I can't overemphasize this point enough and this is WAY more relevant probably to most on this board. Most police officers are trained in the action v. reaction theorem that equates gun in hand to gun in use. We taught that in our acdemy for many years and without any contextual issues it holds true. Don't wanna' get shot by the police? Don't have a gun in hand.
Another story: I'm buying cookies from "Man-Man" who we're gonna' rip on the fourth buy. Deal goes down in a hotel room and the plan is for the team to page me (showing my age) and my job is to open the door thus allowing the team entry.
Page fails and the team falls back to a breach which doesn't go clean. Man-Man draws a gat, I jump him and start whipping his ass and get the pistol right as the door swings open.
First guys in are two uniforms augmenting the narcs, who don't know me and I can see both initiating a shot. I throw the gun over my head and behind me and scream "I'M THE F*CKIN' U/C!!!!!!!!" as I throw myself behind one of the twin beds. Fortunately no one shot me.
That's not the only story I have like that. Point being, gun not in hand is better for you when dealing with the po-po.