<p>In the present paper, we’ll introduce quantities measuring how far a (Schauder) basis is from being semi-boundedly complete or semi-shrinking. These quantities will be proved to be continuous at zero in a sense, which is different from the well-established quantities measuring non-bounded completeness or non-shrinkingness of a basis introduced by the authors and T. Kania in a previous work. As applications, they will be used to prove quantitative versions of the well-known dual relationships between semi-boundedly complete bases and semi-shrinking bases. We’ll also show that several natural measures of weak non-compactness are not equivalent to a natural quantity measuring weak non-null of a bounded sequence for semi-normalized bases.</p>