I posted this in another thread, but I think it deserves its own thread. This is intended for as broad an audience as I can hit so, I'm including some basics on trajectory.
Hitting your target is all about understanding the trajectory of the bullet. Trajectory is the path the bullet follows toward the target.
Since gravity works, the bullet doesn't travel in a straight line.
Because the sights are higher than the bore, the barrel will need to be angled up a little in order to hit the same point you're looking at.
Because the barrel is elevated in relation to the line of sight, and because the bullet travels in an arc, there are two points of convergence where the line of sight and the path of the bullet are the same. Look at this picture:
Line of sight is referred to as Point-Of-Aim (POA).
Where the bullet impacts the target is Point-Of-Impact (POI).
So, a simpler way to state it is POA=POI at two points along the trajectory. This is true with every distance you zero at unless you zero at the apex of the trajectory.
Now let's do some real math. Here is an example of zeroing at 50 yards. With a normal AR and a sight height over bore of approximately 2.5", this is what the trajectory will look like:
Notice that at 50 yards and ~235 yards the bullet path crosses 0. This means POA=POI at those two points. The problem with this is everything between 50 and 235 will hit higher than POA. That means you'd have to hold under for those ranges. Everything closer than 50 and further than 235 will hit lower than POA. This means you'd have to hold over for those ranges. I know it's only 2" either way, but that translates to a 4" spread and some are high and some are low.
Change that to a zero at 100 yards and we get this:
Notice that there is only one place where POA=POI in this chart; 100 yards. Also notice that from 0 to ~205 the POI will be anywhere from 2.5" low to 0. This means that at any distance other than 100 yards, you'd have to hold over a little. At no time will you ever have to hold under. This simplifies the aiming from 0-200 yards because you know your round will hit within 0-2.5" low. That's only a 2.5" total spread.
So, the question comes down to, how often will you shoot beyond 200 yards? If you shoot past 200 a lot, then the 50 yard zero might be for you. If you're like me and never use an AR to shoot beyond 200 yards, and only rarely shoot beyond 100, the 100 yard zero makes more sense.
Anyway, that's why I zero at 100 yards.