If it's time to draw, it's time to shoot. A gun isn't for scaring people.
In the 1.5-2 seconds it takes to draw and fire a lot of things can change. The question is, in the 3/4 sec. it takes you to react to that change will you be able to adjust to the new situation presented???
Simply acting is much quicker than reacting. First the BG has to react to your change in status @ 3/4 second. Then you have to respond and react to any new situation presented @ 3/4 second. This does not leave a whole lot of time to think about and exercise discression.
If there is a bladed weapon or striking weapon involved with a BG in motion in my direction I don't think my reaction will change from draw to fire even if the BG has started to back off it may be too late for my response time to adjust. His poor selection on assaulting an armed person.
Force Science Research Center has gone a long way into studing response times and the tunnel vision along with all of the physiological changes that happen when the response from a life and death situation arises.