Documentation of \mathop

The description in tex.web is clearer. An op_noad is an atom built with \mathop or a mathchar of class 1. It follows that a single character is centered with respect to the math axis, but a “complex” nucleus won't. Note that \mathop{{\delta}} would not work, because the braces around a single character are always removed in math mode; more technically, a subformula consisting of a single character or of a single Acc atom is stripped off the braces and inserted as a normal atom.

Appendix G rule 13 ends with the text

Shift box~$x$ down by ${1\over2}\bigl(h(x)-d(x)\bigr) -a$, where $a=\sigma_{22}$, so that the operator character is centered vertically on the axis; this shifted box becomes the nucleus of the Op atom.