is 25 feet away would incur a –4 penalty. A thrown weapon has a maximum range of five range increments. A projectile weapon can shoot to 10 range increments.

So while most weapon types tend to have a particular range, there are some weapons which have better range, just like damage and crit. Dont forget that weapon properties, feats, and magic can also change the range at which weapons can work.

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