Baseball is probably the greatest sport in the world for statisticians, math fanatics or just people who love to over analyze things. Not only does it have a ton of statistics, but unlike most other sports the statistics can often be used as a predictor of future performance for individual players, regardless of changes to the team as a whole. This is because each player, while on a team, has to perform certian tasks (pitching and hitting) on their own. So while Karl Malone, now playing with Shaq and Kobe on the Lakers, cannot be expected to do as well statistically, moving Barry Bonds to another team in baseball should have no effect on his statistics, outside of park effects, which are also measurable.
Baseball also has an advantage over other sports in this regard because of sample sizes. A regular starter could have 650 plate apperances a year, a pitcher could pitch well over 200 innings. Teams play all of the other teams (at least the ones in their league) and while not every influential factor is controlled for it is much closer to perfect than any other major sport.
Unfortunately (or fortunately, if you're an elitist as well as a math freak) the most common, popular, whatever baseball statistics, such as RBIs, Runs, Batting average, and Strikeouts, are also the least meaningful. While there is a cottage industry for meaningful statistics, a quick-and dirty look at baseball can show you that on base percentage and slugging percentage are the most meaningful offensive statistics. A pretty good estimation of a players offensive value can be derived from the sum of these numbers (referred to as OPS). The product of these numbers is slightly better, but not nearly as easy to calculate by a quick glance, so OPS is normally used.
OPS is useful because it is teammate-neutral, and because it looks at all the possible results of every plate appearance. Your RBI or Runs total is partly a factor of who hit behind or before you; Your batting average does not take into account extra base hits or walks. My favorite example of the problems with batting average is the obsession with the .300 hitter. Trust me, a guy who bats .300, almost never walks, and almost never gets anything other than a single is hurting your team. And there are a lot of these guys in Baseball. Which leads me to the last thing I love about baseball statistics; The fact that baseball experts, columnists, and the such have such a problem with the statistical analysis. They slowly adopt sabermetric ideas (I see OPS mentioned all the time now in articles), but constantly rail against it due to the lack of subjectivity involved. Sometimes they are right; For example, there aren't very good methods yet for measuring defensive performance, so offense is very much emphasized by sabermetricians as being more important.
Finally, one of my favorite managers, Earl Weaver, has been somewhat vindicated by sabermetrics. There is a famous incident where Earl blew up in a radio interview:
Announcer: (A fan) from Frederick, Md., wants to know why you don't go out and get some more team speed.
Weaver: Team speed, for Chrissake, you get (expletive) little fleas on the bases getting picked off trying to steal, getting thrown out, taking runs away from you. You get them big (expletives) who can hit the (expletive) ball out of the (expletive) ballpark and you can't make any (expletive) mistakes.
Announcer: Well, certainly this show's going to go down in history, Earl. Terry Elliott of Washington, D.C., wants to know why you don't use Terry Crowley as a designated hitter all the time.
Weaver: Terry Crowley is lucky he's in (expletive) baseball, for Chrissake. He was released by the Cincinnati Reds, he was released by the (expletive) Atlanta Braves. We saw that Terry Crowley could sit on his (expletive) ass for eight innings and enjoy watching a baseball game just like any other fan, and has the ability to get up there and break one open in the (expletive) ninth. So if this (expletive) would mind his own business and let me manage the (expletive) team we'd be a lot better off.
Announcer: Well , certainly you've made your opinions known on the fans' questions about baseball, Earl, but let's get to something else. Alice Sweet from Norfolk wants to know the best time to put in a tomato plant.
Anyway, I love baseball.