The question of which factors contribute to system stability for complex systems is foundational. I will present how the Energetic Equivalence Rule (EER)—different species populations use approximately the same total amount of energy per unit of time, thus roughly equipartitioning available resources in a habitat—helps resolve the complexity-stability paradox for food webs. The paradox is that increasingly complex systems are less stable according to theory, yet are commonly observed in nature. As part of this, I will derive a new mathematical bound that provides novel insights into how ecological constraints directly relate to system stability. Namely, the EER leads to approximately constant row sums of the Jacobian matrix that defines system stability, and our new bound shows that this means increasing complexity will not lead to system instability. Instead, and in direct opposition to previous results, increasing complexity can improve system stability. Conversely, systems that do not exhibit a version of EER would become unstable and thus less likely to exist in nature, offering a reason for why strong violations of EER are not frequently observed. These conclusions are consistent with our analysis of experimental data for stable microbial systems taken from the human gut.