A Worldwide Historical Clubs Ranking based on Mathematics

(Last update: 21/12/2009)

Versão em Português

• I - THE RANKING
• II - EXPLANATIONS
  • 1. Introduction
  • 2. Choosing the competitions to be considered
  • 3. Defining the ranked teams
  • 4. Defining the variables
    • 4.1 Strength
    • 4.2 Difficulty
  • 5. The weights of each competition
  • 6. The "self weights"
  • 7. Re-proportionalizing the weights
    • 7.1 Weights based on the performances in Brazilian Championship
    • 7.2 Weights based on the performances in Taça Libertadores
    • 7.3 Weights based on the performances in Intercontinental and World Cups
    • 7.4 Weights based on the performances in UEFA Champions League
  • 8. Weighting the world competitions
• III - THE CURRENT PUNCTUATION
• IV - ONE FAIRER PURPOSE

I - THE RANKING

II - EXPLANATIONS

1. Introduction

All historical rankings that we can find in the Net (not only in RSSSF, but in several other sites) are based on the "I think" method. All points attributed are argued as "I think that each title of Italian League must earn XX points" or "I think that the runner-up of UEFA Champions League must earn YY points". My ranking, on the other hand, attributes points based on mathematical considerations and calculations with virtually no "I think" statements. In fact, I use only one "I think" criterium that is equalize, for any competition considered, two runner-ups to one title.

2. Choosing the competitions to be considered

To allow a equal treatment to all countries and continents, I consider only the most important competition in each level:

- World Level: Intercontinental (Toyota) Cup and FIFA Club World Cup;
- Continental Level*: Taça Libertadores** and UEFA Champions League;
- National Level: National championships;
- State Level: Brazilian state championships***;

* I do not consider the Champions Cup of CONCACAF, Africa, Asia and Oceania because no teams from these continents is ranked yet.
** Including the Tournament of South American Champions of 1948.
*** Included because the Brazilian Championship is very younger than the other national leagues. If I don't include the state competitions, the Brazilian teams' positions in the ranking would be inferior of the actual ones.

3. Defining the ranked teams

I wanted to rank all teams that can de considered as "big teams" for some criterium. As in my "I think" ranking, to be included in the ranking, the team must initially obey (at least) one of these criteria:

1) To be mentioned in PLACAR Magazine - "Grandes Times" (edition nr. 1058)
2) To be mentioned in PLACAR Magazine - "Esquadrões" (edition number 1064)
or in PLACAR Magazine - Esquadrões Brasileiros ("100 Anos de Futebol no Brasil") (edition number 1097)
3) Had won at least 1 (Copa Libertadores, European Champions Cup, FIFA Club World Cup or Intercontinental (Toyota) cup) or 4 (African, CONCACAF, Asian or Oceanian Champions Cup) titles or 1 runner-up of FIFA Club World Cup.
4) To be mentioned in PLACAR Magazine - Ranking dos Melhores Times do Mundo (edition number 1111; revised version - edition number 1157)
5) To be mentioned in The 50 Greater Clubs of The World
6) To be mentioned in "Os Principais Clubes do Mundo" (PLACAR Magazine - Guia do Torcedor) (distributed with edition number 867)****
7) To be mentioned in FOUR-FOUR-TWO Magazine - "World League" (edition number 103 - World Football Supplement)
8) To be mentioned in the book "The Greatest-Ever Football Line-ups"
9) To be mentioned in FIFA Classic Clubs
10) To be mentioned in GOL FC magazine - "Os 100 Maiores Times do Mundo" (special edition number 3)***

**** Except teams from Brazil, Italy, Portugal or Spain
***** Except teams from Brazil

4. Defining the Variables

This ranking is based exclusively on two variables defined for all championships: strength and difficulty.

4.1 Strength

The strength of one championship is defined as the performance of the teams which played these championship in the competition imediately superior. This performance is calculated by attributing 2 points to titles and 1 point to runner-ups.

For example, the french clubs won one title (Olympique Marseille in 1993) and five runner-ups of UEFA Champions League (Stade Reims in 1956 and 1959, Saint-Ettiénne in 1976, Olympique Marseille in 1991 and Monaco in 2004). So, the strength of the French Championship is calculated as (1 x 2) + (5 x 1) = 7.

Calculated by the same method, these are the strength of the various championships:

Obs. Clubs from other states never were Brazilian champions or runner-ups and their state championships have strength 0. Because of this, clubs from other states than the listed above will not be ranked.

Obs. Clubs from other countries never were continental champions or runner-ups and their national championships have strength 0. Because of this, clubs from other countries than the listed above will not be ranked.

Obs.
1) Because Intercontinental (Toyota) Cup was disputed by only two teams, its runner-ups were not considered in calculating the strength of the continental competitions.
2) Clubs from Africa, Asia, CONCACAF and Oceania never won any Intercontinental or World titles or were World Cup runner-up and their continental champions cup have strength 0. Because of this, clubs from these continents will not be ranked.
3) Since Cruz Azul was runner-up of Taça Libertadores and while teams from CONCACAF do not be at least FIFA Club World Cup runner-up, Mexico will be considered, for all effects as an South American country.

4.2 Difficulty

The difficulty of one championship is defined as the level of dispute, or the "internal strength" of this championship and is measured as the number of teams that historically dominate the dispute. This measure is simply the number of teams that won at least one half of the number of titles of the greater winner.

For example, the greater winner of UEFA Champions League is Real Madrid with nine titles. One half of nine is 4,5 and only three teams won more than four titles: Real Madrid (9), Milan (7) and Liverpool (5). So, the difficulty of UEFA Champions League is measured as 3.

Measured by the same method, these are the difficulties of the various championships:

5. The weigths of each competition

The initial weight of each competition is defined and calculated simply as the product of strength and difficulty:

Clearly, this simple comparison is unreal, because the calculations of the weights of Rio de Janeiro state championship and UEFA Champions League, for example, were based (through the "strength" variable) on performances in completely different competitions. So, we need to re-proportionalize the weights.

6. The "self weights"

As the lower competitions, the state championships of Brazil can be considered an initial point of calculations. The strengths of these state championships were calculed based on performances in Brazilian Championship. To allow the comparison among the state championships and the Brazilian Championship, we can apply the same calculation to the Brazilian Championship itself, finding one "self strength" equals to 120 (because in 40 editions of Brazilian Championship, there were, obviously, 40 winners and 40 runner-ups). So, we can calcule the "self weight" of Brazilian Championship, which is equals to 120 x 6 = 720.

Following the same logic, we can allow the comparison among Taça Libertadores and the South American national championships, finding, for the Taça Libertadores, the "self strength", which is equals to 153 (in 51 editions, there were 51 winners and 51 runner-ups), and the "self weight", equals to 153 x 4 = 612.

Also, following the same logic again, we can allow the comparison among UEFA Champions League and the European national championships, finding, for the UEFA Champions League, the "self strength", which is equals to 162 (in 54 years, there were 54 winners and 54 runner-ups) and the "self weight", equals to 162 x 3 = 486.

7. Re-proportionalizing the weigths

Initially, is very important to see that the weights can be divided in four groups:

i) Weights based on the performances in Brazilian Championship (weights of state championships and the "self weight" of Brazilian Championship);
ii) Weights based on the performances in Taça Libertadores (weights of South American national championships and the "self weight" of Taça Libertadores);
iii) Weights based on the performances in UEFA Champions League (weights of European national championships and the "self weight" of UEFA Champions League);
iv) Weights based on the performances in Intercontinental and World Cups (weights of Taça Libertadores and UEFA Champions League).

So, we need to re-proportionalize group by group.

7.1 Weights based on the performances in Brazilian Championship

As the lower competitions, among all considered, we don't need to change the weights of the state championships:

But, to allow the comparison among state championships and Brazilian Championship, we need to set the re-proportionalized weight of Brazilian Championship as 720 (its "self weight").

7.2 Weights based on the performances in Taça Libertadores

As the weight of Brazilian Championship was re-proportionalized from 258 (the initial weight) to 720, we also need to re-proportionalize the other weights of the same group, multiplying them by 720/258:

And, to allow the comparison among South American national championships and Taça Libertadores, we need to set the re-proportionalized weight of Taça Libertadores as 1707,91 (its re-proportionalized "self weight").

7.3 Weights based on the performances in Intercontinental and World Cups

As the weight of Taça Libertadores was re-proportionalized from 216 (the initial weight) to 1707,91, we also need to re-proportionalize the other weights of the same group, multiplying them by 1707,91/216:

And, to allow the comparison among European national championships and UEFA Champions League, we need to set the re-proportionalized "self weight" of UEFA Champions League as 1186,05.

7.4 Weights based on the performances in UEFA Champions League

As the "self weight" of UEFA Champions League was re-proportionalized from 486,00 (the original "self weight") to 1186.05, we also need to re-proportionalize the other weights of the same group, multiplying them by 1186,05/486:

8. Weighting the world competitions

As defined in Section 6, we can find, for the world cups, the "self strength", which is equals to 104 (in 43 editions of Intercontinental Cup, there were 43 winners and in 6 editions of FIFA Club World Cup there were 6 winners and 6 runner-ups), and the "self weight", equals to 104 x 14 = 1456.

Because don't exists a "true weight" ("true" meaning not-"self") of the world cups, we need to estimate it.

As saw in Section 6, we have three championships with both ("true" and "self") weights that can suggest one factor of multiplication:

So, we can adopt as the final re-proportionalized world championships' weight the average (1456 + 4063,26 + 3553.26)/3 = 3024.17.

III - THE CURRENT PUNCTUATION

After all the re-proportionalizations, and adopting the equalization between two runner-ups and one title, we have the following current punctuation attributed:

IV - ONE FAIRER PURPOSE

Somebody can argue that is unfair to compare, for example, the titles of Manchester United with the titles of Paris Saint-Germain, because PSG is almost 100 years younger than MU, which means that Manchester United had much more opportunities to win points than Paris Saint-Germain. So, we can make another ranking based on the average points won by year:

This ranking is part of the Oosterpark Rankings group.