Why are baseball player's so ridiculously over payed compared to other professional athletes?

Alex Rodriguez 27.5m, Joe Mauer 23m, CC Sabathia 23m, and Mark Texiera 22.5m a season compared to contact sport athletes like (NFL) Carson Palmer 16m, (NHL) Alex Ovechkin 9m and (MMA) Andre Arlovski 1.5m(1 fight). The only difficult part of a baseball player's life is figuring out what to do with all their unearned millions! Sure they have tough schedules but all they do is hit a ball with a bat, run around a diamond and throw/catch the ball. They don't even break a sweat for $25,000,000 a year. The only sport that should be making that kind of money are the athletes that put their life on the line for good entertainment such as Mixed Martial Arts, Car Racing, Boxing, Human Hunting(Possible near future, LOL) and that's it. Obviously Baseball has been hugely popular and hyped in North America(mainly U.S.A) but I don't believe any more so than Football, Hockey, and Basketball(all of which pay out considerably less million's of dollars to their athletes).