Pre-training has been widely adopted in deep learning to improve model performance, especially when the training data for a target task is limited. In our work, we seek to understand the implications of this training strategy on the generalization properties of downstream models. More specifically, we ask the following question: how do properties of the pre-training distribution affect the robustness of a fine-tuned model? The properties we explore include the label space, label semantics, image diversity, data domains, and data quantity of the pre-training distribution. We find that the primary factor influencing downstream effective robustness (Taori et al., 2020) is data quantity, while other factors have limited significance.