Having determined the Runs Scored (RS), I needed a source for Runs Against (RA) so I used the team RAs from Baseball Prospectus, but scaled them down to account for the fact that my cumulative RS was lower than BP's projected RA.
With RA and RS, I used the xlsSports MLB Monte Carlo simulator and ran 1,000 seasons. I used a standard deviation of .01 in the AL and .02 in the NL, based on the variation in runs scored by various lineups. Changing a lineup in the AL can make about a 2 win difference, but changing a lineup in the NL can make a 4 win difference. Here are the results, showing the W-L records for the playoff teams, and games back for everyone else.
AL East AL Central AL West Yankees 101-61 Indians 86-76 Athletics 84-78 Red Sox 97-65 Tigers 5 Angels 4 Rays 9 White Sox 9 Mariners 8 Blue Jays 25 Twins 12 Rangers 14 Orioles 34 Royals 12
NL East NL Central NL West Mets 87-75 Cubs 97-65 Dodgers 93-69 Braves 1 Brewers 88-74 D-backs 3 Phillies 1 Cardinals 14 Giants 17 Nationals 7 Reds 20 Padres 18 Marlins 17 Astros 25 Rockies 21 Pirates 34
Worth mentioning that I docked the Yankees a month's worth of A-Rod, and docked the Twins a month's worth of Mauer.
I was surprised at the Orioles' performance. I thought it would be better than the Blue Jays. I was also surprised at the Angels coming in below .500. In the NL, I'm not sure I'm buying the Nats finishing only 7 games and two games shy of .500. I'm also surprised the Rockies are worse than the Padres and Giants. The current Giants lineup is projected to be (by a long shot) the worst offensive team in baseball.
For the playoffs, this would give us the Red Sox and Brewers as the wild card teams, each of whom is in the same division as the team with the best record.
The Division Series would be Athletics at Yankees, and Red Sox at Indians in the AL. Mets at Cubs, and Brewers at Dodgers in the NL. In 50 simulations of these series (a lower number because I had to do them manually):
Yankees beat the A's 80% of the time, most often in a three game sweep.
Red Sox beat the Indians 70% of the time, most often in four games.
Cubs beat the Mets 60% of the time, most often in four games.
Dodgers beat the Brewers 64% of the time, most often in five games.
The ALCS would play out as Red Sox vs. Yankees, and Dodgers vs. Cubs. In 50 sims of those:
Yankees beat the Red Sox 58% of the time, most often in six games.
Cubs beat the Dodgers 54% of the time, most often in six games.
That gives us a Cubs-Yankees World Series. I ran the sims with the AL having the home field advantage, since it typically wins the All-Star game and is the stronger league right now. In 50 sims, the Yankees destroyed the Cubs, winning the series 74% of the time, most often in a full seven game series.
The sleeper teams are the Braves and Diamondbacks in the NL, and the Rays and Angels in the AL, if you can consider two teams from last year's playoffs "sleepers". For a real sleeper, see the Tigers.
The only teams with absolutely no chance of making the playoffs in the 1,000 season sim were the Orioles and the Pirates.