An abstract is not only a mirror of the full article; it also aims to draw attention to the most important information of the document it summarizes. Many studies have compared abstracts with full texts for their informativeness. In contrast to previous studies, we propose to investigate this relation based not only on the amount of information given by the abstract but also on its importance. The main objective of this paper is to introduce a new metric called GEM to measure the " generosity " or representativeness of an abstract. Schematically speaking, a generous abstract should have the best possible score of similarity for the sections important to the reader. Based on a questionnaire gathering information from 630 researchers, we were able to weight sections according to their importance. In our approach, seven sections were first automatically detected in the full text. The accuracy of this classification into sections was above 80% compared with a dataset of documents where sentences were assigned to sections by experts. Second, each section was weighted according to the questionnaire results. The GEM score was then calculated as a sum of weights of sections in the full text corresponding to sentences in the abstract normalized over the total sum of weights of sections in the full text. The correlation between GEM score and the mean of the scores assigned by annotators was higher than the correlation between scores from different experts. As a case study, the GEM score was calculated for 36,237 articles in environmental sciences (1930–2013) retrieved from the French ISTEX database. The main result was that GEM score has increased over time. Moreover, this trend depends on subject area and publisher. No correlation was found between GEM score and citation rate or open access status of articles. We conclude that abstracts are more generous in recent publications and cannot be considered as mere teasers. This research should be pursued in greater depth, particularly by examining structured abstracts. GEM score could be a valuable indicator for exploring large numbers of abstracts, by guiding the reader in his/her choice of whether or not to obtain and read full texts.