Battlepack Puzzle Piece Probability?

I was wondering if anyone knew the exact odds of getting a puzzle piece for each of the battlepack ranks. I want to know which ones I should buy to give me the best probability of getting them. I know superior battlepacks have the best chance of giving you a puzzle piece, but I could buy 4 normal ones with 100 scrap left over instead. Unless I know the exact odds, I can’t make a decision here.