More Math

The math thing. Remember that any model is a model, a way of explaining the world and no more. It is not the world. No model is "truth" whatever truth may be. But many models are useful (and, in my experience, useful can be measured by how well the model predicts the future.)
You can represent the problem with knives as math.  One of the cool things about knives (for math purposes) is that they operate so much like hands.  Baseball bat swings have huge dead zones, but a knife doesn't require any more of a swing that a bare hand.  For that matter, it can do more damage with less speed and distance.
So, for our model, a knife is functionally a hand, but say, increases the effectiveness of a threat's attack by 'sixty'.  Part of that imaginary number is damage/lethality, and part is the way people tend to choke when they see something shiny and sharp rising towards their belly.
So, in our completely imaginary, numbers-pulled-out-of-the-ass mathematical model, we have two people with combative chances of o-100.  Hand one a knife and the balance becomes 0-100 on the unarmed side, 60-160 on the weapon side.  Mean is 50:110, for what it's worth.  All other things being equal, the knife is a huge advantage.
There are other things making that initial score of 1-100.  Size, strength, speed, ferocity... it seems like a some of the dynamics on defending against a knife involve trying to amp one of these.  For that matter, a lot of self-defense: "Your natural ferocity is about a 12 out of 100, like most nice, civilized people.  Let's ramp that up to 80 and you will be a far more effective fighter."
That rise from twelve to eighty is huge... but if the threat started at ninety you have only begun to level the playing field.  It's a big gain in an area where it is easy to make big gains.  Lots of skilled martial artists are shitty fighters.  Teaching them to slip the leash is huge.  But that doesn't mean that the threat started at a twelve, and if you are slipping the leash for the first time and he's been doing it for awhile... it's an increase, but it's still a far cry from an edge.
Hmmmm.... and willingness to use a knife (an up-close, messy and personal weapon) usually indicates that the threat has already pretty much maxed the 'ferocity' and 'disdain for human life' attributes.
Controlling the weapon arm is an attempt to neutralize the knife's sixty percent advantage, but it does so at a cost.  If you don't know how to control a limb without hands, it often ties up two of yours.  Do you lose forty or more points of your own effectiveness?  If you went into any other type of fight and decided that you would use both of your hands to keep a death grip on one of the other guy's hands... how do you think that would work out?
The thing with a knife, not just in skilled hands but in any except spectacularly stupid and brain-washed hands, is that the sixty-point advantage doesn't come at any cost anywhere else.  Swinging a club involves a vulnerability in geometry and another one in momentum.  The only cost to a knife is that you can't grip with that hand, and sticking a piece of steel through flesh and under a bone can do almost everything a grip can do.
*Over-reaching generalization alert*It seems that lots of the RBSD out there focuses on increasing one or more attributes (aggressiveness, ferocity, strength, speed) to give one an edge.  I dunno. There are very few attributes you can increase that the threat can't increase as well.  
Traditional martial arts *over-reaching generalization alert still in effect*  tends to focus on precision and technique, which I've found are pretty unreliable in your first few encounters until you get used to what is going on.  But sometimes it works.  The cool thing is that you can work on efficiency for a long time, but there are genetic limits to most attributes. But... there is nothing in here inherently that says the threat hasn't spent more time on his technique than you have... and he damn sure has more experience with good guys than you have with bad guys.
My focus tends to be on changing the game.  Not because a crook can't be better at it than I am.  Aside from prevention, I find the big gains in in messing with minds, because far more people have practiced or trained with their bodies and weapons than have even considered playing with their own minds.
It's maybe only a few points, but it doesn't cost anything and fewer threats are prepared for it.
-------------I'm tired, and very soon I will be tired of doing serious posts and having the posts (or parts of them) taken seriously. There was a rule I used to teach rookies: You can take yourself seriously or the job seriously, but never both at the same time.
Life is cool and complex. If you aren't laughing at something, you're probably missing the point. Plus being serious all the time isn't good for you. Ulcers and such.