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I am mystified how some sites rank higher than mine in google for my keyword "old widgets".
I have noticed that many of these sites rank highly when you search for "old widgets" in ODP. There seems to be a high correlation between google search result ranking and ODPs.
What determines the ranking of sites in the ODPs search results? Does it influence other search engines?
If you are talking about dmoz.org: I don't think the ranking influences anything. There is some rather unknown algorithm behind the search. Since it's not even completely known to the current staff members, it's highly unlikely to influence anything outside ODP. It does not influence how data is stored in the downloadable RDF file, anyway. So datta users won't be notified of the "ranking"
Iff you are talking about the google directory: Well, its sorted by PR, and PR is still known to influence rankings on Google. And maybe on other SE as well.
The ODP search operates only on the data in the ODP itself: the ODP title and description and the URL. In other words it is not a proper search engine with a spider. It is purely a site search.
It is a misnomer to call it "rank"; it takes into account whether or not all the words occur in ODP description, title, or URL -- a binary function -- and nothing else you can control. (Which is probably a good thing: otherwise, people would be submitting frivolous or malicious "URL update" requests to try to control it.)
Simple? Yes. Unsophisticated by the site-search standards of, um, seven years ago? Yes. Useful? To editors, definitely; to surfers, perhaps sometimes. Not as good as Google directory search? Um, well, OK, if you say so.