Two-legged Series Probabilities

It is hard to construct probabilistic models for two-legged, home-and-home series based on a season of games that were all independent of one another (for the most part). And because our data sets from Opta and MLSsoccer.com only go back to 2011, there isn't much of a sample size to work with come playoff time. Thus I will have to get tricky when trying to construct logical probabilities of victory in these playoff series. The first thing to point out is that our model is based on regular season games that may or may not act like two-legged playoff series. There is a common belief that the team that plays at home for the second leg has an additional advantage. However, much of that belief likely comes from people like Simon Borg, who likes shitting on data and the presenting it. A reasonable study would need to account for the fact that the team playing at home is probably better. One such study attempted to do so for the UEFA Champion's League, and found that the additional advantage due to hosting the second game was effectively nothing once team skill was controlled for. However, it should be noted that UEFA Champions League does not always play extra time when aggregate scores are tied.

As Borg notes, 22 of 36 (61.1%) two-legged series in the MLS playoffs have been won by the team that played the second leg at home. However, because home teams tend to be better, much of that is likely due to skill, and not an additional home-field edge. Our models, which don't give any additional home-boost for second-leg home teams, projected three second-leg home teams to win in the first round top win: Portland with 69 percent, Sporting with 66 percent, and New York with 59 percent. Even factoring in RSL's 46 percent, the average percent of second-leg home teams expected to win in the first round was almost exactly---you guessed it---60 percent. With the data currently available, we have chosen not to include an additional home boost for second-leg home teams. With that out of the way...moving on!

With two first-leg games down and two to go, we see two favorites in opposite positions. Portland is taking a one-goal lead back home, while Sporting returns to Kansas City facing a one-goal deficit. My method of projecting each team's probability of winning its series will be derived from the assumption that teams favor a regulation win to a regulation draw on aggregate (and a draw to a loss) with the same weighted preferences as it would have favored those outcomes during the regular season. Thus, for example, I will treat the Portland-Seattle matchup as though Portland has an early lead in a regular-season-type game, and adjust our model's probabilities according to that one-goal lead.

The probabilities will be adjusted based on some game states research I have been working on. I have shown some nifty graphs below to help us out. The two graphs chart the approximate probability that the home team has of each of the three possible match outcomes based on two things: the goal differential and the minute mark. These graphs were created from game data up through June 8th of this season. The data was smoothed out using a lowess curve.

Portland essentially leads a home match by one goal in the first minute. A league-average team would win this type of match with an estimated 75-percent probability and tie with about 20-percent probability.* Another way to say the same thing is to say that the home team has 3-to-1 (3.00) odds of winning, and 1-to-4 (0.25) odds of tying. Through June 8th of this season, typical home teams won with 46-percent probability (0.85 odds) and tied with 29-percent probability (0.41 odds). Thus I can say that a typical team increases its odds of winning from 0.85 to about 3.00, a factor of 3.53, with an early one-goal lead. Additionally a typical team decreases its odds of tying by a factor of about 1.6 with that one-goal lead.

.Portland's odds of beating Seattle at home from an even game state are approximately 2.00 (66.7%), and its odds of tying are approximately 0.23 (18.8%). Using the appropriate odds ratios, one might conjecture that the Timbers' odds of winning this game on aggregate are about 7.06 (87.6%), and it odds of tying this game are 0.14 (12.3%). A tie would essentially result in the coin-flipping grand finale known as penalty kicks, and thus Portland's chances of a Conference Finals berth are 93.8 percent (.876 + 0.5 x .123).

Instead of going all nutzoid on Sporting KC as I did with Portland, one can trust that I followed the same methodology to arrive at my final conclusion. Sporting's chances to advanced to the Eastern Conference Finals are about 47.8 percent by this use of odds ratios.** These probabilities will go into the simulation after all first legs are complete to update the overall Cup probabilities.

*Due to a small sample size of plus-one goal differentials in the first 15 minutes of matches, the graph is trying to make us believe that a loss is more probable than a tie, when our logic should allow us to infer that---with a one-goal lead---a draw would be more probable than a loss. Thus I am using the more-stabilized figures around the 40-to-60-minute marks. The even goal differential graph---not shown---as well as the two graphs above suggest that probabilities don't begin to change all that much until the 60th minute, an interesting topic for another day.

**For those wanting to check my math, I assumed typical home teams in SKC's position would win with 20-percent, probability and tie with 30-percent probability. SKC's probabilities against New England in an even game state would be 64-percent and 26-percent for a win and tie, respectively. 

Show Down: Juan Agudelo vs. Diego Fagundez

During our podcast on Thursday night, a short side conversation was sparked between Drew and me. Who would you take in a situation where you are starting a new team: Juan Agudelo or Diego Fagundez. While the question and how it's presented matters (i.e. how many years of control do you have, salary cap situation, blah, blah, blah) because it gives us context, let's not go there. The discussion here is more about the general response. We've all, myself included, just generally assumed that the answer to any question between the two is: "Agudelo now, Fagundez later". But what makes us think that Fagundez isn't the better option right now? While doing our podcast I generally have between 9 and 15 browser tabs open with general bits of information. I'm sure my wife would argue that it's more like 50. Whatever. It's a lot. During that point in the podcast, I had Squawka up and quoted a total performance score of 452 for Fagundez, as opposed to Juan Agudelo and his shockingly low score of only 57.

So, the response then transforms itself from the answer that we thought we were sure of, to understanding what exactly Agudelo has done over the course of the season. Trust me, I get that numbers, especially in soccer, can't tell an entire story. But they can help see us things that our brains don't naturally keep track of.

Agudelo, in my mind, is a special case of a lot of talent doing one specific thing and being credited for far more than perhaps initially thought. I know the other side of that argument stresses his physical traits and goal-scoring ability. Sure, those are two HUGE things when it comes to this game. Speed kills and Agudelo knows how to turn it on.

Let's take a look below.

	Mins	Goals	Shots	Goals pSh	Chances Created
Fagundez	2419	13	43	0.30	27
Agudelo	1019	7	17	0.41	4

First, we can see one thing. And it's quiet amazing. Together, the two players produced 20 goals on 60 shots. Take a second to think about that because that's major. The Revolution took 37 shots and scored just one goal over their first five matches of the season. These guys get thrown into the line-up and procure 20 goals on just 60 shots. That's special.

Second, what is most obviously the difference between the two is the number of chances created. You'll see in a second that Agudelo still made a fine amount of passes. The issue isn't that he's a ball hog, or that he just wants the chances for himself. The problem is those passes did not become chances on goal. You'd hope that a guy who gets plenty of attention from the defense has the ability to find open teammates that can create goals.

	Mins	Pass p90	TO p90	Pass pTO	Avg Length	Dribbles	DisPos per 90
Fagundez	2419	22.17	2.08	10.65	14m	0.86	1.71
Agudelo	1019	28.52	3	9.51	13m	0.53	2.91

Alright, onto the possession-based stuff. There are some interesting thoughts here. Such as Agudelo taking less dribbles, making shorter passes, and making more of them. It's not something that I would have generally have thought of about him. I think of an individual who is looking to constantly run at defenders, but maybe that isn't the whole picture. That said, he's still losing the ball quiet a bit, and while Fagundez doesn't make as many passes, he's less error-prone and creates more pockets of space up the field with the ball at his feet.

	Mins	Fouls	Cards	Tackles	Blocks	Interceptions	Clearances
Fagundez	2419	0.81	3	1.3	0.11	0.74	0.33
Agudelo	1019	3.53	2	1.4	0.09	0.35	0.71

The biggest number that stands out to me on this page is the number of fouls committed per 90 minutes by Agudelo. There is no way he makes that many fouls and continues to only pull about 6 cards over the course of a full season. That's impossible. Outside of that, you see that each of these players is rather close to one another. One is a bit more on top of clearances while the other interceptions.

Really, that's probably due to two random factors. 1) Agudelo is in the middle of the box more often for corner kicks, and 2) Fagundez works in the midfield where errant passes are more probable.

It's important to realize these players aren't like for like. Trying to compare them as apples to apples isn't going to work and makes this work less productive. I am willing to acknowledge that. Agudelo did have some opportunities in the midfield this season, however, he was primarily featured up top in the striker role. Likewise, Fagundez had some exciting moments playing center forward, but was primarily used out wide as a left midfielder.

Because they don't occupy the same space, certain statistical attributes that we associate with these players are going to be either more or less inflated. They have different responsibilities so they aren't going to be the same player statistically. We don't have a "Wins Above Replacement" calculator, as awesome as that would be.

There is no key that unlocks all events and makes them equal, as if to say this player is better than that player, regardless of position or team. Maybe this post was a complete waste because we should be comparing these two teammates to the rest of the league, rather than to each other. What I do know is that Fagundez is less a player of the future and more of an MLS standout now, but when Agudelo leaves for Stoke, he is still going to be missed by the Revs.

ASA Podcast XXVII: The one where we preview MLS Playoffs

Okay, it's only been a few days, but our trio returns with a vengeance. We preview the MLS playoff matchups, with the exception of Houston-New York (though we allude to it plenty). It's a short podcast---just one segment long. Have a listen. [audio http://americansocceranalysis.files.wordpress.com/2013/11/asa-episode-xxvii.mp3]

Help Wanted: People With Free Time

I think this is about as opportune a time as any to do this, so I'm just going to throw it out there. While I've been saying it for a while, we're really going to reboot this site to make data much more accessible, articles more engaging, and the experience more palatable.* However, baby steps.

We need some volunteers to make a lot of this happen. People that can help us collect specific pieces of data that we aren't able to poll or scrap. People that can help us transition this site into something usable. People to take the data we find, make something of it and write about it---tell people how this data can transform the beautiful game that we watch.

This isn't about us, and it never has been. We all want to give back to this soccer analytics community in the best possible way. This has been my vision from the start, and I was lucky enough to find two awesome dudes to kick it off with. We would love to see more hands join us in this process.**

I'm not asking for money. Actually, I'm asking for something much more valuable than that, your time. We want to know who else is out there that is like the three of us, and that wants to dive into these numbers, explore them, and improve our understanding of soccer.

If this interests you, please e-mail me at farfromport[at]gmail.com. I'd love to have more brains that can think out these problems, come up with solutions and more efficient methods,  and ultimately refine what I am doing wrong. We're about to head into the off-season, which lasts only about three months, and it gives us little time to make these changes.

The three of us all have important ladies in our lives, cats, other animals, families and college degrees to complete. Oh, and of course, full-time jobs too.*** We aren't asking for your full lives, just some help. Thanks,

Harrison Crow

Matthias Kullowatz

Drew Olsen

*This is one of the biggest words Harrison has ever used correctly.

**Harrison is a soccer data socialist.

***Matthias claims to work full-time. His friends are skeptical.

ASA Podcast XXVI: The one where we talk the last week of the Season

Okay, a crazy lot happened this weekend, and we are here for a bit of a rewind. We give you our take and how we enjoyed the last week of the MLS season. Also, some thoughts on various things that happened and some added talk about MLS expansion. I give a bit of a dissertation on the state of the Sounders, Matty (of course) mentions shot ratios and Drew has some excellent commentary on coaches. We conclude with some discussion on how goalkeepers may better be valued, and how we are going to try to tackle that project. This was the last week of the regular season, enjoy. [audio http://americansocceranalysis.files.wordpress.com/2013/10/asa-episode-xxvi.mp3]

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%

LA Galaxy And A Thought About Jaime Penedo

After a short discussion on twitter here, is the record of the LA Galaxy with Jaime Penedo and then again without him. It's an extremely small sample size (7 games with vs. 25 without), and so you have to, of course, approach it with a sense of skepticism.

Penedo Status	PPG
with Jaime Penedo	1.44
without Jaime Penedo	1.57

How good are they? Are they an MLS Cup contender? Well... I generally believe once you get to the playoffs you're a contender regardless. But the question still remains, can the Galaxy still be a team that wins silverware? Maybe, maybe not. It's really hard to judge at this point. For what it's worth, I think it's clear that they are a much better team with him than without. Small sample sizes leave me with only my eyes.

Also, I still think they made a mistake signing Omar Gonzalez to DP contract. I guess that's another can of worms.