Q-measure is a graded-relevance version of the well-known Average Precision. Let R denote the number of known relevant documents for a topic; let gain_l denote the gain value for a document of relevance level l: for example, let it be 3 for a highly relevant document, 2 for a relevant document, and 1 for a partially relevant document. For a given ranked list of documents, let I(r) = 0 if the document at rank r is nonrelevant, and I(r) = 1 otherwise; then C(r) = ∑_{k = 1}^rI(k): the number of relevant documents within top r. Note that Precision at r is given by C(r)∕r. Let g(r) = gain_l if the document at rank r is l-relevant and let g(r) = 0 otherwise; let the cumulative gain be cg(r) = ∑_{k = 1}^rg(k). Define an ideal ranked list for the topic by sorting the R relevant documents by relevance level; let cg^∗(r) denote the cumulative gain at r for the ideal list. Then Q-measure is defined as: