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I am trying to determine if my site has been manually or semi-automatically dropped to around pages 3 to 4 for its main keyword. If I try those special searches my site ranks around 20 positions higher in top 15 along with the other major sites.
I'm just curious. There is little competition (~200,000 results), my site is optimized for it (not over-optimized) and starting on page 2 the results are mostly from outdates news, blog tags and directories. I think it's realistic to expect to rank somewhere on top of page 2, right where I see it with the special *** searches.
It's a popular "money" keyword so maybe I need to achieve a certain level of Trust Rank before I can get an unfiltered position for it? The domain is 6 months old so it's still relatively new in Google's eyes. All traffic now is from 2 or 3 word searches where rankings are okay.
I'm happy that you asked this question, because there may be some value in noticing WHICH extra words are included and rank near the top.
If I were to take a guess, I'd say that the data collected by Google's phrase-based indexing [webmasterworld.com] is at work here - words that have a higher frequency of co-occurence may be more highly ranked on a wild card phrase. That's just a hypothesis at the moment, but it's one I'm going to experiment with.
And this is the kind of indexing that I theorize might be in use with the * wildcard search results.
If you search widget*, the highlighting function will highlight that and the next word (or next punctuation character, the highlighting is very imprecise). Each asterisk will highlight an additional word.
What's also interesting is that the inclusion of a space (or lack of) changes results too - [google*] is not the same as [google *].
I don't think it's to do with related words though - it seems to me that a query for an unknown words is pretty tricky relevancy-wise, in a similar way to ultra generics like [0..9999999] or [site:com] - so there's some kind of fallback to trust or authority or some such thing ;)
you may find this site interesting - they have lots of ngrams freely available based on the British National Corpus [phrasesinenglish.org...]
"I don't think it's to do with related words though" - I'm thinking it doesn't show "related" words as much as it shows what words co-occur with the search term within Google's index.