Large online social rating networks (e.g., Epinions, Blippr) have recently come into being containing information related to various types of products. Typically, each product in these networks is associated with a group of members who have provided ratings and comments on it. These people form a product community. A potential member can join a product community by giving a new rating to the product. We refer to this phenomenon of a product community's ability to “attract” new members as product affinity. The knowledge of a ranked list of products based on product affinity is of much importance for implementing policies, marketing research, online advertisement, and other applications. In this article, we identify and analyze an array of features that exert effect on product affinity and propose a novel model, called AffRank, that utilizes these features to predict the future rank of products according to their affinities. Evaluated on two real-world datasets, we demonstrate the effectiveness and superior prediction quality of AffRank compared with baseline methods. Our experiments show that features such as affinity rank history, affinity evolution distance, and average rating are the most important factors affecting future rank of products. At the same time, interestingly, traditional community features (e.g., community size, member connectivity, and social context) have negligible influence on product affinities.