A blog is a great way to have an affiliate site. You do need a decent amount of traffic however to get enough people to click through to the betting site and sign up. There are lots of ways to get more traffic, look around these forums or click on the link at the top of this page that says “Education”.
One thing to keep in mind is that most people don’t like banners so sometimes it is easier to send people to the betting site if you include a link within your post.
Perhaps you can make a prediction about a game outcome, show the odds and link to a site where they can place a bet, that would be logical and probably convert fairly well.