Rethinking How to Extend Average Precision to Graded Relevance

We present two new measures of retrieval effectiveness, inspired by Graded Average Precision (GAP), which extends Average Precision (AP) to graded relevance judgements. Starting from the random choice of a user, we define Extended Graded Average Precision (xGAP) and Expected Graded Average Precision (eGAP), which are more accurate than GAP in the case of a small number of highly relevant documents with high probability to be considered relevant by the users. The proposed measures are then evaluated on TREC 10, TREC 14, and TREC 21 collections showing that they actually grasp a different angle from GAP and that they are robust when it comes to incomplete judgments and shallow pools.