My thought is that it would be impossible to know. A clump with 2-3 eyes and some nice fat roots might bloom sooner than a plant with more eyes and just the min. amount of root. I'd guess that any peony being sold cheaply is probably vigorous and easy to propagate.

I'm such an optimist that if they looked healthy, I'd take them home whatever the size.

Nucci, the usual advice when dividing peony is to give each clump 3 - 5 eyes in each to give the best chance of survival.
Since the new root has as many as 3 eyes, I would think it stands a pretty good chnace of coming through well.
As far as blooming the first year....ugh, ugh....not a chance. Divided plants wont bloom the first year...maybe not the second, so any new root wouldn't provide much.

As a matter of fact, early budding should be discouraged.
If a bud does form on a new tender plant, it probably wont come to anything anyway....and for that reason, it should be nipped off. This sends energy to the production of the plant instead of it trying to create something it cant possibly do properly.

Even lifting a plant for transplanting, the plant is generally recognized as one that will not bloom that year...and maybe not the next.
Peony gardeners are aware of this and don't get discouraged when their favorite plant doesn't bloom when they think it might.

I purchased a box of 4 peony roots from Sam's in the spring of 2005 that were called Peony "Muskoka". I planted them right away and hoped they would come up very soon. Only one came up, but it did not bloom, and I thought the rest were dead for sure.

The next spring (2006) all 4 roots came up and one of them had two blooms on it! The blooms looked nothing like the picture, but there were very beautiful, nonetheless.

Also, Muskoka is not even a registered peony name. So the variety I have was mislabeled and a made up name. The box it came in pictured a double dark pink variety, but the peony bloomed as red Japenese type bloom. I noticed they are using the same picture this year on the peonies at Sam's with a different variety name on the box.

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