In this article, a novel important-data-based (IDB) attack strategy and stochastic IDB attack power allocation scheme are proposed, from the attacker's perspective, to degrade the remote state estimation in sensor networks. The main feature of the proposed IDB attack is that, by intercepting the measurement output, the adversary can identify the important packets transmitting among sensing nodes, and by injecting more power to increase the attack success probability (ASP) of these packets, thereby enhancing the attack destructiveness. Then, according to the identified ASP of packets, a scheme is designed to allocate the attack power to each channel with the help of the signal-to-noise ratio such that packets with higher ASP would face attacks with more power. Subsequently, the relationships are characterized among the attack parameter, the ASP, the attack power, and the constrained energy via stochastic analysis method, and the threshold of the attack parameter is designed to achieve a balance between the attack effects and the energy constraint. Finally, an illustrative simulation is given to verify the effectiveness of the stochastic IDB attack strategy and stochastic IDB attack power allocation method.