If the issue is whether you can shoot when someone has a gun pointed at you, that's an old one.
The key is the attentional allocation of the gun 'pointer'. You have a limited capacity of attention to detect stimuli and react. Diverting from the opponent leads to you being behind the curve. Attentional problems, called perceptual narrowing, selective attention, the popular in the gun world - tunnel vision - all well know in the literature. The old OODA loop disruption.
Anecdotally as that is alway more interesting that science:
At an Insights (Greg Hamilton and John Holschen's outfit) class at KRtraining, we discussed the issue. It was claimed by someone that if had the gun on you, you could not shoot him before you shot him. Greg said you could if you disrupted the pointer. One way to do this was if the pointer was blabbing. The verbalization diverted attentional and motor resources. Thus, Greg had the claimant 'hold up' Greg and babble about giving him the money, blah, blah. Greg had a revolver with Code Eagle in his belt, IIRC (might have been holstered but I don't think so). In mid-babble, Greg drew and 'shot' him. So not a head turn but diversion of attention.
We also did one where you stood face to face with an opponent. The opponent was to draw from the belt and shoot you. The idea was that you could not respond quick enough given the RT processing. Mostly you couldn't. I did beat that an stop the draw by: 1. Focusing and mentally rehearsing my move. That was a straight hand move to the gun. 2. Just looking at the gun carrier's gun hand (Karl). When it twitched, I moved - in a sense the motion was cocked. So I played the attentional focus game and ignored everything but that hand.
Now science (we don't need no stinking science).
I refer our membership to a general book:
a.
The Psychology of Police Deadly Force Encounters by Laurence Miller - a general resource on the issues of DFEs with a focus on OIS. Good solid review of reaction issues. Good review of other deadly force issues with very competent psychological and neuroscience. Well referenced, so not just street wisdom. Lots of useful overlap to the civilian.
b. Miller mentions:
Reasonableness and Reaction Time J. Pete Blair et al.
Police Quarterly, 2011, 14 324-343.
https://www.researchgate.net/profile...ction-Time.pdf
Abstract:
When the police use deadly force, their actions are judged by the reasonableness standard. This article seeks to inform the reasonableness standard by examining the ability of police officers to respond to armed suspects. The results of a reaction time experiment are presented. In this experiment, police officers encountered a suspect armed with a gun, pointing down and not at the police officer. The police officer had his gun aimed at the suspect and ordered the suspect to drop the gun. The suspect then either surrendered or attempted to shoot the officer. The speed with which the officer fired if the suspect chose to shoot was assessed. Results suggest that the officers were generally not able to fire before the suspect. Implications for the reasonableness standard and policy are discussed.
Read the article for details. Here's some:
Glock 17 Sims guns were used.
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There is much more detail in the article.
So much for science - back to anecdotes. So I'm a terrorist in a school shooting exercise. I'm in an office with a long arm (paint ball in those days). Airsoft handgun in the small of my back. The team enters - I surrender. I am at gun point. Hands up. I'm sorry, I sez. I draw the airsoft and shoot an officer in the head at about 10 feet. Pellet bounces off the center his full face mask. I then 'die' in the proverbial hail of paint.
At KRtraining. We are in line at a stop and rob. I am in back of customer (Karl) at the register. Karl is a crook. Karl shoots the clerk. Oh, dear - I take Karl down to ground (oops). Tell him not to move as I have drawn. His hidden backup (surprise) yells at me to get off him. I turn and shoot him (in the shoulder, we later determine). General shoot out starts with other armed patrons.
Summary - attention and focus, allocation of processing - all affects what you see, your action decision and your motor skills. What else is new. Can you beat the the drawn gun? Look at the bolded part of my quotes from Blair, et al.