  We investigate the behavior of a greedy sequence on the sphere $\mathbb{S}^d$
defined so that at each step the point that minimizes the Riesz $s$-energy is
added to the existing set of points. We show that for $0<s<d$, the greedy
sequence achieves optimal second-order behavior for the Riesz $s$-energy (up to
constants). In order to obtain this result, we prove that the second-order term
of the maximal polarization with Riesz $s$-kernels is of order $N^{s/d}$ in the
same range $0<s<d$. Furthermore, using the Stolarsky principle relating the
$L^2$-discrepancy of a point set with the pairwise sum of distances (Riesz
energy with $s=-1$), we also obtain a simple upper bound on the $L^2$-spherical
cap discrepancy of the greedy sequence and give numerical examples that
indicate that the true discrepancy is much lower.
