OK, so this should work to get some of you a leggo ring but it's going to be one hell of a gamble.
Save up 1,000 Legionfall resources.
Once 7.2.5 hits go cash them all in.
Swap to a spec you have NEVER USED.
This will give you the highest amount of Bad Luck Protection possible and greatly increase the chance of picking up a legendary. Your BLP doesn't really reset until after you score 2 so you can set your loot spec to healing/tanking/off-dps too and hit the mythic+ circuit, LFR, world bosses and even regular raids and world quests. Then once you have 2 swap to your 3rd spec if you've never touched it to hopefully score again.
May the odds be ever in your favor.
Now let's hear everyone scream at me about how I'm wrong. :-)