It's probably like 1/2 to 1/4 to get an item from the lockbox.
So you're looking at 290 bg wins before you'll "probably" get one if it's 0.7% (cause 1/29 * 1/5 * 1/2 = 1/290 and 290wins *1/290chance =1) and a 1 in 2 chance of getting an item from the lockbox (and not honor or gold).
Really it feels more like 1 in 3 to 1 in 4 to me, so 4*29*5= 580 wins before you'll probably get one from a bg. More of course for a gem slotted one.
To put that further into context let's say you do premades and each bg takes 15 minutes to win on average it will take you 8700 minutes or 145 hours or 20 days playing ~7 hours per day of nothing but premade battlegrounds.
Enjoy your farming.....