Supreme Court has indicated, "No one may claim originality as to facts." (The Copyright Office seconds that emotion.) In a 1997 case, the NBA went after a paging service that borrowed a live feed from a basketball game. A court of appeals ruled that sports stats couldn't be protected -- for example, no one can claim rights to the name of the teams playing, changes in score, team in possession of the ball, whether the team was in free-throw bonus, the quarter of the game, and the remaining time in the quarter. Despite that ruling, other leagues such as the NFL, PGA, and MLB have unsuccessfully gone after fantasy sports leagues or other users who have ported their stats.
You're unlikely to run into problems because ... Keep in mind that many of these legal battles deal with more than stats -- for example, some of these cases also dealt with a company's right to use a sports star's name or likeness. And, also, these sports franchises tend to flex their muscles in cases where they have big targets such as Motorola or Yahoo! Aside from the exceptions cited below, we think you can freely use sports statistics in your books.
When could it be an issue? You could run into problems if you seek to lift a complete database of information -- for example, you copy a 10,000 entry database entitled "A statistical analysis of home runs scored when a right handed pitcher faces a left-handed batter." That's because a collection of facts can sometimes be protected under copyright as a compilation (if selected and organized with some creativity). In addition, databases are also sometimes protected under license agreements. So, for example, if you're at a league website and you click on a "I Agree" button under which you promise not to copy data, you may be bound by that agreement despite the fact that copyright doesn't protect the underlying data.