I think you have to click into their profile and go to "view stats" or something like that.
Win/loss

If you hover over a player's name, right click, Open link in new tab - this will take you to their profile page. Then clicking on My online chess (or My live chess) will take you to the relevant statistics. That's a few clicks - but at least you haven't lost your original window.
There are two problems with the existing mouse-over; first, it only works in certain contexts (mainly only in the forums); secondly, it contains limited information and everybody want to see a slightly different dataset.
Is there anyway that players' win/loss record and/or opp avg rating be displayed on the game screen? I try to find these statistics before a game, but my opponent always aborts before I can find them and navigate back.