16. A system comprising: one or more server devices comprising: one or more memory devices to store instructions; and one or more processors to execute the instructions to: obtain a rank position map, the rank position map specifying, for a plurality of rank positions, an expected utility rate for a document presented at a particular one of the plurality of rank positions as a search result, the expected utility rate being derived from an aggregate quantity of selections of the document presented as a search result at the particular one of the plurality of rank positions; determine an expected utility rate, for a particular document, based on the obtained rank position map and based on a quantity of times that the particular document was presented as a search result at particular ones of the plurality of rank positions; determine an actual utility rate for the particular document based on an actual quantity of selections of the particular document and based on a total quantity of times that the particular document was presented as a search result; calculate a correction factor, for the particular document, based on the determined expected utility rate and the determined actual utility rate; determine a confidence level for the correction factor, the confidence level representing a measure of confidence associated with the correction factor; adjust the correction factor based on the determined confidence level; select, based on determining that the confidence level is less than a threshold, a set of documents, the particular document being included in the set of documents; calculate an aggregated correction factor for the set of documents; use the aggregated correction factor as the correction factor for the particular document; adjust a score of the particular document based on the correction factor; and provide, for presentation, a ranked list of search results, one of the search results corresponding to the particular document, and a ranking of the search result corresponding to the particular document being based on the adjusted score.
17. The system of claim 16 , where the one or more processors are further to: determine a decaying average expected utility rate for the particular document based on the determined expected utility rate, a previously determined average expected utility rate, and a decay constant, and where, when the one or more processors are to calculate the correction factor for the particular document, the one or more processors are to calculate the correction factor based on the decaying average expected utility rate.