Below is a bit of Tussock theorizing. Please keep nickers twist free if you don't agree
Trigger pull and follow through @R93. I have two for this rifle. One when I am shooting for a group at 100m and one when I am shooting with hold over and at greater ranges.
When I add the element of holding over my trigger pull becomes sub-conscious. I shoot off a backpack like on a field rest. Lock time and follow through are a big deal when shooting from field rests because you have a lot more opportunity to move the rifle between the trigger breaking and the projectile departing the end of the barrel. The trigger breaks, firing pin moves forward and hits firing pin, primer goes, powder goes, projectile departs barrel. It is not instant.
When you have a rifle set up rock solid on a bench, it moves in a very controlled way. You could have a very long slow lock time and still shoot well because there is no movement in the rifle as the above sequence takes place.
You will note some characters on this forum shoot bug holes off a backpack in a paddock. Not many, but it can be done. More might do it if there was a reason to try.
When you shoot in the field, it is less about that flawless trigger break on a stable rifle, and more about synchronizing the trigger break with the moment you bring your body to absolute stillness, while the cross hairs are where you want them.
The better follow through comes from being more deliberate with each shot. When I shoot a group at 100m I can see each round hit the paper and for me, the pressure builds not to blow the group out and it is a distraction. This alone can mean your groups tighten up when you shoot further out.
This is why as an exercise, I think you should shoot at a single point, one shot, one target. To get a group equivalent measure the difference between the point of impact and the point of aim. I'm trying to factor this tension build effect out of my shooting.
What Friwi said is important. I have been doing this in 50 round sessions and I come back to 100m from time to time. Going back to 100m feels like driving in a car at 100ks an hour right after you have been going 200ks. 100m suddenly seems very close.
I'm very interested in lock time now. I think the ammo I am using has slow primers or the rifle has long lock time. As I get 3-4 missfires a box there is something up. I increasingly felt with the rifle every time I felt a really sweet shot, it went where I wanted and every flier I pulled. The better it felt, the closer to the point of impact. This is not how it feels with an inherently inaccurate rifle. It feels like things are random. With this Sauer it feels like it is very easy to shoot 1" and very hard, but possible, to do better.
If my theory is correct, then once I have churned through the next 150 rounds currently sitting in my range bag, I should be able to synchronize my trigger break, reticle hold and moment of stillness and tighten my groups up significantly.
The accuracy of the reticle hold is brain magic usually reserved for open sights. Your brain is wired for projectile weapons and has an inbuilt ballistics calculator. Scopes etc get in the way to a degree. I'm not sure if my ability to visualize a point on the cross hairs in precisely the right spot it common, as I spent a few years of my life looking down a microscope measuring things with a reticle. I assume anyone can do it.
The hold over off a plain reticle actually has about ten fold increase in accuracy and precision over how the rifle groups. Your brain clearly has a nack for this. It is basically just image retention.
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