Indium oxide thin films deposited by Pulsed Laser Deposition have local maxima in carrier mobility in the transition region between amorphous and crystalline phases. Using Molecular Dynamics Liquid Quench simulations, and validated by agreement with Extended X-ray Absorption Fine Structure measurements, a possible mechanism for this observation has been proposed. As the cooling rate in the MD simulations is decreased the amorphous structure changes from containing small isolated InO6 clusters, to ones containing InO6 chains, and finally to those containing large isolated InO6 clusters. Local maxima in carrier mobility are also observed in the transition regions for more complex oxides, such as zinc- indium-tin oxide.