As network utilization continues to grow in the coming years, there will be increased pressure on network operators to use traffic engineering to provision resources more efficiently. One way to do this is to allow backup paths associated with disjoint working paths to share bandwidth. Increasing the amount of sharing will naturally increase the risk that a failed working path will either be unrecovered or forced to use dynamic recovery mechanisms. To examine the trade-offs between robustness and efficiency and to develop useful performance bounds, we develop theoretical models for (1:1)n recovery schemes that are independent of the network's topology and management plane. We confirm our results using simulations of uncorrelated failures in a wide-area optical network with various degrees of resource sharing.