This is an announcement for the paper "On quantification of weak sequential completeness" by O.F.K. Kalenda, H. Pfitzner and J. Spurny. Abstract: We consider several quantities related to weak sequential completeness of a Banach space and prove some of their properties in general and in $L$-embedded Banach spaces, improving in particular an inequality of G.~Godefroy, N.~Kalton and D.~Li. We show some examples witnessing natural limits of our positive results, in particular, we construct a separable Banach space $X$ with the Schur property that cannot be renormed to have a certain quantitative form of weak sequential completeness, thus providing a partial answer to a question of G.~Godefroy. Archive classification: math.FA Mathematics Subject Classification: 46B20 Remarks: 9 pages Submitted from: kalenda@karlin.mff.cuni.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1011.6553 or http://arXiv.org/abs/1011.6553