In my case -- and likely enough, I'm not as good a shooter as you are -- my own variability is way more than adequate to explain a single target such as the one that began this thread, without having to conclude I should adjust my sights. For me -- and I suspect, others of similar ability -- adjusting my sights without more data is not the way to bet. The odds just don't favor it. What more is there to say???
Nicole:
What I am going to say may be strange, but the answer is for that group in the first picture (or a series of shots with that distribution) and the shooter is calling your shots consistently centered, then adjust the sights. And record it and continue to shoot to see if the shots migrate towards the center of the target.
Suppose the shooter is are doing something different that is not related to the environment. So what, for 20 shots (1/3 or 1/2 of the match) the shooter did it and it's produced a pretty consistent pattern. Maybe the way they were setting up before had been overridden by something better. Who knows. What we do know (or are tracking) is that the shooter can gain center hits (and increase points) by adjusting the sights.
Training in an ongoing process. Yes, we want to limit the variables, but like my Grandpa told me about the mule. "After hitting it one time and it still don't move, you might want to check and see if it knows something that you don't." Saved my stupid butt from a run in with a snake one time. Durn mule was smarter than me.
Anyway, back to the point. I'm not your or the shooters coach, but a shooter good enough to shoot that group IS consistent enough to move the sights. Maybe that's where the support / explaination needs to be.
One time I was shooting in a 2700 Bullseye match where that sun was kinda behind the targets. At the start of the .45 agg, Willie Trowell (one time .22 Champ at Perry) looked and me and said move your sights. Well, I had fired one of the best centerfire matches I'd ever had to date, so I wasn't really intending on adjusting the sights. I was going to put them exactly where they were for the centerfire long line.
After the first .45 slow fire string and we came back to the line, Willie said adjust your sights. And pointed to the target. Well after shooting a solid 94 or something like that, I said why, I had a pretty good score? Willie points at the target and says "LOOK!" Illuminated from behind you could see that my top target that was shadowed by the backer had a very nice and round hole behind it, but about 1.5 inches high. But since I "thought" I was shooting well, I had not listened at first or even noticed it when I was shooting the centerfire portion. Adding up the extra points for the strings I could have probably have gained 6 to 8 points on the centerfire aggegrate with just a couple of clicks. It taught me a lesson.
Yes, that group is good enough to move the sights by, if the shooter is consistently calling the shots good. It doesn't take a lot of math for that (And I didn't even have to fall back on my engineering degrees get to the explaination). I think that's all I (and a couple of others) are trying to say.
Cecil