Brendan doesn't really need to win the tournament to provide for his family. If Sparta is as big of a deal as it's presented, making it into the second or third round would generate enough publicity for his dual life angle that he could earn quite a bit in speaking engagements, endorsements and so forth, even if he didn't want to fight again.
Throughout the movie, Paddy Conlon listens to Moby Dick on tape, with long passages audible to the audience. Given that Moby Dick is commonly used as symbolism, it makes sense that a part of the story and/or the characters would mirror the themes of the book. It would make the most sense for Patty's character arc to mirror Moby Dick; he's the one listening to the book on tape. However, Moby Dick is very much about revenge/drive destroying Ahab; he and everyone else dies, while the whale lives on. Paddy doesn't reflect that concept at all; he's much more about atonement and redemption. It bothered me for a while, and it took my third viewing to figure it out: Tommy is Captain Ahab. He is incredibly driven out of feelings of anger and vengeance, and in the end, he is alone and in enormous amounts of pain, having failed to do the thing he set out to do, and the promise of a desertion charge and a severe sentence afterwards.
Tommy's brutal beating of Mad Dog would, at first, seem to be because Mad Dog has been antagonizing him since he first stepped into the gym, but consider this: The Corps are there cheering for Tommy, they sang his intro, and Mad Dog purposefully dyed his mohawk camouflage-colored to mess with Tommy. Tommy beat Mad Dog like the jerkoff he is because Mad Dog was insulting the only family Tommy felt he had.