This script will always make sure that the video is covering the browser window and it is centred, whilst the aspect ratio is maintained.

resizeVideo.js

function resizeVideo() {
  var videoEl = document.getElementsByTagName('video')[0];
	var videoOriginalWidth = 854;
	var videoOriginalHeight = 480;
	var videoRatio = videoOriginalWidth/videoOriginalHeight;
	var winWidth = window.innerWidth;
	var winHeight = window.innerHeight;
	var videoWidth;
	var videoHeight;
	var videoDimensionMultiplier = 1.1;

	// Calculate the video dimensions based on the window dimensions
	videoWidth = Math.ceil(winWidth);
	videoHeight = Math.ceil(videoWidth / videoRatio);
	if(winWidth / winHeight < videoRatio) {
		videoHeight = Math.ceil(winHeight);
		videoWidth = Math.ceil(videoHeight * videoRatio);
	}

	// Multiply the calculated values (to cover off gaps around edges for instance)
	videoWidth *= videoDimensionMultiplier;
	videoHeight *= videoDimensionMultiplier;
	
	// Set the dimensions and positions of the video element
	videoEl.style.width = videoWidth + 'px';
	videoEl.style.height = videoHeight + 'px';
	videoEl.style.left = 0.5 * (winWidth - videoWidth) + 'px';
	videoEl.style.top = Math.floor(winHeight * 0.5 - videoHeight * 0.5) + 'px';
};