The GRAND SLAM BASEBALL ASSOCIATION (GSBA) is a simulation league playing  Diamond Mind Baseball
We had 20 teams and play a 162-game season based on the probability distributions determined by the statistics from the previous real-life season. We actually play each game, determining lineups, strategies, relief pitchers, etc - this is not a rotisserie league. Our season lasts 6 months starting in August, so in October 1999 we are playing with the 1998 real-life stats. Teams keep the same players year to year, except for the many trades. You can read our constitution and view the rosters for the 1999-2000 GSBA season.
(Update: unfortunately the league folded, and I'm too busy to join another league now.)

Last season, my Madison Lightning got lucky and won the championship after beating two far superior teams in the playoffs. The team was getting old, would have been not as good every year into the future, and the competition is better next year. So, I completely remade them, and renamed them the Maryland Lightning as a result of my move from Madison to Maryland. Now I have a cellar-dweller but the team should be pretty good before too long, especially with the help of good draft picks brought about by a poor record.You can see my playoff boxscores and scoresheets and series stats for each round of the playoffs and see just how tight the championship series was and the awesome lineups my pitchers kept in check:
 
Playoff round Opposing team Boxscores and play-by-play Madison series stats
Wild card Valencia Vipers  games   stats 
Semifinals Western Wranglers  games   stats 
Championship Thorndale Thunder  games   stats