Playoff Probabilities and Seeding

Now that the "Playoff Push" has given way to the actual playoffs, we have included the probabilities of all the various outcomes in this year's edition of the MLS Cup. One sees that our model's darling, Sporting Kansas City, has the best chances at an MLS Cup trophy of all teams, which is not surprising. But what this simulation really articulated to me were the differences between the three, four, and five seeds in each conference, as well as the top seeds overall. Despite the fact that our model thinks that fifth-seeded Colorado is nearly as good as Portland and Real Salt Lake, its chances at the MLS Cup are significantly lower as a five seed. Having to play that extra match on the road essentially chops the Rapids' chances in half right away, and then its slight disadvantage in a home-and-home against Portland---a 42-percent chance in that series---leaves Colorado with just a 3.2-percent chance at the silverware.

In the Eastern Conference, the same issue arises for fourth-seeded Houston. The Dynamo are not thought to be significantly worse than New York---the model projects the Red Bulls to win that potential home-and-home matchup with 59-percent probability---but the additional uncertainty of the play-in game really screws them over.

The three seeds, however, are well-represented in Cup probabilities. Though New England's Cup chances sit at just 5.1 percent, you have to remember that they play Sporting KC in the first round. We love SKC around here, if you weren't aware. And then Los Angeles, the West's third-seeded team, actually has the third-best chance overall at a Cup win---15.0 percent.

Finally, the potential for home-field advantage in an MLS Cup Final really has Sporting and New York drooling. Together those two teams hog nearly 44 percent of all the Cup probability. Given that Sporting makes the finals, the probability that it goes on to win them is about 64 percent (26.5/41.2). New York's conditional probability is similar at about 62 percent (17.4/27.9). That home-field advantage gives each of those teams a huge boost if  they can make it that far.

For Cinderella teams that make it that far, having to play a superior opponent on the road in the championship one-game-off doesn't bode well for a storybook ending.

Keep track of all the playoff outcome probabilities on our Cup Chances 2013 page under MLS Tables.

Supporters' Shield Probabilities

After completing the Eastern and Western Conference playoff scenarios yesterday, it only makes sense to move on to each team's chances at the Supporters' Shield and a potential home-field advantage in the MLS Cup Final. Only four teams could mathematically win the shield: New York, Sporting KC, Portland and Real Salt Lake.

New York has the best chance due its current lead in the tables and the fact that it's playing a home game. If New York wins at home against Chicago, then it will be the Shield winner, regardless of other outcomes, but that's not the only way the Red Bulls could hoist the trophy. A tie against Chicago would eliminate both RSL and Portland from contention---since New York holds the "wins" tie-breaker over Portland---and then an SKC tie or loss would leave the Red Bulls as Shield winners, as well. In fact, even a loss from New York could leave them in first overall if SKC, Portland and RSL all don't win. However, it's not probable that both Portland and RSL would each earn less than three points against Chivas USA. In the end, New York's Shield chances sit at 73.7 percent, with 61.8 percent of that coming from its probability of beating Chicago this weekend.

Sporting Kansas City has the next-best chance at the trophy at 15.5 percent. Obviously it needs New York to lose or tie and then---due to SKC losing the potential tie-breaker to New York,---SKC would need to win. The only scenario where SKC ties and still gets the Shield involves crazy scenarios like an 8-to-8 tie with Philly.

Like SKC, Portland and Real Salt Lake both need to win, and then things need to go their way. RSL would (likely) hold tie-breakers over both SKC and New York, so RSL would need SKC to lose or tie, Portland to lose or tie, and then New York has to lose. Portland loses tie-breakers to SKC and New York, so it needs to win, and then have SKC lose or tie and New York lose. In the end, Portland's probability at the Supporters' Shield is just 6.0 percent, while RSL's is 4.8 percent.

Team	Shield%
NYRB	0.737
SKC	0.155
POR	0.060
RSL	0.048

Eastern Conference Playoff Seeding

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:

	1st	2nd	3rd	4th	5th	Out
NYRB	84.5%	15.5%	0.0%	0.0%	0.0%	0.0%
SKC	15.5%	84.5%	0.0%	0.0%	0.0%	0.0%
MTL	0.0%	0.0%	53.1%	31.7%	13.4%	1.8%
CHI	0.0%	0.0%	17.1%	43.8%	32.9%	6.3%
NE	0.0%	0.0%	12.5%	8.2%	30.2%	49.1%
HOU	0.0%	0.0%	17.3%	16.3%	15.6%	50.8%
PHI	0.0%	0.0%	0.0%	0.0%	8.0%	92.0%

Western Conference Playoff Seeding

For the past few weeks, we have been including each team's probabilities of earning a playoff spot and each team's probabilities of winning the Supporters' Shield (for most points in MLS). Due to the complexity of the tie-breaker system, I have avoided that topic altogether. Until now. Now that every team with at least 7 caring fans has just one match remaining---Chivas USA has two---I have recalculated the actual playoff chances below using our model, accounting for the various tie-breakers. Let's get started easy. The five Western Conference playoff teams may not be mathematically determined; however, by probability, the top five teams today are certain to remain the same. San Jose could tie Seattle and/or Colorado for the fifth-and-final spot, but the first tie-breaker is total wins, and Seattle has that one covered. The second tie-breaker (which would go into effect only against Colorado) is goals scored. Right now San Jose trails Colorado by 12 goals, meaning that San Jose would have to score at least 13 goals to win all the relevant tie-breakers. So yes, the top five in the West can safely be etched in stone.

Seeds are still important, though. Earning a top-three finish allows a team to avoid that one-game playoff between the fourth and fifth-ranked teams in each conference. Below I have given some relevant probabilities for each team's seeding:

The Portland Timbers could theoretically finish anywhere from first to fourth, though with their final game against Chivas, first place is the most likely. Our model gives Portland a 52-percent chance to beat Chivas on the road and lock up the top spot regardless of other outcomes. However, a tie or loss to Chivas leaves the door wide open for the other playoff teams, and thus Portland's overall chances at first place increase only marginally to about 54 percent. Its chances of a dreaded fourth-place finish require a string of results that has just a four-percent likelihood.

Real Salt Lake guarantees itself at least second place in the West with a win. It has about a 42-percent shot at first place, and only a one-percent shot at fourth place---a result that would require a loss to Chivas at home, a Colorado win at Vancouver, and a tie between Los Angeles and Seattle. Thus both RSL and Portland are not likely to find themselves playing in a one-game playoff, and even in that worst-case scenario, either team would get to play at home.

Probabilities surround the LA Galaxy are a little trickier. Finishing in first place would require a win against the Sounders in addition to Chivas getting points in consecutive matches against RSL and the Timbers. That probability is only about three percent. There is, however, a very real chance that the Galaxy finish in fourth or fifth. A loss to Seattle coupled with a Colorado win leaves them in fifth, while a tie in Seattle and a Colorado win would drop LA to fourth. Those probabilities are 11 and 10 percent, respectively. Thus the remaining 76 percent has the Galaxy finishing in either third or second place.

Seattle's football club could finish anywhere between first and fifth. The unlikely sequence that would vault the Sounders into first place includes them beating the Galaxy, Chivas getting points at RSL on Wednesday, and then Chivas returning home to beat Portland at home on Saturday...but that has just a one-percent likelihood. A loss or tie against the Galaxy locks Seattle into the play-in game. Though playing at home, our model really likes LA and gives the Sounders just a 30-percent chance of winning that matchup. That leaves them with a 32-percent chance at fourth and a 38-percent chance at fifth place.

Colorado is in a rough spot, as it would lose potential tie-breakers to Seattle, LA and RSL. Taking first place would require that Colorado win at Vancouver, that Portland and RSL both lose to Chivas, and that Seattle and LA tie. That string of events has virtually a zero-percent chance of happening. Colorado is much more likely to find itself in fifth place. A loss would guarantee the Rapids the last playoff spot, and a tie would stick them there, too, so long as Seattle earned at least a point against LA. All that adds up to a 51-percent chance at finishing fifth and having to play a one-game playoff on the road.

Here's the chart that sums up all of the probabilities for each playoff contender:

	1st	2nd/3rd	4th	5th
POR	54.7%	41.3%	4.0%	0.0%
RSL	41.7%	57.4%	0.8%	0.0%
LA	2.9%	56.8%	29.2%	11.2%
SEA	0.7%	29.4%	32.4%	37.5%
COL	0.0%	15.0%	33.6%	51.3%

A few key games this week...

Since we now have playoff and Supporters' Shield chances on the site, it provides us with a means of weighting each upcoming game by its effect on playoff odds. What if, for instance, Montreal were to lose to New England at home this weekend? There's no doubt it would hurt Montreal and keep New England alive, but just how much would it matter? The same question can be asked of the San Jose and Colorado, who play tonight. Currently, our model gives Colorado and Montreal 90.4 and 82.8 percent chances,* respectively, to make the playoffs, while San Jose and New England sit at 6.0 and 14.1 percent. Remember that our playoff chances refer to earning at least fifth place in the conference, and they do not include probability associated with ties for fifth.

I re-ran our simulations three times, accounting for the three possible conclusions to each of those games. I allowed the simulator to pick winners as usual for the other matches this week and beyond. To the results!

A San Jose tie or loss at home tonight would effectively end its chances of a playoff berth. In just 11 of the 10,000 simulated seasons (0.11%) did San Jose recover from a loss to claim a playoff spot (not counting ties for fifth), and even a tie only doubled those chances to about 0.23 percent. A win boosted its playoff chances from 6.0 to 12.0 percent. Playoffs would still not be likely for the Earthquakes, but at least a win tonight would give them something to play for in the final two games.

Their opponent, Colorado, is the West's most likely team to give up its playoff spot, according to our model. That said, its playoff chances are still quite high. Even a loss to San Jose tonight would only lower the Rapids' playoff chances to about 78.4 percent. A tie or win for Colorado tonight essentially assures it a tie-breaker-free route to the playoffs with at least 98.7 percent probability (99.9% with a win tonight).

Moving over to the East, the game most likely to swing playoff percentage points around is the Montreal---New England matchup. New England could increase its playoff chances from 14.1 to nearly 39 percent with a road win. However, like San Jose, a tie or loss would hurt New England a lot. A tie would leave New England with only about a 5.6 percent shot at the playoffs, and a loss would render the Revs' situation quite hopeless at 1.6 percent.

Conversely, a win or tie for the Montreal Impact would have a mirrored result, boosting its playoff chances to 91.0 percent with a tie and 99.2 percent with win against the Revs. Like Colorado, a loss would not ruin Montreal, and their playoff chances would sit right around 63.3 percent.

A lot of playoff probability is waiting to swing---as much as 12 percent in San Jose's case and 38 percent in New England's case. In my opinion, this speaks as much to the weight resting on these final few weeks as it does to the weight that was on the games that led us to this point. Teams like Colorado and Montreal have performed well enough in the first 30 or 31 games to put themselves in a position where a loss still leaves them with better than 50 percent chances at a playoff spot.

Oh, in case your were curious, our model gives San Jose a 39-percent shot at a win tonight, 31-percent chances of a loss, and 30-percent chances of a tie. As for New England, those probabilities are 29 percent, 39 percent and 32 percent.

*The margins of error for 95% confidence are, at most, 1.0 percent for each playoff percentage calculation.