In wireless sensor networks, multi-path routing is proposed for energy balancing which prolongs the network lifetime as compared to single-path routing where utilization of a single route between a source node and the base station results in imbalanced energy dissipation. While it is evident that increasing the number of routing paths mitigates the problem of energy over-utilization in a subset of nodes acting as relays, the net effect of the proliferation of multiple routing paths on energy balancing remains unclear. It is imperative to keep the number of routing paths as low as possible without significantly deteriorating the network lifetime; therefore, determination of the optimal number of routing paths in multi-path routing by considering the tradeoff in routing complexity and network lifetime extension is an interesting research problem. In this study, to investigate the impact of the number of routing paths in multi-path routing on network-wide energy balancing under optimal operating conditions, we build a novel mixed integer programming framework. We explore the parameter space consisting of a number of paths, number of nodes, maximum transmission range, network area, and network topology. The results of the analysis show that by utilizing the optimization scheme proposed, it is possible to achieve near-optimal energy consumption (within 1.0% neighborhood of the case where no restrictions are imposed on the number of routing paths in multi-path routing) using at most two paths for each node.