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The nature of the bottomonium-like states $Z_b(10610)$ and $Z_b(10650)$ isstudied by calculating the $B^{(*)}\overline B^{*}$ compositeness ($X$) inthose 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 anddeduce the expression $X=1/\sqrt{2r/a-1}$, which is then applied to the systemsof interest. Finally, the actual compositeness parameters are calculated interms 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\'eparameterizations to discuss the applicability of the last two ones fornear-threshold resonances with explicit examples.

General considerations on the nature of $Z_b(10610)$ and $Z_b(10650)$ from their pole positions