"Makes a mockery of the 'ranking reports' so beloved of some people."
That would be me! Been watching them for years. Well, just by doing my own searches.
I do notice a jump in visits when my site moves from page 2 to page 1, or up on page 1.
Since I began this topic, I have resolved the issue another way. My website stats for visitors who found my site with a search show the place my site appeared in their search results. So if I just look at the results for the search string I'm interested in monitoring, I can see where it falls in my visitors' search results.
Of course this only works if the results of the search string are high enough in the results that people actually find my site searching for them.