I know volume because I am running broad, modified broad, phrase, and exact in an attempt to get my adwords ads "on top" of the page more often.
I also can see what is going on from the "See Search Terms" Adwords report and I'm logging and paying attention to the actual search terms coming from my Adwords ads server side in MySQL.
For a big site like mine, which has lots of different widgets, its pretty daunting to think I need to put effort into optimizing for each widget in order to show for search terms that include my non-common domain name. The number of of possible widget terms that could be combined with my domain is in the 100's of millions.
I have these widget terms in search results that look like ?kw=widget, but I guess Google doesn't like that as much as /mydomain/widget.... I thought they fixed that?