Dead State Design Update
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Shotguns are pretty much what you would expect lots of damage for little skill at close range. Their critical chance is high, and their critical damage can be devastating. They would be a perfect weapon for closer range if not for the amount of noise they make and their long reload rates they attract zombies when fired, and frequent reloading (for basic models) means you won't fire fast enough to take out a group if surrounded. They are, with one exception, all two-handed. In a pinch, the shotgun can do some major damage, but over-reliance on it will have every zombie in the area heading your way.
Let's take a look at the stats for the basic model of shotgun, the Hunting Shotgun.
Hands: 2 (AP cost for switching weapons)
Range: 4 (Average range)
AP Cost Firing: 4 AP
AP Cost Reloading: 8 AP
Ammo Capacity: 2 (Low, double barrel capacity)
Ammo Type: Shells
Type: Ballistic (Good against humans/non-ballistic armor)
Damage: 45-70 (High at close range, drops off due to spread at longer ranges)
Noise: 20 (Very Loud)
Critical Hit Chance: 10% (Good chance for criticals)
Critical Multiplier: 2 (Good critical multiplier)
Weight: 7.5 (Moderately heavy)
Break: 0 (Weapon will not break)
Mods:
Sawed-Off Barrel Permanently transforms gun into a Sawed-Off Shotgun.
As you can see, if you can get a hit with the shotgun, your target's going to be in bad shape. Note that the damage range may come down a bit with combat balance - but guns always do a lot of damage for the noise risk they carry. Remember, this is just the basic model shotgun, so expect to see some better ones in future updates.