@Neotech
those are good points, which is why I asked the question about it. I re-think B-Ring almost everytime I think about Burn.
To me though, I ave a philosophy with Burn, where I do not want a card in my deck that will be a dead draw. (Obviously, this cannot be 100%) because anytime after three, a mountain -for me- is a dead draw.) But, you need to have (X) amounts of lands, so I do not count lands.
As for creatures, again, in the meta game currently, we need creatures, and most of our creatures are never Dead draws.
When it comes to late game critical situations, if you draw a creature, it can usually save you the game, (if only to block a would be killing creature.)

For Barbarian Ring, I cannot get over drawing it late game when I need a Firebalst, and a mountain to cast it.

For me as well, it is also the same argument against Flame Rift. Flame Rift deals me and my opponent four damage. Barbarian Ring will deal me two damage, before it deals my opponent two damage.

B-Ring works, but it is another Flame Rift philosophy. We either love them or hate them, personally I hate them, but I will still always re-consider them every I go over my deck.