Energy savings performance contracts between the energy users and the energy service companies (ESCO) are used to finance energy efficiency investments by using the future energy savings that will result from these investments. We present an analytical model to characterize the energy savings performance contracts and discuss how the risks of estimating the energy savings affect the energy user and the service provider. This characterization allows determination of the contract parameters for a balanced contract with the information about the energy savings that are expected from the planned energy efficiency investments. Since it is difficult to get the statistical information about the energy savings before investing in an energy efficiency project, we develop a distribution-free contract that sets the guaranteed energy savings level based on the mean and the standard deviation of the energy savings and the profit-sharing ratio between the ESCO and the energy user. We show that a simple distribution-free balanced contract performs satisfactorily when the distribution of the energy savings is not known and its mean and the standard deviation are estimated with error. Our analytical results show that the energy savings contracts with the right parameters can mitigate the risks related to realization of the anticipated energy savings.