Disclaimer: Most wow players are familiar with this. However, I still run into a lot of players in game and in BG forums asking 'how is your battlegroup?' or 'which side wins the most games?' So I'm posting just in case you did not know about this already.
Go to WarcraftRealms.com - WarcraftRealms.com
On the main page, scroll over the 'Realm Data' tab.
On the bottom of the drop down menu click on 'Battleground Stats'
You will be directed to a main survey page. From there, using the drop-down menus you can pick the level bracket and the battlegroup (US and EU). The data is not entirely accurate and obviously not predictive of future faction wins/losses. It just represents an average number of wins/losses for either side within the last few days.
Using this over the course of a few days or weeks, you can monitor how strong a faction is in a particular battlegroup. It might help your decision in transferring or rolling a new toon/twink on a new realm.
Again I'm sorry if you already knew this. If you didn't, I hope it helped .