Many of the highest-performing polymer photocatalysts for sacrificial hydrogen evolution from water have contained dibenzo[b,d]thiophene sulfone units in their polymer backbones. However, the reasons behind the dominance of this building block are not well understood. We study films, dispersions, and solutions of a new set of solution-processable materials, where the sulfone content is systematically controlled, to understand how the sulfone unit affects the three key processes involved in photocatalytic hydrogen generation in this system: light absorption; transfer of the photogenerated hole to the hole scavenger triethylamine (TEA); and transfer of the photogenerated electron to the palladium metal co-catalyst that remains in the polymer from synthesis. Transient absorption spectroscopy and electrochemical measurements, combined with molecular dynamics and density functional theory simulations, show that the sulfone unit has two primary effects. On the picosecond timescale, it dictates the thermodynamics of hole transfer out of the polymer. The sulfone unit attracts water molecules such that the average permittivity experienced by the solvated polymer is increased. We show that TEA oxidation is only thermodynamically favorable above a certain permittivity threshold. On the microsecond timescale, we present experimental evidence that the sulfone unit acts as the electron transfer site out of the polymer, with the kinetics of electron extraction to palladium dictated by the ratio of photogenerated electrons to the number of sulfone units. For the highest-performing, sulfone-rich material, hydrogen evolution seems to be limited by the photogeneration rate of electrons rather than their extraction from the polymer.