  The nature of the bottomonium-like states $Z_b(10610)$ and $Z_b(10650)$ is
studied by calculating the $B^{(*)}\overline B^{*}$ compositeness ($X$) in
those resonances. We first consider uncoupled isovector $S$-wave scattering of
$B^{(*)}\overline B^{*}$ within the framework of effective-range expansion
(ERE). Expressions for the scattering length ($a$) and effective range ($r$)
are derived exclusively in terms of the masses and widths of the two $Z_b$
states. We then develop compositeness within ERE for the resonance case and
deduce the expression $X=1/\sqrt{2r/a-1}$, which is then applied to the systems
of interest. Finally, the actual compositeness parameters are calculated in
terms of resonance pole positions and their experimental branching ratios into
$B^{(*)}\overline{B}^*$ by using the method of Ref.[1]. We find the values
$X=0.66\pm 0.11$ and $0.51\pm 0.10$ for the $Z_b(10610)$ and $Z_b(10650)$,
respectively. We also compare the ERE with Breit-Wigner and Flatt\'e
parameterizations to discuss the applicability of the last two ones for
near-threshold resonances with explicit examples.
