I'm at work so I'm not going to try and do some experiments, but my guess at relative frequency of (under)promotion being the best move (Queen = 1) is something

I'm at work so I'm not going to try and do some experiments, but my guess at relative frequency of (under)promotion being the best move (Queen = 1) is something like; Knight 1e-3 Rook 1e-5 Bishop 1e-7 A complicating factor in measuring this is that often a rook serves just as well as a queen, the opponent is going to capture immediately anyway, so players sometimes underpromote to a rook just for the fun factor. My number is more meant to represent cases where underpromotion really is the best move. Knight underpromotion is by far the most important, because a knight can do things a Queen can't, most typically give check to keep a combination going without giving the opponent an opportunity to play an active move. Rook and Bishop underpromotions can only be advantageous when they simultaneously avoid stalemate and keep a winning advantage. This is much more likely with a rook, for example in the famous Saavedra position, perhaps the most famous chess problem of all (it featured as decoration on our wedding cake :).