“Predictive analytics”(PA) defines the use of algorithms and techniques such as data analytics and Machine Learning to infer sensitive attributes (personal information, future behavior) of target individuals based on large data sets about many other individuals. The pervasiveness of PA raises ethical questions about its legitimacy, and claims of legal shield against the imposed harms. As predictive systems do not extort information and merely generate probabilistic predictions, however, public discussions, normative conceptualizations, and legal frameworks are not adequately equipped to address moral and regulatory demands. This paper argues that, while concerns are legitimate, most attempts in the literature, which appeal to the concept of privacy, do not answer them successfully. Rather, I shift the focus here on a critical albeit unexplored issue: while other cases of elicitation of information or privacy breaches impose harms on us as identified victims, we are statistical victims of predictive systems, as the identity of target individuals cannot be known ex-ante, when training data are collected. The statistical victim problem, a key issue in moral philosophy, thus provides useful conceptual lenses to normatively assess PA. As different responses to the normative relevance of statistical victims are reasonable, more or less stringent obligations might be justified.