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Friday, July 18, 2014

Confederation weightings for the next 4 years

Unless FIFA tweaks the formula somehow, these are the values that will be used for the next 4 years (up to and including the 2018 FIFA World Cup final).

The formula used to compute the weightings:

weightConf x = 4√(av06-14 of Conf x/av06-14 of best Conf)



2006 2010 2014 '06-'14 av 06-14 weight
UEFA total games 34 34 41 109


win 26 20 24.5 70.5


av per game 0.76 0.59 0.6 1.95 0.65 0.99
CONMEBOL total games 17 24 24 65


win 10.5 16 17 43.5


av per game 0.62 0.67 0.71 2 0.67 1.00
CONCACAF total games 13 11 16 40


win 2.5 4 7.5 14


av per game 0.19 0.36 0.47 1.02 0.34 0.84
AFC total games 14 14 12 40


win 3.5 5 1.5 10


av per game 0.25 0.36 0.13 0.74 0.25 0.78
CAF total games 16 20 17 53


win 4.5 6.5 4.5 15.5


av per game 0.28 0.33 0.26 0.87 0.29 0.81
OFC total games 0 3 0 3


win 0 1.5 0 1.5


av per game 0 0.5 0 0.5 0.17 0.71


The minimum possible value is 0.85, so the final values are:

CONMEBOL 1
UEFA 0.99
CONCACAF, CAF, AFC, OFC 0.85

This will be the first time when UEFA drops below 1.

9 comments:

  1. Is this a recommendation? But, FIFA uses and states following weightings:
    UEFA, CONMEBOL : 1.00
    CONCACAF: 0.88
    The rest ; 0.85

    ReplyDelete
    Replies
    1. Metin,
      these FIFA-weightings you mention are the confederations weightings as applied to matches played on or before July 13th 2014. From July 14th on matches should be calculated with the new confederation weightings as published above.
      Or do you have a link to a FIFA-publication dated after the World Cup with these weightings ?

      Delete
  2. Here is the link. Obviously not updated yet.
    http://www.fifa.com/worldranking/procedureandschedule/menprocedure/index.html

    ReplyDelete
  3. I think you've made a rounding error in your computations: CONCACAF's raw weight should be 0.85 (rounded from 0.8468197...).

    ReplyDelete
    Replies
    1. Could you detail your calculation steps?

      Delete
    2. The raw numbers for points and matches are as listed above.
      The differences occur if one calculates the averages with rounded or unrounded numbers.

      For instance the denominator (CONMEBOL) could be calculated as:
      a) ((10.5/17) + (16/24) + (17/24))/3 = 0.6642 (rounded 0.66) or
      b) (0.62 + 0.67 + 0.71)/3 = 0.6667 (rounded 0.67)

      For CONCACAF:
      a) ((2.5/13) + (4/11) + (7.5/16))/3 = 0.3416 (rounded 0.34) or
      b) (0.19 + 0.36 + 0.47)/3 = 0.3400 (rounded 0.34)

      The CONCACAF-weight could be calculated as:
      a) (0.3416/0.6642)^1/4 = 0.8468 (rounded 0.85)
      b) (0.3400/0.6667)^1/4 = 0.8451 (rounded 0.85)
      c) (0.34/0.66)^1/4 = 0.8472 (rounded 0.85)
      d) (0.34/0.67)^1/4 = 0.8440 (rounded 0.84)

      From the official FIFA-document with the calculation of the WC-2010 weights one can conclude that the complete calculation should be done with unrounded numbers, otherwise the CONCACAF-weight for WC2010 would be 0.87 instead of 0.88.
      So for 2014 the CONCACAF weight should be a) 0.8468 rounded 0.85.
      Not that it matters a great deal :)

      Delete
    3. I realize this is a really late reply, but...

      Working in exact terms, the denominator, from CONMEBOL, is (21/34 + 2/3 + 17/24)/3 = 271/408. CONCACAF's value is (5/26 + 4/11 + 15/32)/3 = 1563/4576. After normalization, this becomes 79713/155012, and taking the fourth root gives 0.8468197...

      As noted, though, this doesn't matter a great deal.

      Delete
  4. I still think FIFA's taking the fourth root of a value is not only arbitrary, but not as strong as a mathematical application as possible. The confederation with the highest average wins is already assigned a specific value (1.00). Why not then assign the lowest confederation a specific value as well (e.g. 0.85) and simply interpolate the final values of all the other confederations in between these two specific values?

    I also think It would be better to count draws as 1/3 of a win, and that the last three would cups should be weighted based on recency with 3x for most recent, 2x for next, and 1x for the oldest.

    ReplyDelete
  5. Of course, if FIFA's ranking was any good at ranking teams on a global basis, it wouldn't need confederational weightings. If Team A (CONMEBOL) and Team B (AFC) are ranked equal, and they both beat Brazil 1-0, why should one of those teams (Team A) get more points? They both did exactly the same thing. The weightings are simply unnecessary.

    ReplyDelete