Carteach0 put up a post where he asked the question, “How far (in thousandths of an inch) must the muzzle deflect to change the point of impact 1moa at 100 yards?” I answered in text in his comments, but it seemed like such an interesting question I wanted to explore it here.
He was considering the full length of the rifle, but I think you could consider the problem from the rear sight forward, as it would be the same whether there is a stock mounted on the rifle or not. On most rifles the rear sight sits over the chamber, the front sight is close to the muzzle. To eliminate all other variables, assume no wind and that perfect ammo is being used, so that if the rifle doesn’t move, every round would impact the same hole. With that, here goes my thoughts on the topic.
Imagine a line that begins at the center of the rear sight, passes over the tip of the front sight, and impacts the target in the center. How much does the front sight move to move the impact point one inch? In my calculation, I assumed my rifle had a sight radius of 16 inches. I used this on-line calculator to solve the angles. Essentially you are solving for a long skinny triangle. Two sides are 3600 inches, the third side is one inch. That makes the small angle 0.0159 degrees. A movement of 0.0159 degrees moves the bullet impact 1 inch. If your sight radius is 16 inches, that means your front sight has to move 0.0044 inches to move the bullet impact 1 inch.
It puts the whole “sight picture / sight alignment” issue in a new light.