Sometimes the point of a Web search is not to find a specific item, but rather to determine an item's popularity or notoriety. For example, I can put my full name into Google, and it'll turn up results that relate directly to me. But if I put only my first name in, it comes up with more than 60 million
hits. I know I'm in there somewhere, but I'd like to know exactly where. If I refine my search terms I'm more likely to find the exact term, but I lose the greater context. Call it vanity, or perhaps it could be considered valid research, but I'd like to know how likely I am to be found on the Web given only one piece of information about me. It could be my first name, last name, date of birth, a club affiliation, or any piece of data about me that is on the web somewhere.
I would provide a function that allows me to search within the previous search results, such that typing in a second word or phrase jumps me directly to the matching hits within the first search. For example, in a list of 60 million hits matching my first name, adding my last name to the search would jump me directly to, say, hit 21,234,893--which just happens to be about me. Subsequent secondary hits could be navigated to as well with conveniently provided buttons.
Taking it a step further, it would be possible to display a graph of the universe of primary hits along the X axis, with the Y axis representing the frequency of secondary hits among those items. That would allow you to see if most of your secondary hits are clustered in popularity around a certain point, as well as quickly jump to portions of the primary search that are more likely to be relevant.