Can we quantify how position within search results is related to click-through probability?
you might want to look at this paper
Predicting Clicks: Estimating the Click-Through Rate for New Ads


  Whenever an ad is displayed on the search results page, it has 
  some chance of being viewed by the user. The farther down the 
  page an ad is displayed, the less likely it is to be viewed. As a 
  simplification, we consider the probability that an ad is clicked on 
  to be dependent on two factors: a) the probability that it is viewed, 
  and b) the probability that it is clicked on, given that it is viewed: