Re: Bullets "going to sleep."
OK. You caught me after my coffee...
Here are a couple of graphics to further illustrate what's been said above by me and others.
First, is "Yaw", the tendancy of the bullet to be leave the muzzle at a random angle at the moment of exit. Over time, the bullet will even out, but at the very first moment, there's no telling where you are.
Here's a graphic that shows the effect of Yaw:
Over time, the bullet's spin axis and line of flight will align. This is called "dynamic stability". But again, it takes time.
Second, this effect gets married to rotational or "gyroscopic stability". GS is said to be true if the bullet's rotation around the axis exactly balances the linear force placed upon it by wind and air friction.
The preponderance of loads will be "over stable" at the time they leave the muzzle. This is because the effects of under stability is so dramatic, you want to give it MORE at the time it leaves so that as force bleeds off, it reaches the optimal.
Over stable bullets will react more randomly, and be subject to all kinds of destabilizing results. Think of the vibration that comes from an engine that's being over-reved.
Putting DS with GS on a graph will yield results that are shown conceptually in this graphic:
In this case, one axis in GS and the other is DS and their combination leads to an optimal stability during flight. At the start of the flight, the bullet's location is hard to predict, as is also true at the end of the flight. Along the way, things align and the flight is very predictable. Hence the phenomenon of tighter (more predictable) groups at 200yds than, say 100yds (in some set-ups).
If you're really into the physics, you can read to your heart's content here:
http://www.snipersparadise.com/wound/formulas.htm