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Wednesday, March 10, 2010

FIFA Ranking: Confederation weighting factor calculation

Three days ago I received from FIFA's media department a detailed description of the confederation weighting factor calculation. Hats off to them - they are the only (con)federation to actually reply to e-mails. UEFA, CAF, CONCACAF, AFC and OFC should take a couple of public relations classes. Special note: CFU reply to e-mails too. I was actually trying to get an interview with FIFA's General Secretary, Mr. Jérôme Valcke, regarding these questions.

Now, on to the method.

In the revised ranking procedure the weighting factor is determined on the basis of the last three World Cup final rounds. To calculate the confederation weights the following steps are carried out (see also the table below):

1) The perspective is confined to interconfederational matches in the framework of World Cup finals, i.e. matches between teams from the same confederation are excluded in order not to distort the calculation (see row „total games“ in the following table).

2) Calculation of the number of interconfederation matches won by each confederation (see row „win“).

3) Calculation of the average number of won interconfederational matches by confederation (see row „av. per game“):

avYear x = av. per game = win/total games

4) Calculation of the average number of won interconfedertional games over the past three World Cup final rounds by confederation (see column „av 94-02):

av94-02 = (av94+av98+av02)/3

5) Calculation of the confederational weighting factor on the basis of a comparison with the best confederation (see column „weight“).

weightConf x = 4√(av94-02 of Conf x/ av94-02 of best Conf)

Supplementary conditions:

a) if weightConf x < 85 =""> weightConf x = 0.85

b) Confederations not participating in World Cup final rounds (e.g. OFC) will be assigned the value of the weighting factor of the weakest confederation.

Note: Test calculations have shown that using the “pure differences” documented in column „av 94-02“ would lead to an exaggeration of strength differences in the calculation of the world ranking. Using the fourth root instead of the pure differences reduces the differences between confederations and thus ensures that the confederational weighting factor only has a moderate effect. The first supplementary condition plays a similar role: Fixing the minimal confederational weight at a value of 0.85 ensures that the top teams from weaker confederations can still reach good positions in the world ranking.

1994

1998

2002

1994 -02

av 94-02

weight

Game total

52

64

64

180

Interconfederational game total

36

49

54

139

UEFA

total games

30

39

44

113

win

14

20

18

52

av per game

0.47

0.51

0.41

1.38

0.46

1.00

CONMEBOL

total games

17

21

20

58

win

8

8

10

26

av per game

0.47

0.38

0.50

1.35

0.45

0.99

CONCACAF

total games

8

10

10

28

win

2

2

4

8

av per game

0.25

0.20

0.40

0.85

0.28

0.88

AFC

total games

7

12

17

36

win

2

1

5

8

av per game

0.29

0.08

0.29

0.66

0.22

0.83

=> 0.85

CAF

total games

10

16

17

43

win

2

3

4

9

av per game

0.20

0.19

0.24

0.63

0.21

0.82

=> 0.85


9 comments:

  1. Edgar,

    Thanks for sharing! A few comments:

    (1) Taking the fourth root seems a bit arbitrary -- why not the fifth root or third root? Guess it's a rhetorical question...

    (2) Would be interesting to see the post-WC2006 calculations.

    (3) Would also be interesting to see pro forma post-WC2010 calculations (using either Elo-based results or Voros probabilities)!

    (4) I had expected "home confederation" to have a larger impact on the 3-WC average. Looks like there is some advantage, but not huge.

    ReplyDelete
  2. Why isn't the 2006 World Cup included in stead of the 1994? Or isn't there supposed to be change in the condeferation factor?

    ReplyDelete
  3. Took a first cut at WC2006 (48 inter-confederation matches):

    UEFA: won 22 of 34 (65%)
    CONMEBOL: won 10 of 17 (59%)
    CONCACAF: won 1 of 13 (8%) - dismal
    AFC: won 1 of 12 (8%) - dismal
    CAF: won 3 of 16 (19%)
    OFC: won 1 of 4 (25%)

    Averaging these with WC2002 and WC1998 and applying the fourth root:

    UEFA: 1.00
    CONMEBOL: 0.98
    CONCACAF: 0.81
    AFC: 0.74
    CAF: 0.79
    OFC: 0.83?

    The "0.85" rule then applies to four of the six confederations!

    Seems a bit harsh to have the final "0.85" rule override all the prior calculation steps for the majority of the confederations... Seems like a better result might come from either changing the "0.85" to something lower, like "0.75", and/or use a higher root, like the eighth root.

    Then there's the question about whether OFC's number should reflect the Australian WC2006 performance as they are no longer part of that confederation...

    ReplyDelete
  4. great that your calculations after the 2006 world cup match what FIFA are applying, as they mention in their fact sheet.

    http://www.fifa.com/mm/document/fifafacts/r&a-wr/52/00/97/fs-590_10e_worldrankingpointcalculation.pdf

    still seems to be biased on the results of the very best teams (who should make the QFs or better) dragging up the entire confederation.

    If say Australia and Korea Republic do really well in this next world cup, this might make future matches between Tajikistan and Turkmenistan worth more.bizarre.

    ReplyDelete
  5. Dorian, I have 0.63 for OFC since both the 1998 and 2002 WC average wins per game are 0.

    Intermediate values (without the 2010 WC):

    CONMEBOL 1
    UEFA 0.98
    CONCACAF 0.85 (0.79)
    CAF 0.85 (0.79)
    AFC 0.85 (0.78)
    OFC 0.85 (0.74)

    And with Elo ratings probable results:

    UEFA 1
    CONMEBOL 0.99
    CONCACAF 0.85 (0.82)
    CAF 0.85 (0.75)
    AFC 0.85 (0.73)
    OFC 0.85 (0.66)

    ReplyDelete
  6. Very interesting. Thanks for sharing!
    The confederation weighting factor calculation was the only step of the Fifa ranking that was unknow yet..

    ReplyDelete
  7. Edgar this is Amazing to know.

    I thought i could never ever know where the hell FIFA got those numbers.

    Thank you very much for your work

    ReplyDelete