Reliably predicting video quality as perceived by humans remains challenging and is of high practical relevance. A significant research trend is to investigate visual saliency and its implications for video quality assessment. Fundamental problems regarding how to acquire reliable eye-tracking data for the purpose of video quality research and how saliency should be incorporated in objective video quality metrics (VQMs) are largely unsolved. In this paper, we propose a refined methodology for reliably collecting eye-tracking data, which essentially eliminates bias induced by each subject having to view multiple variations of the same scene in a conventional experiment. We performed a large-scale eye-tracking experiment that involved 160 human observers and 160 video stimuli distorted with different distortion types at various degradation levels. The measured saliency was integrated into several best known VQMs in the literature. With the assurance of the reliability of the saliency data, we thoroughly assessed the capabilities of saliency in improving the performance of VQMs, and devised a novel approach for optimal use of saliency in VQMs. We also evaluated to what extent the state-of-the-art computational saliency models can improve VQMs in comparison to the improvement achieved by using "ground truth" eye-tracking data. The eye-tracking database is made publicly available to the research community.