I've shot a few hundred rounds now with multiple Ruger 10/22's in various stages of gunsmithing and the Limbsaver vibration dampening. Legal in Appleseed.

tl;dr: If you do NOT have a free-floated barrel, it will help group size.

What's the Limbsaver? It's $10 of vibration absorbing rubber you put on your barrel. I used Hornady's One Shot to lube it over the front sight.
The speed of sound in steel means that the shockwave of detonation goes up and down your barrel FOUR TIMES before the bullet leaves the crown. The limbsaver tries to dampen this. There is likely a weight factor acting like a "tuner".

With a 10/22, the very first thing you should do every day at the range is make sure your takedown screw is tightened. This gun came from the factory at 20 in-lbs. I didn't group at less because it just should be DONE before and during every Appleseed or day at the range. Some people get a torque driver and play, finding a setting that works for their gun between 10 and 20 in-lbs. I've tested and found anything up from 15 in lbs works in my laminate stock. More than 30 in-lbs and I fret about crushing the wood, making the gun loosen up, or cracking my glass bedding. Even with a pillar, I doubt more than 25 in-lbs would benefit, but you should get a torque driver for $42 and USE IT.

EDIT: Sorry about pic size, they're reduced at Imgur now, still showing huge here. Sorry.

Here's a typical 50 yard group out of a fresh from the box Ruger 10/22. = 1.775" (~3.6 MOA)


Gain half an inch group size at 50 yards by doing something FREE: Remove the barrel band ! That barrel band touching the barrel reduces accuracy. If you use the barrel band to attach your sling, I'm sorry. It's harming your accuracy. It's plastic in modern 10/22's, some people sand it back so it doesn't touch. Life's too short. Throw it away.

Brownell's has "muzzle cap" if you don't like how it looks.
In Silver
https://www.brownells.com/rifl...l_1=Ruger__10zz1zz22

and in Black
https://www.brownells.com/rifl...l_1=Ruger__10zz1zz22

With barrel band removed: 1.35"


So, on to the Limbsaver vibration dampener. $10 at Amazon.
https://smile.amazon.com/LimbS...words=limbsaver&th=1

With the limbsaver positioned 2" from crown:



and the 10 shot group at 50 yards, measuring 0.8" !:


Wow. Halving the group size for $10. Ten bux ! Let's try it in different positions:
Next to forend:

Not as good. 1.10". Statistically close.


What about ramming it into the fore?Might absorb some vibration from fore, maybe lifts up barrel?
Blurry Photographic Evidence


Same result as just in front to the fore:


So, the Limbsaver WORKS. for $10 and removing the barrel band for free, you halve the group size!

Well, what about free floated barrels?


Turns out, No real difference with one Limbsaver. The group without at 100 yards with my uber-Ruger was 1.8" (1.6" with best 9 shots).
With just one Limbsaver 2 inches from crown, the group was WORSE, at 2.1", 1.75" with best 9 shots.

Well... What about FIVE LIMBSAVERS AT ONCE ?!?




WARNING ! REMOVE YOUR ELUDIUM 236 EXPLOSIVE SPACE MODULATOR or there may be an EARTH-SHATTERING 'KABOOM '!


The groups. In my free-floated barrel, one limbsaver at 2" from crown HURT group size. FIVE limbsavers helped the group by 0.15". Likely weight addition increased the vibration node length. Or it absorbed vibration. Dunno.
Conclusion is that a Limbsaver does NOT help my free-floated barrel.

Interesting.