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I know that search engines value subdomains more than paths.
I was going to make all of the pages (thousands) subdomains
This is something that the SE's became much more aware of from an SEO perspective, a couple of years ago. There was a time when it seemed that a majority of listings in competitive SERP's were subdomains. Now there seems to be a reasonable ratio of those pages appearing, i.e., more as it might be in the so-callled 'natural Web.'
My 2 cents anyway.
Finally, how are we to know what the statistical distribution of the natural web is? I mean, there does not seem to be a way to make the IA of my site exactly as the normal distribution for a typical site. Do SEs really penelize for this?
The general wisdom for a while seemed to be it was less a matter of folders away from the root than clicks away from the homepage. But I'm not sure I believe that. In any case, there seems to be little reason to go more then four levels down, and we mainly stay with three...beyond the homepage that is (four total). Often it depends upon the subject matter.
That said, here's some pretty sage advice on site architecure and theme pyramids [searchengineworld.com], here.
If anything, recently it seems that G in particular is worrying less about whether a page is linked form the homepage or not. Right now, they seem to like well optimized pages that are two clicks away from the homepage.
Whatever, it all goes back to make a structure the use can navigate easily and that makes sense logically to SE's and users alike.
Widgets.com/small-widgets/blue.htm makes sense to most everyone.