For the last 50 years, the journal impact factor (IF) has been the most prominent of all bibliometric indicators. Since the first Journal Citation Report was launched, the IF has been used, often improperly, to evaluate institutions, publications, and individuals. Its well-known significant technical limitations have not detracted from its popularity, and they contrast with the lack of consensus over the numerous alternatives suggested as complements or replacements. This paper presents a percentile-distribution-based proposal for assessing the influence of scientific journals and publications that corrects several of the IF's main technical limitations using the same set of documents as is used to calculate the IF. Nearly 400 journals of Library Science and Information Science and Biochemistry and Molecular Biology categories were analyzed for this purpose. The results show that the new indicator retains many of its predecessor's advantages and adds benefits of its own: It is more accurate, more gaming resistant, more complete, and less influenced by the citation window or extreme observations.