With the increasing abundance of pretrained models in recent years, the problem of selecting the best pretrained checkpoint for a particular downstream classification task has been gaining increased attention. Although several methods have recently been proposed to tackle the selection problem (e.g. LEEP, H-score), these methods resort to applying heuristics that are not well motivated by learning theory. In this paper we present PACTran, a theoretically grounded family of metrics for pretrained model selection and transferability measurement. We first show how to derive PACTran metrics from the optimal PAC-Bayesian bound under the transfer learning setting. We then empirically evaluate three metric instantiations of PACTran on a number of vision tasks (VTAB) as well as a language-and-vision (OKVQA) task. An analysis of the results shows PACTran is a more consistent and effective transferability measure compared to existing selection methods.