The sight picture is less important than you might think. Firstly, your eyes aren't supporting the rifle and, secondly, only a fool trusts everything they see. Reality is only so real.
I've always preferred open sights, I'm not a fan of telescopic sights. Yes, they magnify the image but they also magnify the wobble. Yes, they have cross hairs but that's a limitation in itself and nor do I play Call of Duty...Quick Scope my fanny!
So you have a foresight and a rearsight, the first near the end of the barrel and the other near the breech closer to your eye. You look through the rear one and centralise the front one. To do that most effectively you focus on the foresight. The distance between the two sights is known as the sight base and the longer the distance the more accurately you can line up the barrel. There is no sight base as such with a telescopic sight making it more difficult to ascertain the rifles alignment.
My air rifles had beautifully basic blade and V sights. The rearsight was a V shaped notch in which you align the blade centrally at the bottom of the V and level with the top of it. You don't want to obscure what you're aiming at with the sights so the target should sit above the blade. I used to have a confusing time wondering whether it was best to have a clear image of the rear sight, foresight or target. All I could tell you is I certainly couldn't focus on all three.
One of my favourite games was to fill a 2 litre pop bottle with water and fire as many shots as I could from top to bottom in a vertical line to have as many holes as possible spewing water before the water ran out. Within the whole process of firing one shot the sight picture was pretty unimportant, there was barely time for it.
The kind of shots you'd often miss were exactly those you tried the hardest not to. The longer you hold the rifle or stare through the sights the more effort you impart and naturally you get tired. Target rifle is always moving because of the sight picture and so it's as much a game of releasing the shot at the right moment just like clay pigeon. The movement is a lot less but the scoring zone is significantly smaller. That moment may be fractions of a second and I often say as soon as your conscious mind has told you it's a good sight picture, you have already missed.
We are beings preoccupied with the world outside of us. We are easily distracted and forget the truths found within us. Shooting is the same. You will not find answers to your true alignment through your sights. You must breathe, relax, feel and think about what your body is saying. Do not rely on the implement in your hands to tell you how you are doing. You are responsible for it, and it is inanimate.
So, essentially all the sights do is confirm visually where you are pointing the rifle. If you're supporting it incorrectly they won't do much to help you.