Exact Expected Average Precision of the Random Baseline for System Evaluation

Average precision (AP) is one of the most widely used metrics in information retrieval and natural language processing research. It is usually thought that the expected AP of a system that ranks documents randomly is equal to the proportion of relevant documents in the collection. This paper shows that this value is only approximate, and provides a procedure for efficiently computing the exact value. An analysis of the difference between the approximate and the exact value shows that the discrepancy is large when the collection contains few documents, but becomes very small when it contains at least 600 documents.