I'm pleasantly surprised by the revealing nature of this post on Edgar's website. FIFA explained how they come up with the confederation weights in their ranking formula; the confederation weights are based on the normalized fourth roots of average fractions of wins for each confederation in interconfederational matches in the previous three World Cup finals. Draws in interconfederational matches are as bad as losses for both confederations involved in the matches. A comment on the post by "Dorian" on Edgar's website calculates the 2006 World Cup fraction of wins as: UEFA 0.65 (22 of 34), CONMEBOL 0.59 (10 of 17), CONCACAF 0.08 (1 of 13), AFC 0.08 (1 of 12), CAF 0.19 (3 of 16), OFC 0.25 (1 of 4).
Well ... like ... obviously. What other formula could you possibly use? More spots for Oceania!!! They deserve 6 as they did better than CAF!!!!!eleven!!!! (Actually, being vaguely serious. If you do include Australia as an OFC nation for 2006 - which I personally wouldn't - means that on FIFA's own calculations OFC is the 3rd highest rated confederation in the world at present - Edgar's page was final ranks of UEFA=1.000, CSF=0.98, OFC=0.83, CONCACAF=0.81, CAF=0.79, AFC=0.74) J
Dorian made a mistake - it should be 0.63 for OFC since both the 1998 and 2002 WC wins per game averages are 0. I'm a bit of celebrity - there's a thread on BigSoccer containing my name
No, they aren't. OFC does not have wins per game averages in '98 and '02 - 0 / 0 is not 0, it does not have a dertemined result.
But that's not how the formula works. 0/0 isn't 0. Then again, the formula doesn't work like Cirdan suggests either. It isn't (98ppg+02ppg+06ppg)/3. It's (all wins 98-02/all games 98-02)/3. So Dorian is incorrect. OFC only gets the "lowest confederation" ranking if they miss all three WCs (which is in a sense quite stupid - their best result, with Australian reaching the second round actually lowers their ranking). Note - If Australia were considered an AFC team then not only would the OFC ranking rise (to equal the lowest other rank - the AFC), but the AFC ranking would ALSO be higher (as Japan's loss against Australia would disappear from the calculation of the AFC result as it would be an intraconfederation match). J
Yes it is Well, actually wpg, not ppg. Check the post again. FIFA Ranking: Confederation weighting factor calculation Everything after "Now, on to the method" is from FIFA.
Every mathematician will tell you that this does not have a result. For a wins-per-game ratio with 0 wins and 0 games, you have to divide 0 by 0, and division by zero is not an allowed operation. See http://en.wikipedia.org/wiki/Divide_by_zero
Cirdan, really now I didn't say that 0/0 = 0. I just said a confederation with no teams at a world cup should have 0 points for that tournament. Something like: if (wins = 0) avg = 0; else avg = wins / games;
I'm not sure exactly what you mean by this statement, but at least one possible interpretation of it is "the average in step 4 is calculated as the sum of the number of the interconfederational wins over the last three world cups, divided by the sum of the number of the interconfederational matches over the last three world cups." However, that is not what FIFA said; they said: "av_{94-02} = (av_{94}+av_{98}+av_{02})/3", that is, "the average in step 4 is calculated as the average of the interconfederational win ratios over the last three world cups." We can see this from CONCACAF in the example given: the "sum then divide" algorithm would give 8/28 = 0.285714... ~= 0.29, but the "divide then average" algorithm gives (0.25 + 0.20 + 0.40)/3 = 0.85/3 = 0.283333... ~= 0.28. Why exactly FIFA chooses to risk Simpson's paradox and similar effects with the "divide then average" algorithm is not clear to me.
Jep, look at the following scenario: Team A wins 1 group match and ties the other 2, while team B wins 1 match and loses the other 2. Now team A progresses and loses and team B is out in groupstage, but for the confederation the result of team B is better.
These things always make my head hurt, and increase my respect for guys like Edgar, JLSA and Dr. Gamera who take an interest in it. When they explain how it works with small words, crayon diagrams and the absence of phrases like 'Simpson's paradox' and 'normalised fourth roots', I am always grateful. Humanities ftw!
As a qualified Numberographer - I know that the dark arts can be confusing to those who are untrained. But, I thank you for the acknowledgement of the prowess those of us "in the know" possess. So, in the spirit of reciprocal friendship - let me utter those immortal words of greeting to those in the humanities. "Yes, I WILL have fries with that". J
FIFA have changed the formula to also include draws as half-wins. Confederation weightings: One answer, more questions
Is it the case that changing the formula to include draws was necessary for UEFA to keep its 1.00 weighting, after the success of CONMEBOL in 2010? Apologies if I missed a key post on Edgar's website. Yay (I guess), this cycle, CONCACAF teams only lose 12% of the rating points they are fairly entitled to, rather than 15%. (All right, scientific accuracy requires me to concede that there may be some justification for regionally weighting a team's opponent - but there's no justification for regionally weighting a team itself.)
