Pretty much what he said.
People seem to think that handgun bullets have horrible trajectories where it makes a difference if it is sighted in at 5 yards versus 25 yards versus 50 yards.
It doesn't.
Let's take a run of the mill 9mm Para with a 124 gr bullet at 1200 fps. With a 5 yard zero it will impact:
.4" high at 10 yards
.8" high at 15 yards
1.1" high at 20 yards
1.4" high at 25 yards
1.6" high at 50 yards
0" at 75 yards
3.6" low at 100 yards.
If you zero at 15 yards instead you get:
.3" low at 5 yards
.1" low at 10 yards
0 at 15 yards
0 at 20 yards
0 at 25 yards
1.1" low at 50 yards
4.1" low at 75 yards
9.1" low at 100 yards.
If you zero at 25 yards you get:
.3" low at 5 yards
.1" low at 10 yards
0 at 15 yards
0 at 20 yards
0 at 25 yards
1.2" low at 50 yards
4.2" low at 75 yards
9.1" low at 100 yards.
Those last two are not copy/paste errors - the difference between 15 yards and 25 yards makes almost no difference as the differences in angles of departure are so minor as the angle is is so flat with the low sight height on a pistol.
The 5 yard zero is flatter shooting because the 5 yard zero with a 1/2" sight height is really a 75 yard zero - I just haven't met many pistol shooters who can zero a pistol at 75 yards and get a group small enough to determine the actual zero. It'll sound unkind but most shooters can't shoot a pistol worth a hoot at 5 yards either - not enough for the differences in trajectory at 5 to 50 yards to be noticeable.
Got a pistol and a person sized target? Shoot center of mass from 0 to 100 yards and don't think twice about it.
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Elevation adjustable rear sights exist on handguns to regulate the pistol or revolver for the load, rather than to adjust the zero. As noted above at social shooting ranges, the zero range doesn't matter.
However recoil does matter in a pistols and revolvers as it does affect the angle of departure of the bullet.
For example, most .38 specials are regulated for a 158 gr standard pressure load. Shoot a 125 gr load in it and it will shoot low - maybe 2-3 inches at 12 yards - due to the shorter time in the barrel and less resulting muzzle rise before it exits the bore.
The elevation adjustment then allows for the sight to be adjusted to compensate for that difference between loads and will enable you to adjust a target pistol or revolver to hit the bullseye dead center at your chose range with your chosen load.
On a combat handgun it really doesn't matter as 2-3" over 12 yards isn't going to matter in the big picture.
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Some shooters, particularly those who are accuracy challenged, are tempted to zero their pistol off a rest to get more precise accuracy. That might allow them to get smaller groups, but it changes the dynamics of how the handgun and shooter react in recoil, which means the zero is only valid when shooting off a rest.
If you have to use this approach, because you can't hit the broad side of barn with handgun, then sit behind the gun in a more or less up right position with your forearms resting on a support, rather than your hand or handgun, so that it recoils closer to how it will in the off hand position.
But if you need to zero that way, don't bother as the difference in zero will be minor and will be lost in the noise of your much larger "all over the target" accuracy problem.
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The other problem with adjustable sights on a handgun is that people will have problems with their shooting technique that might throw shots, right, or left, high or low, in a more or els consistent manner. That means the shooter is then using the sight adjustment as a crutch for poor technique (poor, inconsistent grip, tightening the grip just before the shot breaks, too much or too little finger on the trigger, poor trigger squeeze, poor sight alignment, heeling the pistol, anticipating the recoil, etc) and if their technique improves, they'll start shooting in the other direction(s) from their point of aim.
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You also don't need to adjust handgun sights as much as you probably think you do, as the sight radius is short and small adjustments have a large effect on the target.
For example I was shooting a new to me 4" Model 15 the other day with my usual 158 gr LSWC target load at 25 yards. The first 6 shots were centered on a point about 1.5" high and 2.5" right of point of aim (the center of the 3"x3" in the center of the head) on a QIT-03 target. Two clicks left and 1 click down was all it took to adjust and bring the entire group inside the box.