Ice recrystallization inhibitors (IRI) are of critical importance in biology, cryopreservation of cells and organs, and frozen foods. Antifreeze glycoproteins (AFGPs) are the most potent IRI. Their cost and cytotoxicity drive the design of synthetic flexible polymers that mimic their function. Poly(vinyl alcohol) (PVA) is the most potent biomimetic found to date, although it is orders of magnitude less potent than AFGPs. A lack of molecular understanding of the factors that limit the IRI efficiency of PVA and other flexible ice-binding polymers hinders the design of more potent IRI. Here, we use molecular and numerical simulations to elucidate how the degree of polymerization (DP) and functionalization of PVA impact its IRI. Our simulations indicate that the onset of IRI activity of PVA occurs for IS < DP < 20, in agreement with experiments. We predict that polymers with stronger binding to ice per monomer attain IRI activity at lower DP and identify this as a contributor to the higher IRI potency of AFGPs. The simulations reveal that the limiting step for binding of flexible molecules to ice is not the alignment of the molecule to the surface or the initiation of the binding but the propagation to reach its full binding potential. This distinguishes AFGPs and PVA from rigid antifreeze proteins and, we argue, is responsible for their different scaling of efficiencies with molecular size. We use the analysis of PVA to identify the factors that control the IRI activity of flexible polymers and assess the molecular characteristics that endow AFGPs with their exceptional IRI potency.