The Roll the Dice league, run by commissioner mountainjack, has been running for (I think) 5 seasons now. Its particularity is that unlike most other progressive leagues, owners don't know for sure which kind of season their players are statistically likely to have at the time that they turn in keepers lists for that team's next season, or when they draft players in the annual draft. 

Instead, within a certain range (say 4 seasons in most cases) which season a player will actually have is determined by the roll of a normal 6-sided die. So if it is the 1972 season, Reggie Jackson may play his 1972 stats, but may instead play anything from 1970-73 or 74, depending on the die roll. This can mean players that were expected to be starters who are part-time at best, or who have very poor seasons and need to be replaced for that year. 

A season or two ago, I posted my team's stats for the season in the Progressive League Classifieds, to show that with few exceptions, which were minor, this league seems for some reason to have final WIS stats that are closer to RL outcomes than any other I play a team in. 

Here are a few examples from this latest regular season which just finished:

Reggie Jackson RL: .293, 32 HRs, Roll the Dice results: .295 31 HRs
Felix Millan RL .290 .332 OBP  RTD: .301 .338 OBP
Oscar Gamble .258 20 HRs  RTD .267 28 HRs 
Richie Zisk: .324 7 HRs  RTD: .318 8 HRs

There were a few outlyers: Freddie Patek hit .244 instead of .225 and Doug Rader hit 23 HRs instead of 12 (Candlestick Park instead of the RL Astrodome might account for that one). 

But on the whole it is a fairly believable set of outcomes. I know we are contracting teams but don't remember if we may need an owner or two in the near future. But if you are looking for a league with believable results, within a reasonable range of difference with RL outcomes, take a look at the prog classifieds every now and then and see if mountainjack has posted something asking for an owner. It is an interesting league, very competitive. Though my Berkeley Radicals team is probably about to get shut down by NappyRootz' pitching staff for the second year in a row in the playoffs, after we muddled through to win a division title for the 2nd year running. 

(hope this counts toward a reverse jinx on the message boards).