Nielsen: users so search-reliant it undermines their problem-solving abilities
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Basically it boils down to this: the average person overwhelmingly sucks at Google searching.
If the single search box "worked", the search would provide the results the user wanted without having to use arcane search techniques.
The expectation for a user presented with the single search box is for simplicity and accuracy.
I would bet that there are very few SERP "power users" that know all the ways to manipulate the searches.
Going away from the single search box or providing hard links for filtering results might be a way around this. I imagine that there are many bright minds working on this issue.
What if my definition of "works" includes the ability to use "arcane" search techniques? For example, I wish I could use quotes around my search terms everywhere, to get exact matches. Google now often insists that I need stemming applied in such queries, which I find to be the opposite of "works".
Faceted search is clearly being used by people on sites like Yelp and Amazon but they might not realize it (and might not think of it as "advanced search".) Unfortunately it's harder to add faceted search to a general purpose, free-text search site like Google, so users may not take advantage of it as readily when doing those kinds of searches.