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in a perfect curve, but not throwing out one tail can shift the picture when specifically targeting one aspect of the overall system eg., the rifle itself. ... More later. ... best regards, Harry.Harry,
I totally agree with all your remarks. You also are absolutely right that a "flyer" which hits the POA should still be discarded - but not too many shooters would want to throw out a "good" shot!
From a different point of view the idea behind discarding flyers is to improve the overall measure of group size. Group size is very susceptible to a "wild" shot. But if you throw out +/-2.5% tails you don't perturb the measure of average. So a statistical method of analysis would expect to discard some data which is "truly" representative in order to protect against data which is not.
Of course this still doesn't do anything to explain why the flyer occurred, nor what you can do to prevent them.
It also doesn't really help if you're shooting in a competition for points. You don't get do-overs. Same thing when taking a shot hunting. "Hey God, that was an oops. Please reposition the rabbit and let me try again..."
As you reduce the probability of a flyer, it will be harder and harder to prevent them. Think of a quality control type situation. You're sampling pellets to determine if they are good or not. the best you can really expect is to increase the probability that the pellets which pass the tests are good.