I have seen a fair number of cop shooting videos where the cop blasts through a magazine and fails to hit anything, and then reloads and does the same thing again, sometimes at amazingly close distances. One would think the sheer number of chunks of lead in the air would result in a hit at some point.
I also recall the case of an armored car guard who shot it out with a robber in the basement of a hospital in Chicago back in the late 70s. The robber and the guard blasted away at each other from 10-15 feet. The guard had a second revolver (a snubby as the story goes) and somehow managed to hit the robber with the second gun, after missing him 6 times with the first. IIRC, total of 17 rounds fired from 10-15 feet results in one hit in the foot.
I vote for extra mags. I think carrying an extra box of ammo is maybe pushing things a bit, but whatever trips your trigger.