In all my years, even as I have gotten older with poorer eyesight, I am never outshot by a cop. The only one I have known personally who could shoot was a retired officer from WAAAAAY back. He is now long dead and was sure a different era. I think he had retired in the 70's. He could actually SHOOT his revolver. He was the sort who could put it in a perp's eye over the shoulder of a hostage. Most cops nowadays just spray the area, and most use semi-auto, high capacity handguns. You could almost pick out cops at the range by their shooting style. Lots of shots, at close range targets, none hitting, with the real danger to bystanders as being anywhere BUT the target for the cops' sloppy gun-waving. And almost to a person they will not take instruction either.
I did know a prison guard who was half-way decent....but he kept saying "front sight, front sight, front sight," aloud every time he fired. He could not hit the bullseye, but he at least put them all on the paper.