On Looking Backward with the Poisson Model
Something I'm doing in this article and will likely do in the future is applying the Poisson model to past results to analyze the probability of various events having happened in the past. This is a bit weird because in some sense the probability of what happened happening is 1 and 0 is the probability of everything that didn't happen having happened. What I'm doing is taking the results, if using the full season then this essentially boils down to the goals for and against for each team, and asking "If this league were run millions of times in a parallel universe where each team plays at the level reflected in their number of goals scored and conceded, how often would they finish this way?". Put another way, I'm looking at how often a team scoring X goals in a season and allowing Y goals to be scored would finish in a certain spot in a league where the other teams have their given number of goals scored and allowed.
This is related to what is called Pythagorean Expectation in baseball and other sports. The idea there is to derive a formula for win percentage based on the number of runs a team scores and allows. For other sports, this stat is used to analyze how lucky a team was. The argument is that in baseball, while luck plays a part, scoring runs and preventing runs from being scored are largely based on skill - at least if you have a sufficiently large number of games played. On the other hand, scoring them at convenient times is much more based on luck than skill. So if a team tends to win a lot of blowouts and lose a lot of close games then this is unlucky and they will have a record that is worse than it should be given their skill level. There is ample evidence in baseball, and I believe other sports, that run differential (runs scored minus runs allowed, think of it like goal difference) is a better indicator than record of how a team will do the next season. This is yet another thing I want to examine in the future, but I suspect it will be similar in football.
I ran the 2008-2009 results through the Poisson model and simulated 100,000 seasons. The Poisson Expected Points is the average number of points the team got in those simulated seasons. Again, you can think of this as how many league points they would get in an average season where all teams play at the level reflected in the goals scored and allowed by each team last year. Along with Poisson Expected Points, I also recorded how often they finished in each league position at the end of the simulated seasons.
A Brief Review of 2008-2009
2008-2009 was the year of the FC Barcelona. They won the 'triple', taking down the Liga, the Copa del Rey and of course the Champions League. The league they won in convincing fashion, having effectively won it in the 34th matchday by destroying 2nd-place Real Madrid 2-6 in the Bernabeu. They went on to finish 9 points clear. Though the champion was obvious, there were some interesting battles the last few weeks of the season. On the second to last week of the season, Sevilla secured third place, guaranteeing them a spot in the group stage of the Champions League. Fourth place, and a spot in the Champions League playoff round, was in doubt to the end. It was secured by Atletico de Madrid with their 3-0 win over Almeria. This win dropped Villarreal into the UEFA Cup. At the bottom of the table, Huelva and Numancia were relegated with a couple matches to go. The battle for what the Spanish call permanence was fought by Gijon, Osasuna, Valladolid, Getafe and Betis. In the end Betis came up on the short end, only managing a 1-1 draw at home against Valladolid the last week of the season.
Here's a preview of the top six, ordered by their finish last year.
Fútbol Club Barcelona
2008-2009:
Record: 27-6-5, 87 points (1st)
Home Record: 14-3-2, 45 points (1st)
Away Record: 13-3-3, 42 points (1st)
Goals Scored: 105 (1st)
Goals Conceded: 35 (1st)
Poisson Expected Points: 90.2 (1st)
Poisson probability of winning league: 80%
Players Out:
Eto'o - 34 starts, 2 sub appearances, 85 minutes per game played, 30 goals
Gudjohnson - 11 starts, 13 sub apps, 46 minutes per game played, 3 goals
Sylvinho - 10 starts, 5 sub apps, 62 minutes per game played
Hleb - 8 starts, 11 sub apps, 41 minutes per game played
Víctor Sánchez - 3 starts, 4 sub apps, 38 minutes per game played
Players In:
Zlatan Ibrahimovic - F Inter Milan
Dmytro Chygrynskiy - CB Shakhtar Donetsk
Maxwell - LB Inter Milan
Barcelona made one high profile change at the top, swapping out Eto'o for Ibrahimovic. Otherwise they lost a few players that came on regularly as subs and added Chygrynskiy and Maxwell to supplement their back line. Maxwell is a solid option at left back. Chygrynskiy, at 22, is quite capable of contributing now and has the potential to become an elite center back in a few years. Also important given their style of play, Chygrynskiy is very good at passing the ball for his position.
The key is that Barcelona should be very similar this season to what they were last year, a scary proposition for the other 19 clubs in the Primera and the other 31 teams in the Champions League for that matter.
They'll likely start like this when Iniesta is back in full health:
No real surprises there.
My Prediction: Despite the action at Real Madrid, the blaugrana should still be the best club in the Liga and remain favorites to finish top.
Real Madrid Club de Fútbol
2008-2009:
Record: 25-3-10, 78 points (2nd)
Home Record: 14-2-3, 44 points (2nd)
Away Record: 11-1-7, 34 points (3rd)
Goals Scored: 83 (2nd)
Goals Conceded: 52 (7th)
Poisson Expected Points: 70.9 (2nd)
Poisson probability of winning the league: 10%
Players Out:
Cannavaro - 29 starts, 88 minutes per match played
Robben - 25 starts, 4 sub appearances, 78 mpm, 7 goals
Heinze - 24 starts, 90 mpm, 2 goals
Sneijder - 18 starts, 4 sub apps, 64 mpm, 2 goals
Huntelaar - 13 starts, 7 sub apps, 59 mpm, 8 goals
Michel Salgado - 6 starts, 3 sub apps, 76 mpm
Javi Garcia - 3 starts, 12 sub apps, 35 mpm
Saviola - 1 start, 7 sub apps, 26 mpm, 1 goal
Parejo - 5 sub apps, 18 mpm
Bueno - 3 sub apps, 12 mpm
Players In:
Cristiano Ronaldo - AMF/W/F Manchester United
Kaká - AMF/W/F AC Milan
Benzema - F Olympique Lyonnais
Xabi Alonso - MF Liverpool
Raul Albiol - D Valencia
Ezequiel Garay - D Racing de Santander (returning from loan)
Esteban Granero - MF Getafe
Alvaro Arbeloa - D Liverpool
Needless to say, it was a pretty crazy summer in Chamartin. Florentino Perez and his big-spending ways are once again in charge and they have entered the second Galactico era. At the start, I was quite skeptical because in my view Real Madrid last season did not have a problem scoring goals. While Barcelona scored 22 goals more than they did, 83 goals is still a big number and strong enough to compete for the league title. Where they had problems was at the defensive end, where they were only 7th best in goals conceded. I will write more about whether scoring or strong defense is more important, but I think it's clear that they have to be better defensively this season than they were last year in order to have a reasonable chance of sitting on Cibeles's lap next spring.
Defensively, they got a lot better when Lassana Diarra came during the winter break. Looking just at league results, they conceded better than a goal per game less in the 22 matches after his arrival than the 16 matches before and got 10 clean sheets in those 22 games compared to just 3 in the 16 before his arrival. If anything, this understates things because their last three matches weren't important after their loss to Barcelona all-but guaranteed that the league title would be out of reach. They allowed 8 goals in these three matches. They were particularly strong defensively when they played with two defensive-minded central midfielders in "Lass" and Fernando Gago. In the 12 matches that both started, they allowed just 11 goals - 6 of those in a 2-6 loss against Barcelona! Even including that, their goals allowed per game was just 0.92, and they got 7 clean sheets in the 12 matches. When those two didn't start, they allowed 1.58 goals per game, with 2.13 per game conceded if you look only at the matches from the start of the season until Lass made his first appearance.
With that in mind, I thought in the early days of the summer that the new buys would seriously hurt their chances because they would not be able to get all of that galactico power out there without losing a defensive midfielder. Bringing in Xabi Alonso changed all that for me. Lass has come through and now seems popular enough that Pellegrini won't get much pressure to take him off in favor of an attacking player (especially after his game-winning goal in the season opener), and Xabi Alonso is a superstar in his own right and he won't likely be relegated to the bench any time soon. They now have the freedom to play a winning style - something they could not do in the first Galactico era once Perez ran Makelele out of town. Given that and the improvement defensively that they should get from adding Albiol, Arbeloa and even Garay, I expect Real Madrid to be more competitive for the league title than they were a season ago.
Should they win it then you can expect Ronaldo and Kaka to get all the attention, but for my money Xabi Alonso was their most important pickup and it will be the improved defense that is the difference between going to Cibeles and begrudgingly admitting that 'el Barcelona ha sido mejor'.
Here is how I see them lining up:
A big question mark is what they should do with Raul. In my somewhat biased opinion, he does not deserve a spot in the starting lineup. I think they have a couple better options, most notably Higuain. Raul makes the usual controversies that happen at a club full of stars, some of which have to sit, worse because of his status in the dressing room. If you ask me, the sooner they rip that band-aid off and go through the blow up from him not being a regular starter the better off they'll be.
My prediction: I think Real Madrid will mount a better challenge than last season when they made a strong run late but never seemed like digging out of the early deficit. If they start out strong and things don't blow up quickly on them, they definitely have a shot at winning the Primera. Even if things do blow up, I don't expect them to finish outside the top 3.
Sevilla Fútbol Club
2008-2009:
Record: 21-7-10, 70 points (3rd)
Home Record: 11-2-6, 35 points (8th)
Away Record: 10-5-4, 35 points (2nd)
Goals For: 54 (7th)
Goals Against: 39 (2nd)
Poisson Expected Points: 62.7 (4th)
Poisson probability of winning league: 3%
Players Out:
Mosquera - 16 starts, 1 sub appearance, 88 minutes per appearance
Maresca - 14 starts, 7 sub apps, 58 minutes per, 2 goals
David Prieto - 13 starts, 87 minutes per match
Players In:
Negredo - F Almeria via Real Madrid
Sergio Sanchez - D Racing de Santander via Espanyol
Zokora - DMF Tottenham Hotspur
They weren't busy in Nervion this summer. They sold off a few role players and bought Zokora as well as a couple young players who will likely be subs now primarily with the potential to become great players in the future. Given that it's a young team, that's not necessarily a bad thing, but unfortunately it's tough to imagine Sevilla competing with the two giants for the league.
Looking at the results from last year there are two things that strike me as odd. Firstly, Sevilla finished with the same number of points in home and away matches. Without digging up historical records, my feeling is that Sevilla historically have done significantly better at home compared to on the road when compared to the average team. They had a quite long streak of European matches without suffering a defeat. Fans of both teams in the city are famously passionate - in recent times, the national team has played in Seville more often by far than anywhere else. Weather is often a factor as it is significantly hotter there than most of the rest of the country at the beginning and end of the season. None the less, Sevilla were only the 8th best team when playing at home. Oddly enough, Betis, the other team in Sevilla, were the only team in the league that got fewer points at home than away. Sevilla were very good away, finishing second-best overall in that category.
The other thing is that Sevilla did not score a lot of goals in the 2008-2009 campaign. The squad was very similar to the year before. Then they scored 75 goals, some 21 more than last season. They allowed 10 more goals, 49 to just 39 last year, so a possible explanation is a more defensive style. Perhaps this was due to Manolo Jimenez taking charge in full for 2008-2009. He started when Juande Ramos left the club in October of 2007. While he was on for most of the 2007-2008 season, maybe being able to fully set up his system and how he wanted the guys to play during preseason made a difference. From watching them, it's not obvious to me that they played a more defensive style last year than the year before, but the results certainly indicate something to that effect. This sort of thing is a reason that I think it's important to look at objective statistics - watching the matches often doesn't tell the whole story, particularly when you have a rooting interest.
Having said that, I anticipate them scoring more goals this year. They have a lot of young, strong, attacking talent. Capel and Jesus Navas should continue to get better. Romaric looks a lot better physically than he did at this point a year ago and I expect him to have a better year and be able to contribute more at both ends. Kanoute doesn't look like he's slowing down any and Negredo should fill in nicely if and when he is gone to play the African Cup of Nations.
Here's a likely lineup:
Sevilla have a lot of depth and the above is just an example. Other than up top and in goal, every position will see a lot of players rotating trhough.
Prediction: Sevilla will fight for third, bowing out of the title race all too early. It will be pretty similar to last year and I expect them to finish third, potentially solidifying themselves as the third club as Valencia did in the early part of this decade. Having said that, fourth place and the Champions League playoff would be a fine result, and there is a decent chance that they'll fall into a Europa League spot. Anything less would be an unlikely disaster.
Club Atlético de Madrid
2008-2009:
Record: 20-7-11, 67 points (4th)
Home Record: 13-1-5, 40 points (Tied for 3rd)
Away Record: 7-6-6, 27 points (4th)
Goals Scored: 80 (3rd)
Goals Conceded: 57 (Tied for 11th)
Poisson Expected Points: 66.5 (3rd)
Poisson Probability of Winning League; 4%
Players Out:
Leo Franco - GK 32 starts, allowed 48 goals
Seitaridis - 10 starts, 4 sub appearances, 75 minutes per match played
Luis Garcia - 5 starts, 14 sub apps, 30 minutes per match played
Coupet - GK 6 starts, allowed 11 goals
Players In:
Asengjo - GK Valladolid
Juanito - CB Betis
Jurado - AM Mallorca (returning from loan)
Reyes - AM Benfica (returning from loan)
Valera - D Racing (returning from loan)
As you can see, not much action from Atleti this summer. Last season they played an entertaining style of football and we can expect more of that this year. Last year they were an elite attacking team and thoroughly mediocre defensively. There's no major reason to believe that will change this time around, that I can see. There are rumors that Heitinga may be making the last-minute move to Everton, which would weaken them further at the back for this season.
Likely lineup:
Prediction: I think Atleti will have enough defensive problems to keep them well out of the title hunt. Expect them to fight with Sevilla, Valencia, and Villarreal for the two Champions League spots. If you pinned me down and forced me to guess which place they finish in I'd say 5th, putting them in the Europa League.
Villarreal Club de Fútbol
2008-2009:
Record: 18-11-9, 65 points (5th)
Home Record: 12-3-4, 39 points (5th)
Away Record: 6-8-5, 26 points (5th)
Goals Scored: 61 (5th)
Goals Conceded: 54 (Tied for 8th)
Poisson Expected Points: 57.5 (6th)
Poisson Probability of Winning League: 1%
Players Out:
Nihat - 8 starts, 11 sub appearances, 43 minutes per match played
Mati Fernandez - 5 starts, 16 sub appearances, 33 minutes per, 3 goals
Guillermo Franco - 5 starts, 13 sub apps, 38 minutes per match
Cygan - 4 starts, 4 sub apps, 77 mins per match
Altidor - 2 starts, 4 sub apps, 46 minutes per match, 1 goal
Players In:
Nilmar - F Internacional (Brazil)
David Fuster - MF Elche
Marcano - D Racing de Santander
Pereira - F Racing de Santander (returning from loan)
Another team that didn't make any huge moves over the summer, Villarreal should be similar to last year; solid, though unspectacular at both ends of the pitch. I am surprised that Cazorla, Capdevila and Senna didn't get more attention in the summer from the bigger clubs as all three are class players.
Projected Lineup:
As usual, expect a lot of rotating. I'm sure Llorente will get a lot of play up top, for example.
Prediction: I'm going boring. I think Villarreal will finish this season in a Europa League spot. I can't see them finishing second as they did two years ago and it's less likely that they fall out of the European spots. They'll certainly put up a fight for third or fourth but I don't think they are as good as the three obvious rivals and in the end will fall out of the Champions League spots.
Valencia Club de Fútbol
2008-2009:
Record: 18-8-12, 62 points (6th)
Home Record: 12-4-2, 40 points (Tied for 3rd)
Away Record: 6-4-9, 22 points (Tied for 8th)
Goals Scored: 68 (4th)
Goals Conceded: 54 (tied for 8th)
Poisson Expected Points: 61.78 (5th)
Poisson Probability of League Title: 2%
Players Out:
Albiol - 33 starts, 1 sub appearance, 90 minutes per match, 2 goals
Moretti - 25 starts, 3 sub apps, 80 minutes per match
Renan - GK, 19 matches, 25 goals allowed
Edu - 9 starts, 12 sub apps, 44 minutes per match, 1 goal
Vicente - 6 starts, 21 sub apps, 34 minutes per match, 6 goals
Morientes - 7 starts, 13 sub apps, 44 minutes per match, 1 goal
Angulo - 5 starts, 6 sub apps, 51 minutes per match
Carleto - 1 sub apps, played 81 minutes
Players In:
Moya - GK Mallorca
Mathieu - D Toulouse
Dealbert - D Castellon
Bruno - D Almeria
Miku - F Salamanca (returning from loan)
Zigic - F Racing (returning from loan)
If you read Marca about once a week on the wrong day, you'd think that Valencia had a crazy summer in which all of their top players left for Real Madrid or Barcelona. As usual with transfer rumors, things didn't turn out nearly as crazy at it seemed they would. I think Valencia is a bit of a combination of the above teams. Like Sevilla, I expect them to improve in attacking from last year even with the same cast of characters. Mata is an elite winger, and at 21 I'd expect him to have an even better year than he did in 2008-2009 even though he was excellent then. He and the also-elite forwards seem to be well in sync and could be even more dangerous than last year. Pablo Hernandez also seems ready to take over for Joaquin, who has not been able to fulfill the promise he showed while at Betis. Like Atletico de Madrid, I think Valencia are not nearly good enough defensively to mount any serious title challenge. The loss of Albiol shouldn't help matters.
Here's how I see them lining up:
Prediction: I think they will almost certainly be in a four-team fight for the last two Champions League spots, with the two losers likely finishing in the Europa League positions. As I said above, I think there is a good chance that they are even more dangerous going forward next year. If I had to guess, I'd say the Che will finish 4th, behind Sevilla and ahead of Atletico de Madrid.
The Other 11
While I have focused on the 6 top finishers last season, it's certainly possible that one or more of the remaining teams get in there and edge them out for a spot in Europe. Of the others, Deportivo de la Coruña are my pick for most likely team to make a run at the Europa League. None the less, I don't rate their chances very highly. Espanyol is another team that could get up there, but with the tragic death of Dani Jarque it's tough to say how things will turn out.
I perhaps shouldn't add this until I've analyzed how well results from the previous season can be used to predict the results the next season, but just for fun here are a few predictions based mainly on what happened last season:
- Getafe, who finished tied with relegated Betis last season, will turn things around and finish near the middle of the table than the
- Osasuna, in relegation danger themselves finishing just a point clear, will not be as high but will be in a much safer position
- Almeria, who finished 4 points clear of relegation last season, will be relegated or finish even closer to the danger zone
- Sporting Gijon will be playing in the Segunda a year from now
The Promoted 3
To be perfectly honest, I don't much of anything about the three promoted teams. More importantly, I don't have any great ideas on how to rate them based on previous results or signings or something along those lines. That is yet another thing to add to the list of topics to hopefully be covered later. I suspect that it's really hard to predict where teams that get promoted or relegated will finish because the rosters are often completely different. I do not even wish to make a guess at where they'll finish or which is the most likely to stay up.
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