  We investigate possible quantifications of R. C. James' classical work on
bases and reflexivity of Banach spaces. By introducing new quantities measuring
how far a basic sequence is from being shrinking and/or boundedly complete, we
prove quantitative versions of James' famous characterisations of reflexivity
in terms of bases. Furthermore, we establish quantitative versions of James'
characterisations of reflexivity of Banach spaces with unconditional bases.
