Network data needs to be shared for distributed security analysis. Anonymization of network data for sharing sets up a fundamental tradeoff between privacy protection versus security analysis capability. This privacy/analysis tradeoff has been acknowledged by many researchers but this is the first paper to provide empirical measurements to characterize the privacy/analysis tradeoff for an enterprise dataset. Specifically we perform anonymization options on single-fields within network packet traces and then make measurements using intrusion detection system alarms as a proxy for security analysis capability. Our results show: (1) two fields have a zero sum tradeoff (more privacy lessens security analysis and vice versa) and (2) eight fields have a more complex tradeoff (that is not zero sum) in which both privacy and analysis can both be simultaneously accomplished.