Much recent activity in our group and the MRSEC has focused on the connection between local structure and localized rearrangements in a variety of systems. Focusing on packings of soft spheres, sheared at zero temperature, I will explore the limits of this predictiveness. There are reasons to believe local structure should be less predictive in higher spatial dimensions - can we see any signature of this? Does proximity to the unjamming transition have a strong effect on the predictiveness of local structure? We will see that, at least for some notion of short-term predictiveness of the dynamics, these parameters don't seem to have as much effect on predictiveness as we might have expected.