In this paper, we evaluate the saturation throughput for an IEEE 802.11 based wireless network considering capture effect at the receiver, while nodes transmit with random powers. In this respect, we consider a scenario consisting of a specific number of wireless nodes. Then, we derive the transmission as well as collision probabilities with respect to the perfect capture effect. In order to maximize the saturation throughput we set up an optimization problem and obtain how to compute optimum values for the probabilities corresponding to different power levels. By providing the numerical results, we deduce that power randomization may lead to a significant improvement in saturation throughput.