CONCACAF Champions League Coefficient

Thanks, good catch. It must be a mistake because the total teams I had listed for the first edition was only 23. It doesn't make much difference in the final rankings though. Ok, so here goes the update after the latest phase.

2010-11 Final Results
Pts/Teams
Mex 10/4
USA 5/4
CR 2/2
Can 1/1
Carib 2/3
Hon 2/3
ES 1/2
Guat 0/2
Panama 0/3

Total in new format through 2010-11
Pts/Teams
Mex 35/12
Carib 9/9
Can 3/3
USA 8/12
Hon 6/8
Panama 4/7
CR 2/7
ES 1/6
Guat 1/6
Bel 0/1
Nic 0/1


2011-12
Pts/Teams
Can 2/1*
Mex 6/4*
USA 4/4*
ES 2/2*
CR 1/2
Hon 1/3
Nic 0/1
Guat 0/2
Panama 0/2
Carib 0/3

Total in new format as of now
Pts/Teams
Mex 41/16* (2.5625)
Can 5/4* (1.25)
USA 12/16* (.75)
Carib 9/12 (.75)
Hon 7/11 (.6363)
Panama 4/9 (.4444)
CR 3/9 (.3333)
ES 3/8* (.375)
Guat 1/8 (.125)
Bel 0/1 (0)
Nic 0/2 (0)

*Can still earn points.

Those last two groups are going to be a bit off until the competition is completed because I've included all the teams from the group stage in the denominators and they have not completed their chances to earn points.

If you care to see the reasoning behind this coefficient system, please see the following posts before commenting/criticizing. This isn't my system, this is the system that I think they may be using. It's getting a bit too much to quote every time now.

http://www.bigsoccer.com/forum/showthread.php?p=20158678#post20158678
http://www.bigsoccer.com/forum/showthread.php?p=20195366#post20195366
http://www.bigsoccer.com/forum/showthread.php?p=20741919#post20741919
http://www.bigsoccer.com/forum/showthread.php?p=22060916#post22060916

Greetings fellow Futbol Fanatics... my name is Tonatiuh and I have been reading the Big Soccer forums for a couple of years without joining because it looks addictive and I don't think I have enough time to waste.... but I have been bored recently and decided to give it a go.


The reason I am posting here is because I wanted to propose a new way of ranking teams & leagues participating in continental championships.. and get your collaboration on how to design the best system.

A little bit of background, when I was studying at UNAM, I was so frustrated that the FIFA & IFFHS Nation Team ranking systems make no sense... that decided to use it as a case study for a statistics class.. demonstrating that their rankings have almost no predictive success. This later turned into a semester project to design a better (more predictive) ranking system.

A few years later when I was working in the gambling industry, I realized I could use my very accurate / predictive system to make some money in web based Euro gambling sites... and that has worked out quite well. (I scored on Holland reaching the Final & Uruguay reaching Semi Finals in South Africa).


I was bored recently and decided to work on a new ranking system for the CONCACHAMPIONS, so I joined to talk about the first draft and see what you guys think.


What Problem Are We Trying To Solve?

1) Winning a match in the Preliminary round should not count as much as winning the Final

2) Losing by 1 goal should not be punished as much as losing by 3

3) Winning against a Belizean team should not count as much as beating a Mexican team

4) Losing to a Costa Rica team should not be punished as much as losing to a Trinitarian team

5) How do you rank Federations when some Federations might only have 1 very successful team, another Federation might have 3 teams... 1 that might have been as successful as the Federation with 1.. and then 2 that are less successful than the Federation with 1 team etc., How do you not punish Federations for sending more teams... but why punish a Federation that peforms well but wasn't given the opportunity to send more teams?

But how do we establish an objective / empirical regime to incorporate those concerns? Well, technically we could build a model using chi-squared distributions / Pearson Test... but we don't have enough observations / data... and frankly I don't think the model would be that superior to the simpler, more common sense model I am proposing below.

One way to judge performance at different stages of the competition is to do a comparative difficulty analysis. Look at the following stats for all the clubs that have participated in the 3 year history of the CCL:

https://docs.google.com/open?id=0B8LfR4un7yj3M2E2NGFjNjctMmVhZS00YWMwLWI3NjAtNjM1YmE4ZTBiZGM4

From there we can use the following relationships to establish proxies for the relative difficulty of winning at each stage such at...

it is 1.47 times more difficult to win in the Group Stage then in the Prelim Stage, 2.59 times more difficult to win the Quarter Finals than in the Prelim Stage etc.,

Then I came up with the following system for judging the Margins by which a team wins or loses:

Loss by 2 or More Goals: 0 Points
Loss by 1 Goal: 0.5 points
Draw: 1 point
Win by 1 Goal: 2 points
Win by 2 Goals: 2.5 points
Win by 3 Goals or More: 3 points

That is a little bit subjective... but I think it is reasonable... what do you guys think?


So combining the relative difficulty of success at each stage + the rewards by result & margin gives us the following table

https://docs.google.com/open?id=0B8LfR4un7yj3ZjFiZTYxZWEtODI3Zi00ZGY0LWE4ODMtMjkyYWEwN2VmZmY5


Then to come up with a system of bonuses for wins against teams from successful leagues... I did a high level overview of the sucess of each league:

https://docs.google.com/open?id=0B8LfR4un7yj3ZjI1ZTUwZjgtYjVhZC00OTZlLWI4ZGEtNDQxMTUxYmYyMWI1

... and then compared each Federations 3 Year Stats versus the rest of the CONCACAF to determine a measure of their comparative strength at each stage of the competition.

https://docs.google.com/open?id=0B8LfR4un7yj3NzA3ZjRjODktYmQ3My00NWU4LWI3MmQtMzUyMTc3M2ZhZTA3

Finally I established the Bonus points for wins against x Federation at y Stage:

https://docs.google.com/open?id=0B8LfR4un7yj3OTY3YWFkNDMtOWEwMS00M2ZmLWI3MWEtOWJiNDNiZThmNjRl

So with our point system in place I scored all the Matches and developed this sample ranking for 2010-2011 tournament.

https://docs.google.com/open?id=0B8LfR4un7yj3NmRkMDhlNjctNjBkMy00NmI4LWJkZGEtM2Y3YTI2ODQ4NzA2

As you can see we rank leagues first by their best performing team... then for leagues with multiple participants we find the least common denominator. For example Trinidad had two participants & Panama three... Trinidad had the best team.. but if we aggregate Trinidad's two against Panama's best two.. then Panama edges Trinidad out... so in an argument of whether we should yank Panama's 3rd spot & give it to Trinidad this model would argue no etc.,

Here is the aggregated 3 Year Ranking.. which I think we all can agree "feels right"?


Now I haven't feed the results of the current tournament... it would be interesting to see how predictive the model is versus pundit or fan predictions.

https://docs.google.com/open?id=0B8LfR4un7yj3YzE3MmQyMDgtNTRlZC00YjNiLTk1OGItMWNkNzQwMzkzYzE5

Here is a link to the spreadsheet with the Match database & all the calculations:

https://docs.google.com/spreadsheet/ccc?key=0AsLfR4un7yj3dG1uV3hYMTZuOGU2bXoyWTJXRHlCX2c



What do you guys think?

I haven't had a chance to check out the detail you gave, but I applaud the effort. I'd just like to point out that coefficients and FIFA rankings are not intended to be predictive. They are intended to show the best team over a given period of time based upon their performance. It's more of a reward for a job done well than anything else.

Thank you sir.

Wholeheartedly agree. At this point, half their point total should be allotted to the USA, as they are playing in a USA league (half joking).

Still, if the Canadian rep wins the prelim and qualifies for group, they are going to generate a lot of points, as they are usually superior to the 4th place team. Still, they have gotten 2 teams to the QF's in four years, pretty impressive.

i wouldn't say canada needs its own league to merit more CCL spots (afterall, MLS is not a "USA" league). of course they would need more teams in the MLS and NASL for that to be considered, but surely as soon as next year it would be logical to have the canadian champions put directly into group stage.

very informative.

thanks for the info. keep it up.

With the pending changes to the CCL, I obviously need to make a few adjustments to the coefficient for next year. Any suggestions? My first thought is to just remove the group stage bonus and go from there...

I would say reduce the bonus. to maybe 1 point.

Maybe show two totals, the pre change total and then a total of the new format.

I think you may need to do more than just eliminate the group stage bonus to keep the comparisons meaningful.

Last year, the most points a country or a team could earn in the preliminaries + group stage was 18. 2 for preliminary wins, 4 as an appearance bonus, and 12 for group stage wins.

This year, if you eliminate the group stage bonus, the most points a country will be able to earn in the group stage will be 8, for 4 group stage games.

That has a few effects:

1) It places much more emphasis on the knockout rounds than in previous years. A team or a one-team confed can still earn 15 points for a perfect run in the knockouts. Before, that was a little less than was available in the early stages; now it's twice the amount.

2) It overvalues past years. Right now, the U.S. and Honduras are separated by about two points in the all-time total. Reducing the total points available makes it harder for either country to either close the gap or pull away. This would be even more pronounced in the individual team totals.

One possibility: Leave the group stage "bonus" (for every country/team), and make the group stage games worth 3 points. That gives you a possible total of 16 group stage points.

Or make every win worth 3 points, and eliminate the knockout round bonuses; knockout win values will already be inflated, so they're not really necessary.

MLS is not a USA league? What do you mean?

USA only I guess.

chapka brings up some interesting points. Whatever new system is devised should produce a similar number of total points as in previous years.

By my calculations, in previous years there were 218 points at stake in the entire competition:

1 point per Prelim Game * 16 games = 16
4 points Group Stage Bonus * 16 teams = 64
2 points per Group Stage Game * 48 games = 96
1 point Knockout Round bonus * (8 QF+4 SF+2 F= 14) = 14
2 points per Knockout Game = 28

16+64+96+14+28 = 218


Various Proposals For the New Coefficient:

1 Keep the Same Formula

If we kept the same formula, we'd instead have 234 points, since we'd eliminate the 16 prelim points but add 32 more group stage bonus points. (Everything else would stay the same, since there are the same number of total group stage games and knockout games as before)

Since 234 is only 7% higher than 218, I think this is an acceptable total point total.

Downside: While the total number of points is ok, giving such a bonus to all the participants in effect redistributes points from stronger teams to weaker teams, rather than rewarding teams for what they do in the competition. I think this is the least tenable option.

2 - Cut group stage bonus to 1 point, make group and knockout stage games worth 3 points, keep 1 knockout round bonus

This makes sense to me. You get the same bonus for each stage of the competition you progress in (group stage, quarters, semi and final) and each game is worth the same amount of points.

It also keeps the total point value very similar to what it was in previous years, 224 instead of 218.

Downside: Deviates from the UEFA system in terms of points per game, and I know that this coefficient project was designed to be comparable to UEFA.

3 - No bonuses, each games worth 3.5 points (1.75 for a draw)

This results in 217 points, virtually the same as the old system. Since everyone qualifies for the group stage, it makes sense to do away with bonuses and make all the points based on what you do on the field.

Downside: 3.5 points per game is kind of clunky.

4 - Eliminate Group Stage Bonus, retroactively change the old numbers.

Eliminating the Group Stage Bonus would result in only 138 points at stake, which, as chapka pointed out, would overvalue old years. But, if we just multiplied all the old numbers by 138/218, then past coefficients wouldn't have extra weight. Since this is all in a spreadsheet, I assume that would be easy to do.

Downside: Would make the old numbers weird, would require extra work, and would inflate the percentage of points available from the knockout stages even more.

The value of knockout stage bonuses and games as a % of total

Old system 42/218 = 19.3%,
Proposal 1 42/234 = 17.9%
Proposal 2 56/224 = 25%
Proposal 3 49/217 = 22.5%
Proposal 4 42/138 = 30.4%


Personally, I favor options 2 or 3. But this is ArsenalMetro's project, and he's the one doing the work, so I'll be fine with whatever he does.

One decimal point isn't clunky. Especially when using Excel. If you dislike it that much then just double all points, even from past tournaments and then it disappears.

And the way that is often done, is to take the "raw" point totals each year, and "normalize" them into a number from 0.0 to 1.0, so every year gets the same possible ranking.

So using this, I calculated a normalized score for each country/region by giving the highest value for the year as 1.0, the lowest value as 0.0 (which was always Belize at raw score of zero), and each country's score as the ratio from the high to the low.

So, say for Guatemala in 2010-2011: we have (High raw score: Mexico at 19) (Low raw score: Belize at 0) (Guatemala raw score at 5.25). So calculate
(5.25 - 0) / (19 - 0) = 0.2763

So the current table (though the 2011-2012 group stage):

2008-09; 2009-10; 2010-11; 2011-12; [Overall]; Nation
1.000; 1.000; 1.000; 1.000; [4.000]; Mexico
0.846; 0.022; 0.605; 1.000; [2.473]; Canada
0.237; 0.362; 0.586; 0.821; [2.006]; United States
0.654; 0.360; 0.412; 0.333; [1.760]; Honduras
0.295; 0.137; 0.513; 0.768; [1.713]; Costa Rica
0.474; 0.303; 0.123; 0.321; [1.221]; Panama
0.470; 0.346; 0.307; 0.036; [1.159]; CFU
0.256; 0.259; 0.276; 0.357; [1.149]; Guatemala
0.269; 0.151; 0.211; 0.429; [1.060]; El Salvador
0.026; 0.000; 0.000; 0.000; [0.026]; Nicaragua
0.000; 0.000; 0.000; 0.000; [0.000]; Belize

Of course, the normalized scores for 2011-2012 will change after the knockout rounds. Specifically, second place in this table will depend highly on the Los Angeles - Toronto matchup.

Another way to run the normalization calculations, is to use the maximum possible score for any particular year (which Mexico almost did in 2009-2010), instead of the maximum scored by any particular country.

Nicely presented. Option 3 is clean and easy.

Or you guys could adopt my clearly superior system.

Actually, whatever the sporting merits of the new system may be, it'll be great for my head-to-head coefficients.

One of the biggest problems with my system was that a few teams get big bonuses based on who they have and haven't played--for example, Nicaraguan teams have never played teams from any country but Canada, artificially inflating Canada's totals. More data on the minnows in the preliminary rounds should make the head-to-head data a lot more robust.

Back to the UEFA coefficient...I'm not sure total tournament points should be the target. If you want to maintain consistency, maximum points per team (or maximum group stage points per team) seems like a better target.

In the old format, a team that started in the prelims could earn a maximum of 18 points for its country, and a team that started in the group stage 16. Either way, the team could earn a maximum of 12 points for its individual ranking.

Now there are four games in the group stage. I think a good compromise system might be three points for a win, one for a draw, in all stages, with no group stage bonus but keeping the existing knockout bonuses.

Well, regardless of what changes I make going forward, we still have the 2011-12 edition to handle. And that resumes tonight.

After that Arsenal loss, I need it.

What was the final score, I mean I did not think they could comeback from 4 down.

Arsenal led 3-0 at halftime, there were no goals in the second half, and the aggregate was 4-3.

wow, I can't believe they almost pulled it off.

After 2011-12 Quarterfinals, first leg

Movement:
- Toronto over Olimpia
- Seattle over Houston
- Los Angeles over Morelia, Arabe Unido
- Isidro Metapan over Municipal, Los Angeles, Morelia, Arabe Unido, Real Espana, D.C. United, Alajuelense

Code:

Federation Coefficient              

Nation         2008-09   2009-10   2010-11   2011-12   Overall   
Mexico          19.500    23.125    19.000    14.500    76.125
Canada          16.500     0.500    11.500    15.000    43.500
United States    4.625     8.375    11.125    12.250    36.375  
Honduras        12.750     8.333     7.833     4.667    33.583
Costa Rica       5.750     3.167     9.750    10.750    29.417    
CFU              9.167     8.000     5.833     0.500    23.500
Panama           9.250     7.000     2.333     4.500    23.083 
Guatemala        5.000     6.000     5.250     5.000    21.250
El Salvador      5.250     3.500     4.000     7.000    19.750
Nicaragua        0.500     0.000     0.000     0.000     0.500
Belize           0.000     0.000     0.000     0.000     0.000
                
                
Club Coefficient
           
Club         2008-09    2009-10   2010-11   2011-12    Overall
Cruz Azul    23.4167    29.6313   20.3333    0.0000    73.3813
UNAM         16.4167    22.6313    0.0000   13.8333    52.8813
Santos       19.4167     0.0000   16.3333   14.8333    50.5833
Monterrey     0.0000     0.0000   30.3333   15.8333    46.1666
Toluca        0.0000    22.6313   14.3333    0.0000    36.9646
Marathon     14.2500    13.7500    6.6111    0.0000    34.6111
Saprissa      8.9167     5.0450   18.2500    0.0000    32.2117
Puerto Rico  17.0556     5.6400    7.9444    0.0000    30.6400
Pachuca       0.0000    28.6313    0.0000    0.0000    28.6313
Atlante      25.4167     0.0000    0.0000    0.0000    25.4167
Columbus      0.0000    10.7638   13.7083    0.0000    24.4721
Toronto       0.0000     0.0000    9.8333   14.0000    23.8333
Olimpia      10.2500     0.0000   12.6111    0.0000    22.8611
Salt Lake     0.0000     0.0000   21.7083    0.0000    21.7083
Seattle       0.0000     0.0000    5.7083   14.0833    19.7916
Houston      10.5417     7.7638    0.0000    0.0000    18.3055
Comunicaciones0.0000     9.9800    0.0000    6.6667    16.6467
Montreal     16.5000     0.0000    0.0000    0.0000    16.5000
Tauro         9.0833     0.0000    0.0000    5.5000    14.5833
Isidro Metapan0.0000     3.1550    0.0000   11.3333    14.4883
Municipal     6.6667     0.0000    7.7500    0.0000    14.4167
Los Angeles   0.0000     0.0000    0.0000   14.0833    14.0833
Morelia       0.0000     0.0000    0.0000   13.8333    13.8333
Arabe Unido   0.0000    10.3100    2.7778    0.0000    13.0878
Real Espana   0.0000     6.7500    0.0000    5.5556    12.3056
D.C. United   2.5417     9.7638    0.0000    0.0000    12.3055
Alajuelense   0.0000     0.0000    0.0000   11.5833    11.5833
Colorado      0.0000     0.0000    0.0000    9.0833     9.0833
Dallas        0.0000     0.0000    0.0000    9.0833     9.0833
Joe Public    5.0556     0.0000    2.9444    0.0000     8.0000
L.A. Firpo    7.7500     0.0000    0.0000    0.0000     7.7500
W Connection  0.0000     7.6400    0.0000    0.0000     7.6400
Herediano     0.0000     0.0000    0.0000    7.5833     7.5833
San Francisco 5.0833     0.0000    0.0000    0.0000     5.0833
FAS           0.0000     0.0000    3.3333    0.0000     3.3333
SJ Jabloteh   0.0000     2.6400    0.0000    0.0000     2.6400
Motagua       0.0000     0.0000    0.0000    1.5556     1.5556

Well Canada will pull away with the #2 spot in Concacaf.