We present a systematic angle-resolved photoemission spectroscopy study of the substitution dependence of the electronic structure of Rb_{0.8}Fe_{2}(Se_{1-z}S_{z})_{2} (z=0, 0.5, 1), where superconductivity is continuously suppressed into a metallic phase. Going from the nonsuperconducting Rb_{0.8}Fe_{2}S_{2} to superconducting Rb_{0.8}Fe_{2}Se_{2}, we observe little change of the Fermi surface topology, but a reduction of the overall bandwidth by a factor of 2. Hence, for these heavily electron-doped iron chalcogenides, we have identified electron correlation as explicitly manifested in the quasiparticle bandwidth to be the important tuning parameter for superconductivity, and that moderate correlation is essential to achieving high T_{C}.