Single-wall carbon nanotube field-effect transistors (CNFETs) have been shown to behave as Schottky barrier (SB) devices. It is not clear, however, what factors control the SB size. Here we present the first statistical analysis of this issue. We show that a large data set of more than 100 devices can be consistently accounted by a model that relates the on-current of a CNFET to a tunneling barrier whose height is determined by the nanotube diameter and the nature of the source/drain metal contacts. Our study permits identification of the desired combination of tube diameter and type of metal that provides the optimum performance of a CNFET.