Tartabull's Throw by Henry Garfield
First book in the Moondog series Cyrus Nygerski is a left-handed second baseman playing for a minor league team belonging to the Chicago White Sox. The year is 1967. He meets a girl named Cassandra. Those are the facts that are true at the beginning of all three possible stories here. Because of time travel, three different stories are outlined over the same time period.
Figuring out what is happening is a big part of the fun in reading this book, so I won't tell you what I think happens. This book is a merger of the sports and fantasy genres, and it doesn't stick to either of those very well. It is also historical fiction, since the story takes place in 1967. The merger of these genres is particularly striking because I can't see any target audience going for it. Hardcore fantasy fans are rarely into sports. The 1967 that the book portrays has the real baseball season in it, in one of these versions. If you know your baseball history, this shuold be an easier read.
One thing about this book that really bugs me is an element that appears to be racist, linking Martin Luther King with warewolves. In one of the realities, blacks are portrayed as warewolves, and if that's not how the book turns out, that maybe mitigates and definitely doesn't obliterate the racism.
Happy reading.