IMHO, all shooting is first and foremost a mind game.
I also think that most people approach shooting wrong by placing too much emphasis on the equipment.
I'm guilty of this as well. I'm (primarily) an off-hand plinker but also enjoy 10 meter and bench shooting. In all cases I'm very fussy as to the setup - the gun fit, the optics and even sorting pellets.
BUT, the biggest thing (again, IMHO) is in "tuning" myself to the equipment, to the sight picture, to the performance of the weapon. I say "weapon" because I'm referring to anything that is held (bow, slingshot, pistol, rifle, etc).
We have all experienced the feeling of "calling the shot", knowing if it's good or bad even before the impact. The difference between a poor shooter and an excellent one is how consistently/frequently they can call a shot. I'm sure that the 10 meter shooters are extremely skilled at calling the shot.
To be able to call a shot you need to know where the point of impact (POI) is relative to the point of aim (POA) for every shot and post-shot follow through is very important. It helps to be as close as possible to the backstop.
To shoot consistently, you need to master the dozens of little things (breathing, tension - muscle ying/yang, trigger discipline etc.) while you work on your focus.
Of all thing shooting, in any discipline, I believe that mental focus is the key to the shot. That all (good) practice goes to improving your focus.
More to the OP's original comments...
To me, it's not relevant as to which shot breaks the group. I shoot one shot at a time, I don't remember/see the last shot; the next shot is not important; I'm totally focused on this shot to the exclusion of everything else. It matters little if I shoot one time, 5 times, or 10 times at the same target, each shot is an individual event. On a good day, I can usually know/feel if a flier is my fault or equipment related.
...Most days I claim the fliers are caused by gremlins.
Just my 2 cents.
Cheers!
