Here are BP's odds, which are based on PECOTA projections for player performance through the end of the year, then run through a Monte Carlo simulation of the rest of the season being played out 1m times. For the NL East -
Phillies - 58.5%
Marlins - 49.6
Braves - 42.4
Nats - 20.0
Mets - 7.2
Note they aren't placing too much weight on the performances to date due to small sample size. But the longer we keep it up the longer we climb.
And I do remember last season they had the Red Sox at about 99% with a month to go in the season. 
This I find more acceptable than ESPNs. I just take issue with Philly being dead last yet running away with the playoffs playoffs 71%. With BP, and I'm not sure I like the Nats at 20% running away with the NL East at 10-3, but this is a much more logical percentage range factoring in we are only a couple weeks in. Philly at 71%, dead last, just irks me as being overly dependent on last year. Like I said, I'd rather everyone be bunched together which is what BPs, based on PECOTA, does.
In fact I just looked... Philly is 4.5 games back, dead last, at 5-7. 63.8% chance still. All the other three teams are deadlocked at 7-5 or 7-6, except the Nats, at 10-3, and we still aren't even 50-50, currently 48.9%. While the Mutts and Marlins are 16%, Atlanta 33%. Yet Philly is dead last, 1.5 games from not being dead last, and are still a near lock? Yeah, I'm obviously just not a fan of weighting it so much on last year's performance when a team like the Nats are running away with the division and yet a team in dead last still has such a significant advantage of playoff percentage likelihood.
But I do get its solely because of the small sample size for the current season, it's just as I said, I'd rather everyone be bunched together due to small sample than weighting so much on last season when a team is dead last, and another is running away with the division thus far. No way should Philly still be at 70% when the Nats still aren't even at 50-50.
