This could be CofV 12.4, but it is really it's own thing and critical to everything. Not just self-defense, but every last damn thing. One internet warrior years ago said, quite pretentiously, "When one can control space and time, one is unbeatable." Or words to that effect.
Distance is not the same as space. Understanding distance is just one dimension of three dimensional space. Understanding space makes most physical skills into a type of geometry study, and usually the geometry of a physical problem is easy.
Aside-- Solutions are easy. Injuring a person is easy. Moving, if you are reasonably athletic, is easy. Reading and manipulating the dynamics of two moving bodies is not so easy, but it is almost exactly what all creatures were evolved to do, so it isn't exactly hard, either. The physical part has never been the hard part of self-defense. Knowing when to act, trusting your judgment, giving yourself permission to do what needs to be done and doing all this from a position of physical and mental disadvantage while surprised-- that's the hard part. And the part most teachers shy away from because (I believe) they don't know what to say.
The only thing easier than the physical part is the intellectual understanding of the physical part. And that is sometimes a trap. Knowing the words is not the same as knowing the music. Knowing something with your head alone is almost useless when it comes time to apply those skills with your body under stress. But people often believe that knowing is the same as understanding, and that the ability to talk about things or answer questions is in some way correlated with the ability to do those things. It is not. -- Aside ends.
There is a lot here, I've got pages on it in an unpublished manuscript. But looking strictly at it from a threat assessment point of view:
Distance is time. The farther away a threat is, the more time it will take to reach you.
The critical distance is inside reach. The person can hit you solidly without any weight shift at that range. Unless the threat telegraphs badly, the strike will land before you can react. You will get hit.
Two corollaries: 1) Bad guys become skilled at getting to this distance without putting you on alert. The more aware you are of unnatural distancing and the more you show your preparation, the less likely you are to be targeted. A little boundary setting doesn't hurt. 2) If the threat attacks with a flurry, the information (each strike is a data point) will come in too fast for you to close your OODA loop and you will freeze. The solution is to bypass the OODA loop through operant conditioning. You spike the attack instead of responding.
Just outside the critical distance, the threat has to shift weight to reach you. This creates an unavoidable telegraph that can give you time if you are quick and ready.
Note-- both critical distance and outside critical distance can be altered by weight shift. If the weight is balanced or on the back leg, the lead hand/lead foot have the longest range. However if the weight is on the front foot, the rear leg has a much longer range. There are some people quick enough with kicks to get surprise with them. Also, weight shifts can be disguised by movements or gestures. The pretending to turn away to coil a strike is one obvious example.
The next level of distance requires a step to make contact.
Just be aware that a skilled drop step can hit without telegraphing from roughly six inches beyond single step distance. Drop step is a good tool.
All changes with weapons and barriers of course, but reading distance is a skill you can develop. Actually, if you have any striking sparring experience at all, you should have this down cold. The test is whether you ignore completely strikes that are out of range anyway. If you still block things that were never going to reach you, go back to basics.
So when is a threat a threat? When he can reach you. You have the big drunk guy in full monkey dance screaming threats, you are in no danger. Until he gets to the critical distance line. Then you will have to make a decision. You have the PCP freak sweating, spitting blood and hyperventilating? If you can appear calm and keep from triggering more adrenaline in him, there is a chance he will run out of steam, and your ability to stay calm involves trusting your reading of distance. And if a stranger in a lonely place is trying to get inside your critical range? Yeah.
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