All the posts before this one have some bit of useful information in them. However some are kinda off base because they come from someone who has mostly only "shooting experience". Others are off because they only apply "science" to the mix - they bring very little learned on the "front lines". And then there are those coming from "thoughts-that-have-been-rattling-around-in my-head". Some demonstrate very clearly that a little bit of learning is a dangerous thing. As I said though, probably all have some value in them.
It seems though there is NEVER any test results given, no numbers, no real measurement made, nothing really concrete as to how much vibration occurs or to a tuners effect. Some say they know how to figure what a tuner should weigh but won't show you how they do this. If some way is suggested to calculate tuner weight it is immediately put down by the "experts". Many say they know how to "tune" a rifle, or a rifle barrel, but never show with numbers how they do this, or even how to test whether it actually been done or not. Many talk of how much this or that improved their accuracy, or their aggs, or scores, or whatever, but they never give a verified, provable amount or number!
I suggest, just suggest, that the bottom line to all this is that the total effect of a tuner on a rifle's accuracy may be very small. So small as to be almost insignificant and thus very hard to measure. This is why nobody can come up with any numbers they can prove are accurate. Accuracy (group size) with modern well made rifles is so good you can't find the slight improvement you get from a tuner or most of the other "improvements" applied to guns nowadays.
From Varmint Al's work I determined with the addition of a tuner you probably could get .01 to .09 min. improvement in accuracy with a centerfire. With a rimfire this falls to .001 to .009 min. improvement. You could take a mean from all this and call it .05 min. with centerfire and .005 min. with rimfire. This is with the normal velocity variations you get with either of these. Remember this is just my take on Varmint Al's results - and he was only working with the recoil effect on vibration, not the bullets effect. There were other data before and in addition to V. A.'s stuff that support this but never the less it still is all approximate. I consider this all still "ball park".
There I've given some "numbers" to use as a starting point. I've told you where they come from and how accurate they might be. Now lets have some more numbers to either support or refute these. Don't tell us how the tuner gives "pretty cloverleaf" groups. or how "much better" you were shooting, or how it "removed the vertical", or how it "helps the aggs", give some test results to show a tuners effect.
None of this is meant to indicate this discussion doesn't serve a purpose. It's good to talk about this and get everybody's ideas. I'd just like to put it on some sort of level playing field where every body is talking about the same thing, that is the SAME tuner effect.