Some methods have been developed for automatic effectiveness evaluation without relevance judgments. We propose to use those methods, and their combination based on a machine learning approach, for query performance prediction. Moreover, since predicting average precision as it is usually done in query performance prediction literature is sensitive to the reference system that is chosen, we focus on predicting the average of average precision values over several systems. Results of an extensive experimental evaluation on ten TREC collections show that our proposed methods outperform state-of-the-art query performance predictors.