It has been brought to attention that the energy-carrying relay system can not only increase the energy harvesting of the system but also reduce the energy loss of the system at the same time. In this paper, a trade-off metric is incorporated in the power allocation of the energy-carrying relay system, which can substantially meet the energy harvesting and data transmission requirements of various application scenarios in a more flexible manner. Subsequently, a trade-off metric is proposed, and an optimization problem for maximizing the trade-off metric value is constructed. Eventually, the optimal solution for optimizing the trade-off metric is obtained by applying Lagrangian multiplier method. It has been shown in experimental simulations that the trade-off metric has the minimum value of 0.4073 when ω=0.54, which represents the intersection of the three curves. It implies that the proposed trade-off metric can precisely describe the relationship between the probability of successful information transmission and the energy harvesting power. Most importantly, the trade-off metric proposed in this paper can well illustrate the relationship between energy harvesting and information transmission. Whether it is a symmetrical channel or an asymmetrical channel, where the optimal solution derived through theoretical calculations is consistent with the experimental result.