stretch resize video in div wrapper

HTML

<div id="wrapper">
    <video id="vid" src="/Users/richrubio/Desktop/PlayVig/video/playvig-hd.mp4" autoplay loop muted>
    </video>
</div>

CSS

#wrapper {
    position: relative;
    width: 400px;
    height: 500px;
    background: red;
    overflow:hidden;
    text-align: center;
}

#vid {
    height: 100%;
    display:inline-block;
}

JavaScript

$(document).ready(function(){

    var $wrapper = $("#wrapper");
    var $vid = $("#vid");

    var deltaW = $vid.width() - $wrapper.width();
    
    $vid.css({
        "position":"absolute",
        "left": (-1) * Math.floor(deltaW / 2)
    });
    
});