There has been considerable work on user browsing models for search engine results, both organic and sponsored. The click-through rate (CTR) of a result is the product of the probability of examination (will the user look at the result) times the perceived relevance of the result (probability of a click given examination). Past papers have assumed that when the CTR of a result varies based on the pattern of clicks in prior positions, this variation is solely due to changes in the probability of examination.
We show that, for sponsored search results, a substantial portion of the change in CTR when conditioned on prior clicks is in fact due to a change in the relevance of results for that query instance, not just due to a change in the probability of examination. We then propose three new user browsing models, which attribute CTR changes solely to changes in relevance, solely to changes in examination (with an enhanced model of user behavior), or to both changes in relevance and examination. The model that attributes all the CTR change to relevance yields substantially better predictors of CTR than models that attribute all the change to examination, and does only slightly worse than the model that attributes CTR change to both relevance and examination. For predicting relevance, the model that attributes all the CTR change to relevance again does better than the model that attributes the change to examination. Surprisingly, we also find that one model might do better than another in predicting CTR, but worse in predicting relevance. Thus it is essential to evaluate user browsing models with respect to accuracy in predicting relevance, not just CTR.