European Cups Ranking System Explanation ECRS Ranking Comparison between nations in European Cups

domenica 20 luglio 2014

European Cups Ranking System

La versione italiana di questo post si trova qui

In this post I explain the new ranking system I will use to determine the best European teams that participate in the UEFA Cups (Champions League and Europa League).
It is a system created by me; I have already explained an old version of it on this post, but since then I have changed some things.
In particular, this new system concerns only the International Cups, and not the domestic competitions.

During the football season I will write some examples of the actual calculations.

This system takes into account points made, goals for, goals against and the strenght of the opponent team.

Base Score
For every match, I use this formula to determine the Base Score of each team: points made + (goals for - goals against) / 2,5

If a team wins a match 3-0, its Base Score is 3 + (3 - 0) / 2,5 = 4,2;
If it draws 0-0, its Base Score is 1 + (0 - 0) / 2,5 = 1 (the Base Score for a tie is always 1);
If it loses 1-2, the Base Score is 0 + (1 - 2) / 2,5 = -0,4.

Match Coefficient
Each team has a Club Triennial Score (CTS), which is determined by the results of the team in the previous three years. It is the strength of that team in UEFA Competitions (see "Calculate the CTS" for the details).
The Match Coefficient (MC) for a team is calculated dividing its opponent's CTS by its own CTS.

For the 2014-2015 season, the CTS of Barcelona is 52,86 and the CTS of Arsenal is 48,57. If in the European Cups there will be a match between these two teams, the MC for Barcelona will be 0,92 and the MC for Arsenal will be 1,09. This means that it should be easier for Barcelona to defeat Arsenal, than for Arsenal to defeat Barcelona.

If one or both teams didn't play the European Cups in the previous three years, they have a CTS of zero. In this case, the Match Coefficient for a team is calculated dividing its opponent's National Triennial Score (NTS) by its own NTS.
The National Triennial Score is calculated, for every country, taking into consideration the results of the teams of that country in the previous three years (see "Calculate the NTS" for the details).

For the 2014-2015 season, the CTS of Torino is zero (it didn't play European Cups in the last three years), and the CTS of Villareal is 27,70. If there is a match between these two teams, the Match Coefficient cannot be calculated with CTS, so the NTS of Italy and the NTS of Spain will be used (46,46 and 53,38, respectively). Then, the MC for Torino will be 1,15 and the MC for Villareal will be 0,87.

Round Score
If the Base Score is positive, it is multiplied by the Match Coefficient.
Otherwise, the Base Score is divided by the Match Coefficient.
The sum of the two legs' scores is the Round Score (RS).
The total score of a team is the sum of all its Round Scores, multiplied by 10.

If Barcelona-Arsenal ends 3-0 (1st leg) and 1-1 (2nd leg), the RS for both teams are:
Barcelona: BS * MC = (4 + (4 - 1) / 2,5) * 0,92 = 5,2 * 0,92 = 4,78
Arsenal: BS * MC = (1 + (1 - 4) / 2,5) / 1,09 = -0,2 / 1,09 = -0,18

Starting from the Round of 16, for each round successfully passed, each team gains 10 points (if in Champions League) or 5 points (if in Europa League). So, for example, the winners of the Champions League and Europa League will have a total bonus of 40 and 20 points, respectively.
Furthermore, only for the Champions League, starting from the Round of 16, if the RS of a team is positive, it is multiplied by 2.

Adjustment to eliminate negative score
After the scores for all the teams have been calculated, they are adjusted to ensure that none of them is negative.
The best score remains unchanged, while the worst is converted to 1, and all the other scores are adjusted proportionally. In this way, the worst teams gain more points in the ranking, while the best teams gain few points (the first team gains no points).
In any case, the positions in the ranking don't change.
This is the formula to make the adjustment (TS = team score, BS = best score, WS = worst score): TS + ((1-WS)/(BS-WS))*(BS-TS).

  1. The total score of a team is the sum of all its Round Scores multiplied by 10, plus Bonuses and final adjustment.
  2. Each Round Score is given by the sum of the scores of the two legs of a round (or by the score of the only leg, if just one is played).
  3. The score of each leg is given by the Base Score multiplied (or divided) by the Match Coefficient.
  4. The Match Coefficient is calculated using the Club Triennial Score or, if not applicable, using the National Triennial Score.
  5. The Base Score is calculated with the formula: points made + (goals for - goals against) / 2,5

Calculate the CTS
The Club Triennial Score is set for each team calculating the average of the team's scores for the last three seasons; if the team participated in two seasons, the average score is multiplied by 1,05; if the team participated in all the three seasons, the average score is multiplied by 1,10.
So, every team has its "modified average" for the last three years.
Then, the average of all teams' modified averages is subtracted by each team's modified average, and the result is divided by 1,25.
This new score is then subtracted from the team's modified average, and the result is divided by 2.

Ajax got these scores for the last three seasons:
2011-2012: 140,67 points
2012-2013: 40,01 points
2013-2014: 60,75 points

The average is 80,48; it is multiplied by 1,1 because Ajax played the International Cups in all the last three seasons. So, the modified average is 88,53.

If we calculate in this way the modified average for all the teams that played at least one international match in the last three seasons, we find that the average of these scores is 77,12.

Then, for Ajax, 77,12 is subtracted from 88,53 and the result is divided by 1,25. The new outcome is 9,13.
This score is then subtracted from 88,53. The result is 79,4.
Finally, we divide by 2. The result is 39,7.

The CTS for Ajax in 2014-2015 season will be 39,7.

The whole calculation, in one formula, is:
((140,67+40,01+60,75)/3*1,1-((140,67+40,01+60,75)/3*1,1- 77,12)/1,25)/2

Calculate the NTS
The National Triennial Score is the average of the CTS of all the country's teams.
As an exception, in this season the matches with a Gibilterra's team have a fixed coefficient of 1 (since this is the first year with Gibilterra's teams in the European Cups).

England has 12 teams that played at least one international match in the last three seasons: the best is Chelsea with 64,07 points, and the worst is Wigan with 34,18 points. The average of the CTS of the 12 teams is 47,38.
The NTS for England in 2014-2015 season is 47,38.

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