Well, we could find a country that is not particularly competent overall, but was very competent and innovative in one specific civilizational subfield.

Soviet Russia did very well with space and nukes. On the other hand, one of the reasons it imploded was that it could not keep up doing very well with space and nukes.

I think the correlation you're talking about exists, but it's not that strong (or, to be more precise, its effects could be overridden by some factors).

There is also the issue of relative position. Brain drain is important and at the moment US is the preferred destination of energetic smart people from all over the world. If that changes, US will lose much of it's edge.