1) Goals-backward. This is taught specifically to most emergency leadership. Drop me off on a desert island and I won't start by going through my pockets to see what I have. I'll list what I need first (shelter-water-fire-food), then check resources to match needs, then gather or create resources to fill the rest. I am also one of those kids who found story problems much easier than the same problem presented as a formula and always found mazes easier to work backwards. Fighting with a clear idea of the goal- to escape, to prevail, to restrain to... is both more efficient and less likely to escalate to something excessive.
2) The Art of Advantage. A practiced sense for vulnerabilities- in balance, position, targeting, but also emotional and logical. Been doing this for so long that I am not sure if it is a 'taught' thing or simply a 'permission' thing. But it takes some deep restraint. To even play with this and not destroy your life you have to understand deeply that defeating someone else is not the same as winning. Knowing how to hurt without knowing when and who is dancing on the edge of evil.
3) Reframing. The ability to look not just at different answers but at different possible meanings for the question. An aspect is to know what the real question is.
4) Context. This is a hard one under stress because your SSR triggers both a visual and mental tunnel vision (that's also why true environmental fighting usually takes experience as well as practice). But sometimes, often (and this is more true with a predator who has moderated his own SSR than with a kid in the Monkey Dance) you can affect what the fight is about. Change the perception of the value of the goal (Ever listen to "The Winner" by Bobby Bare?). Change the perception of risk (Kris' "You guys should probably know the front desk has already called the cops.")
5) Connected thinking. Everybody does this but not everybody does it very well. Everything you do affects other things. Almost everything is connected. The more deeply and subtly you see, the more you can affect things in relatively distant space or time and with relatively little obvious action. One place where I take this is looking at the source of information and then looking at their motives. With practice, if you are objective, you can predict the drift of bias.*
6) Continuity. What you are dealing with in this moment began long ago and will have effects, intended and unintended, long into the future. The past is for research, the far future for prediction and an attempt to mold, only the present and the near future for planning and action. This works two ways. First, avoid getting caught up in a past you can't fix. How a particular criminal became a violent criminal is an academic matter. I might use it in the future to help another kid not become a predator, but when someone is trying to stomp your head against the curb that is so NOT the time to try to figure out if it was due to potty training or not getting breast-fed. The other side: how you deal with the immediate problem will affect future problems that can arise. Treating symptoms is rarely the same as treating causes.
7)Simplifying the problem. The ability to take all this and cut it down in an instant to an immediate problem with an immediate solution.
I need to emphasize here- almost every good operator thinks like this, but they don't think about it. It appears complex, maybe, and in words and explanations, it probably is. Just like no one thinks about the rules of grammar when they are actually speaking in a native language, no operator is consciously extracting a web of past and future. 'This came from here and is going there.' You just see it because it is the way you have learned to see. When you make an error, you re-evaluate and move on. If they have practiced, and this is rarer, they can articulate how they knew 'x' was about to happen, but not all of them can.
* Predictive power is the only way to evaluate your skill in a lot of this. If you are wrong consistently wrong you have misjudged their bias and must look at your own.