sawed off shotguns shoot the shot with less force instead of more, because the shorter barrel doesn't allow the gases from the powder in the shell exploding to expand to it's full potential and accelerate the shot as much as normal. The advantage is in concealment. A shotgun is pretty much a short/intermediate range weapon anyway, so the increased spread of the shot pattern is only an advantage if you can't aim worth shit. Also, since the pattern is more spread out, you don't get the effect of lots of pellets hitting near each other, which is what gives a shotgun it's close range man stopping power.