We perform a high-throughput computational screening of a set of 3240 conjugated alternating binary co-polymers and homo-polymers, in which we predict their ability to drive sacrificial hydrogen evolution and overall water splitting when illuminated with visible light. We use the outcome of this screening to analyse how common the ability to drive either reaction is for conjugated polymers loaded with suitable co-catalysts, and to suggest promising (co-)monomers for polymeric overall water splitting catalysts.