I put together the Western Conference version earlier, but the Eastern Conference and its four million more scenarios are so much more exciting. I used our predictive model to calculate the probabilities of each game's outcome, and then applied those to all possible scenarios. This is going to be fun... New York and Sporting KC have locked up a one-two finish in some order, and then there are five teams with mathematically non-zero chances at the final three playoff spots in the East. There are no San Joses here, as each of Montreal, Chicago, New England, Houston and Philly all have real chances of at least eight percent at a playoff berth. On to the scenarios!
The New York Red Bulls can guarantee themselves both first place in the East and a Supporters' Shield trophy with a win at home against Chicago this weekend, but that's not the only way it could take the top seed. A tie against Chicago coupled with SKC not winning, or losses by both New York and SKC would leave the Red Bulls in first place, as well. Totaled up, the Red Bulls chances at a top seed sit at 84.5 percent, with the other 15.5 percent going to a second place finish.
Sporting Kansas City's outcomes are the exact opposite of those of New York. SKC has to play on the road in Philly while New York plays in a more comfortable home environment, leaving SKC with a 15.5-percent chance of a first place finish. SKC has been our loving model's favorite team in the East since the model was born, and a two-seed shouldn't hurt its chances of a date in the MLS Cup final.
Despite limping into the postseason, its comeback win against the Union has Montreal on firmer ground going into the last week. A win at Toronto guarantees the Impact third place in the East, allowing them to avoid that one-game-off. In total, Montreal has a 53.1-percent chance at third place---remember, the model doesn't think the Impact are all that much better than Toronto, but at least they don't have to go through customs. The sequences leading to fourth or fifth place start to become more complicated, but those probabilities are 31.7 and 13.4 percent, respectively. That leaves the Impact with just a 1.8-percent chance of missing out on the playoffs altogether, a scenario that essentially requires a poor result from Montreal with wins from New England and Houston, and at least a draw for Chicago on the road in New York.
Chicago is in a surprisingly good position going into its game in New York. The outcomes leading to the Fire making the playoffs add up to 93.7 percent. 17.1 percent of that leaves Chicago in third, which would require Montreal to lose or tie and Chicago to subsequently earn a tie or win, depending on Montreal's result. And there's more good news for Chicago. If it gets stuck in the play-in game, it has a better chance of being the home team (43.8 percent) than the away team (32.8 percent). Chicago would win any potential tie-breakers with New England, Houston, and Philly, which is partly why its playoff chances are so high.
The New England Revolution could avoid the play-in game, but that would require a win at Columbus in addition to both Chicago and Montreal not winning. Our model suggests that probability is only 12.5 percent. If it makes the play-in game, New England is more likely do so as the fifth seed (30.2 percent) than the fourth seed (8.2 percent). Those of you keeping score at home know that the Revolution's chances of missing the playoffs altogether are thus 49.1 percent, the most probable outcome of the four. Though New England holds the goals-for tie-breaker over Houston, Houston has an easier opponent in D.C. United.
Speaking of Houston, due to that easier, aforementioned opponent, Houston has a better shot of claiming third place than New England at 17.3 percent. However that tie-breaker plays to New England's favor in all of the ways that each team could finish fourth or fifth. The Dynamo have just a 16.3-percent chance at fourth, and a 15.6% chance at fifth, leaving them out of the playoffs with 50.9-percent probability.
Philadelphia's best chance at the playoffs comes from the fact that they would almost surely win a tie-breaker to Houston if it came to that. A Philly win coupled with a Houston tie would leave both tied at 49 points and 13 wins. Philly currently leads Houston by two goals scored and holds the third tie-breaker, goal differential, as well. Essentially, in this scenario, Houston would have to tie something like 4 - 4, while Philly slipped past SKC 1 - 0. Not likely, so this scenario would lead to Philly's only real shot at the playoffs, an 8.0-percent chance at fifth place. There is no mathematical way the Union could do better than fifth, as it would lose potential tie-breakers to both Chicago and Montreal.
In conclusion, for your viewing pleasure, the table of probabilities: