I have a new (NBS-SEO.com - May 15th 2010), website that I have been tracking closely.
Last week I noticed that the Page Rank went from 0 to 4
I also have another website, FantasticMachines.com that also has a PR4.
Fantastic has been around since the internet was only 4 computers and has built up an organic following of over 5000 websites.
My webstats show only 120 links to the site, not nearly in the same volume as Fantastic.
If Page Rank was being calculated mathematically this simply could not be.
I now suspect that it is based more on relevance than before and less on the math.
All my links to NBS SEO were done in SEO discussions, like this one and that must now count heavily.
In regards to the Caffeine update, Googler Matt Cutts said that it was done to facilitate ranking and not one of indexing.
Ranking is faster for both new websites found by their spider, (no comment on manual submissions yet), and tweaks to existing sites. My last site ranked overnight after it was found on my business website.
In spite of my nbs-seo.com site jumping to PR4, my search results for "organic search engine optimization training" stayed at #2 out of about a million competing sites.
Another factor that swings me to the dissociation of PR and search positions is that a low or even 0PR page can be in a better position than a a page ranking higher.
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