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I think the phrase "successful search" is considerably less accurate than "left the site after searching," because someone can leave a site for lots of different reasons."
Hitwise later confirmed to me that they don't know whether the user actually clicked on a search result or just went to a completely unrelated site. Given all that, I'm surprised to see Hitwise is still pushing this metric and still calling it "search success rate."
Cutts: "It sounds like Hitwise's definition is "A successful search is defined as one where the consumer leaves the search engine after performing a search." In another words, the user does a query and then goes somewhere else. That doesn't sound the same as success to me; it just sounds like leaving the site.
I'd venture to say that at least 5% of the "success rate" differential is due to more people concerned about their Google rankings than their Bing rankings. Meaning, more people follow their Google rankings than their Bing rankings, which artificially deflates google's "success rate."