Energy hole is an inherent problem in multi-hop sensor networks. It may cause the early death of some nodes and result in a short network lifetime. Mixed data transmission, which randomly propagates data one-hop or two-hop away in each step, has been developed for energy balancing. The performance of this scheme depends heavily on the setting of transmission probabilities. However, no general rules have been proposed to guide the calculation of these probabilities, and little study has done on whether the energy of all nodes are able to be balanced by this scheme, especially under the constraints of limited communication ranges. This paper formulates the problem of energy balancing as an optimal transmission probability allocation problem. It reveals that the transmission probability is mainly determined by the locations of each node; however, the values of the probability become invalid if the network size exceeds a threshold. This work theoretically investigates the energy balance conditions and presents guidelines for allocating the transmission probabilities. It proves that the global energy balance can be achieved if and only if the network size is not greater than n₀. It further reveals that n₀ only depends on the communication profiles of the network. Such a profile is indicated by a newly discovered parameter, which is defined as the premium power ratio of the system. Finally, it extends the two-hop based mixed data transmission scheme to a general model and investigates the impact of the combinations of transmission ranges on energy balancing. Comprehensive simulations are conducted to validate the energy balance conditions. Both the numerical results and theoretical analysis confirm that the global energy balance can be achieved if transmission probabilities are allocated according to the proposed rules.