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There are over 100 variables that in various combinations can account for why a site ranks high. Here's a lengthy, detailed discussion that should help, outlining the factors for determining scoring:
The 100 for Google Rankings [webmasterworld.com].
Hope that helps.
The site starts off with 5 pictures of women in different hats and is titled "The different hats of xxxx". That is all there is on the home page. Each picture is a link to another page where you are told all about the wonderful things this person has done while wearing that hat (as a mother, as a good-deed-doer, as a lawyer, etc., ad nauseum).
The particular key word is buried as an incidental comment in one of these self-congratulating "hat" pages.
There is no worthwile content anywhere on this site. My conclusion is that in some cases there is no objective way of figuring out how on earth Google ranks a particular site.
have you read this article...?
Also, "hat" is not part of the key phrase. The phrase appears deep down where she refers to a book title that has the key phrase in it. I guess this is what is called serendipity ranking (hey, did I just coin a phrase?).