A great book with some parts on Ty Cobb is Rob Neyer's Big Book of Baseball Legends: The Truth, the Lies, and Everything Else. In the book, Rob attempts to corroborate baseball stories with statistical box scores and other resources. If you like baseball and stats, it's a great read. It doesn't paint a picture of Cobb's entire life. However, it does discuss some different stories about Cobb. For example, Cobb claimed that his Tiger's could beat the pitcher Carl Mays any time and in 52 games against the Tiger's Mays went 23-12. Keeping in mind at that time pitchers would have gone longer in games and had more control the win statistic today. Neyer, also claims that story of Ty Cobb killing a man in Detroit is fabrication.

I apologize, it's been a while since I read the book and I don't have my copy anymore, but got some of the statistics from an excerpt of the book.