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What scope to use for 100 yard groupings?

4-16 FFP works for me with 5.56 because as my eyes get older than my old eyes already are; I need more magnification to see the reticle and my hits at 100 yards.
Properly adjusting your diopter may help you see your reticle. Also choosing a thicker one might help as well or consider illumination.
 
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Depends on the reticle.
And the target. But it mostly depends on which scope in on the gun. I have never had too much trouble quartering 1 moa dots with anything above 9×. Some reticles like the EBR7 I have to turn the mag up higher to see the center dot because I can shoot more consistently than trying to quarter a dot with it. What ever sig used in the tango 6 was like that for me also. I am not a big fan of tiny center dots. More mag isn't always better.
 
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Agree with above. Less is more. I would only buy scopes that were 30X or more. But after awhile, I realized I only used them up to 17-20X

But I will say, it’s nice to have some extra if you need/want it. Zoom in for spotting paper holes or steel impacts.
 
Properly adjusting your diopter may help you see your reticle. Also choosing a thicker one might help as well or consider illumination.
This becomes even more important the older you get. Younger eyes can more easily shift focus from the reticle to the target and back.

And once you use your diopter to focus your reticle on a blue sky or white wall don't touch it. Tighten the lock ring or mark where it's set or tape it in place. After that all focusing is done with the target focus/parallax knob.
 
Highest magnification my scope has, as long as the mirage isn't too bad, then about 80%. In rifles I've swapped scopes on, I've seen no appreciable difference between 20 - 36 power when shooting groups at 100. It just takes a little more concentration on centering the reticle at 20 than it does 36.

If I were shooting competitive benchrest, I'd have a different answer.
 
One of the things I do when shooting for groups is to use a target with long lines vertical and horizontal off the "bull". I use these more than the crosshair to align the scope on the target by superimposing the reticle lines on those target lines.
 
This becomes even more important the older you get. Younger eyes can more easily shift focus from the reticle to the target and back.
Not trying to derail here, but Rodney's comment is exactly why RDS beats irons for pistol shooting as you get older and your eyes don't want to go from sights to target to sights to target. I noticed the problem first with pistols, and it showed itself with riflescopes when I started shooting precision rifle.
 
I think the original question was what kind of scope to work on 100 yard grouping. I dont think one type is better than the other. Even a basic SFP scope could work. I have a 5-25 on a rifle but at 100 yards, usually I only go to about 10 or 11 ("these all go to eleven.") Using less magnification help reduce the wavering.

West Desert Shooter shoots 1,000 yards on 16x.

So, maybe the one bit of advice would be to get a good scope and pick a middle part of the maginfication to do the work. The key point is to aim at the same point every time.
 
More magnification is better, provided it helps you aim at the exact same spot every time. For me 16x is a little lower than I'd like. 20-25x is ideal for me. Once I've proven a given load, if not shooting bench rest, I don't need that much magnification. But if I want to know how capable a new barrel/load is, I absolutely want high power to take aiming error out of the equation as much as possible.
 
The theory that you’re steadier with lower power is false. You just can’t see the error. If you can’t see it you can’t build the discipline to correct it.
I thought I was misunderstanding someone above... people actually think that because you can't see the shake, it's not there? How do they explain the shaking when they zoom in? lol...

I could see, somehow, that less target movement at lower powers could give you more confidence, but it's still an objective degradation of your ability to hold a precise point of aim. It's like you said... the error is there whether you can see it or not. Better to see it and be able to correct it.