Our work addresses the problem of placement of threads, or virtual cores, onto physical cores in a multicore NUMA system. Different placements result in varying degrees of contention for shared resources, so choosing the right placement can have a large effect on performance. Prior work has studied this problem, but either addressed hardware with specific properties, leaving us unable to generalize the models to other systems, or modeled much simpler effects than the actual performance in different placements. Our contribution is a general framework for reasoning about workload placement on machines with shared resources. It enables us to build an accurate performance model for any machine with a hierarchy of known shared resources automatically, with only minimal input from the user. Using our methodology, data center operators can minimize the number of NUMA (CPU+memory) nodes allocated for an application or a service, while ensuring that it meets performance objectives.