Increasing power costs has renewed interest in software based power optimizations. One of the key question that any software based mechanism needs to decide is: How long should I wait before changing the power state of a device? In this paper, we study the solution space of this problem based on the workload history and device characteristics. We model the workload as a distribution of idle times (collected online) and the device characteristics using break-even time. Our analysis shows that one should not do any power savings if the mean of the idle time distribution is lower than. We also show that being greedy (i.e. wait time = 0) gives the highest power savings for most of the well known distributions. Our model is also able to capture special cases such as bimodal distributions.