Facebook News Feed personalization algorithm has a significant impact, on a daily basis, on the lifestyle, mood and opinion of millions of Internet users. Nonetheless, the behavior of such algorithms usually lacks transparency, motivating measurements, modeling and analysis in order to understand and improve its properties. In this paper, we propose a reproducible methodology encompassing measurements and an analytical model to capture the visibility of publishers over a News Feed. First, measurements are used to parameterize and to validate the expressive power of the proposed model. Then, we conduct a what-if analysis to assess the visibility bias incurred by the users against a baseline derived from the model. Our results indicate that a significant bias exists and it is more prominent at the top position of the News Feed. In addition, we found that the bias is non-negligible even for users that are deliberately set as neutral with respect to their political views.