Para Bellum, consider this. Chances are that in real life where you need to shoot, you will be starting at a disadvantage. This means that the bad guy(s) started things and you are reacting to the danger presented by the situation. Sure, moving to cover can take time, but drawing and firing offers almost zero protection from incoming rounds. Your drawn gun shields what miniscule amount of your person? Sure, we all want to believe that we will draw and fire so fast that we will be able to land incapacitating rounds on target(s) before any of the bad guys could have a chance to hurt us even though they already have their weapons out and aimed at us, right? Don't count on it happening.
Even if your gun does end up as a shield, chances are it won't work after it has defected an incoming round.
So, you move. Moving makes you a harder target to hit. You draw on the move, thereby accomplishing two tasks at the same time (becoming harder to hit and getting your gun out to return fire).
pointfiveoh mentioned moving off the line of attack. Unfortunately, many folks teach this concept and it stops right there. As he mentioned, you need to continue to cover.
In more than one class I have had, I had instuctors have me take one side step, draw and fire. In a carbine class, I had an instructor tell us (while we advanced toward targets) to take one step to the side to get off the line of attack, stopping, while bringing the sights up on target and firing a single shot. This was argued to get us out of the line of attack and the stopping gave us a stable shooting platform. It was reasoned that the sidestep would upset the bad guy(s)' OODA loop so much that we would get off the first shot.
A step to the side isn't going to mess up anyone's OODA loop with the possible exception of a person charging you with a knife or charging you with their car and you move out of the way at the very last moment. You have to make the change after the attacker can no longer alter direction.
When it comes to stepping off the line of attack just one step, the OODA loops isn't upset at all and nothing more is required than a slight adjustment to the gun's sighting for the attacker to shoot you.
Once you move off the line of attack, you don't stop there unless you are behind cover.
As for notions such as OODA loops, don't even bother. The bad guys can point pull and pray without a well defined OODA loop and they may get lucky and hit you, especially if you are standing still. They don't have the concerns of hitting bystanders that you will have, so they can fire freely.
"If you look through your scope and see your shoe, aim higher."
-- said to me by my 11 year old daughter before going out for hogs 8/13/2011