This paper presents a new statistical-analytic approach intended to enable operators to make video bandwidth and QoE decisions with confidence. The method we present is based on a new way of describing video-quality and bandwidth efficiency in terms of statistical probabilities. It can be applied to any video distribution method including ABR, CBR, and statmux for any format. A significant aspect of our method is that is does not require explicit traditional measurement of video quality in terms of PSNR, SSIM, or MOS values. Instead, we show that a metric derived from program complexity can be used as a statistical indicator of quality. Finally, this paper will show how real world data from in-service operations can be used to address key performance questions such as: What is the probability that video quality drops below any given level? Which programs are not receiving enough bandwidth? What is the efficiency of dynamic bandwidth allocation (VBR or ABR) compared to CBR allocation to each video program? Which operational parameters could be changed to improve overall video quality and efficiency? How would introduction of a new service impact existing services?