I was nitpicking with Ted in comments and I used the term "OODA loop". Since it is bad form to use an acronym without spelling it out (although in these days of Google and Wikipedia it is a very forgiveable sin) I am going to write about the OODA loop and police activities.
My opinion here is not formed on anything more than the second hand experience from friends and aquaintences who are MP's or Deputies.
When you represent the side of Angels, law and order and all that bit, and you enter into a situation where there is chaos, the first thing you do is OBSERVE the situation. You will observe the situation until you can ORIENT on what is causing the chaos. Once you are properly targeted you will DECIDE to do something. The very last step in the OODA loop is to ACT out your decision.
The more chaotic the situation the longer the initial "OO" in the loop is. Limited information, conflicting information, and even dated information also prolong the "observe, orient" portion of the loop.
This is why the Police at Columbine hid behind cruisers until they could get a handle on the situation. Every single one of them was talking or listening to dispatch, scanning hands of fleeing students, and trying to get a grip on the situation. The cops in Mumbai hadn't had any real firearms training, so none of them DECIDED to ACT by using the arms that they had.
Cops are not superheros with the ability to immediately discern the truth and put the bad guys to justice. Cops are ordinary people who volunteer to do heroic things and be held to a very high standard. But like all humans, they need time to figure out what to do.
That is what it means to be "stuck in the OODA loop". When you can't make a decision because you can't get a grip on the situation. This is why "A 60% solution today beats a 100% solution tomorrow" when it comes to maneuver warfare. This is why Eisenhower famously said, "Ask me for anything but time". However, if a Cop had the 60% solution to shoot everyone with something threatening in their hands and plugged a jock running from baseball practice along with Sumdood and Assmuncher, well that 33% solution just isn't good enough. Cops are trained to come up with 100% solutions, and that takes time.
This is why training is the most important thing that Soldiers can do. Training gives us something to do IMMEDIATELY when the situation rapidly changes. We have training that shortens the OODA loop to muscle memory.
I cannot draw my pistol from it's concealed position any faster than anyone else, and I'm probably a bit slower. But part of my training is that I won't draw my pistol until I've hit the "D" portion of the OODA loop, the quicker I can get through "Observe" and "Orient" instead of standing there like a dumbass trying to get a grasp of the situation, the more effective I can be.
And please do not get me wrong, PRACTICE DRAWING YOUR WEAPON FROM YOUR CARRY POSITION!!!! But care LESS about speed and MORE about smoothly making it MUSCLE MEMORY, because once it is muscle memory you won't have to think about it when you come to the "D" in your loop.