If you talk about Markov chains at some point there are a lot of cool applications to baseball. For instance using available batting statistics you can construct a team consisting of 9 Alex Rodriguez's and compute (or simulate really) how many runs such a team would score in 9 innings. You can do more detailed analysis of players as well. One place to look for more details about this (and other fun applications in sports) is the book "Mathletics" by Wayne Winston.
