Veterans' Efficiencies Through Savings Act of 2013 or VETS Act of 2013 - Directs the Secretary of Veterans Affairs to conduct a cost-benefit analysis of the provision of medical care by the Department of Veterans Affairs (VA) for: (1) any 75 square mile area where three or more VA outpatient clinics are located, and (2) any 100 square mile area where two or more VA hospitals are located.