  We find upper bounds for the spherical cap discrepancy of the set of
minimizers of the Riesz $s$-energy on the sphere $\mathbb S^d.$ Our results are
based in bounds for a Sobolev discrepancy introduced by Thomas Wolff in an
unpublished manuscript where estimates for the spherical cap discrepancy of the
logarithmic energy minimizers in $\mathbb S^2$ were obtained. Our result
improves previously known bounds for $0\le s<2$ and $s\neq 1$ in $\mathbb S^2,$
where $s=0$ is Wolff's result, and for $d-t_0<s<d$ with $t_0\approx 2.5$ when
$d\ge 3$ and $s\neq d-1.$

Classical Analysis and ODEs