World Football Elo Ratings
The World Football Elo Ratings is a ranking system for men's national teams in association football. The method used to rank teams is based upon the Elo rating system method but modified to take various football-specific variables into account. Elo should not be confused with the FIFA World Rankings, which is more prevalent because it is the official rating system used by the international governing body of football to rank national teams.
The ratings take into account all international "A" matches for which results could be found. Ratings tend to converge on a team's true strength relative to its competitors after about 30 matches. Ratings for teams with fewer than 30 matches should be considered provisional.
Top 100 ranking 
Current table, as of 28 April 2013, of the World Football Elo rankings, compiled by the World Football Elo Ratings web site.
Strongest teams since the mid to late 1960s 
Time averaged Elo or Elo-like scores are routinely used to compare chess player strengths. The following is a list of the national teams with the highest average Elo score from 1 January 1970 to 1 May 2013. Before this time intercontinental play was fairly limited and many nations in Africa, North America, and Asia had played too few games yet to create a representative Elo score. Since Elo scores reflect past accomplishments, the table represents the relative strength of national teams since the mid to late 1960s.
List of number one teams 
The following is the list of nations who have achieved the number one position on the World Football Elo Ratings since 2000:
Ranking by days as leader since 1 January 2000 (as of 1 August 2012) 
|Nation||# of days||Last Date as Leader|
|Brazil||1878||1 July 2010|
|France||1115||10 July 2007|
|Argentina||316||14 July 2007|
|Netherlands||109||6 July 2010|
|Italy||43||15 August 2006|
|Czech Republic||8||7 June 2005|
All-time highest ratings 
The following is a list of national football teams ranked by their highest Elo score ever reached.
|1||Hungary||2166||30 June 1954|
|2||Brazil||2153||17 June 1962|
|3||Spain||2140||11 July 2010|
|4||Argentina||2117||3 April 1957|
|5||France||2105||15 August 2001|
|6||Netherlands||2100||6 July 2010|
|7||Germany||2099||4 September 1974 (as West Germany)|
|8||Italy||2079||20 July 1939|
|9||Poland||2046||1 September 1974|
|10||England||2041||22 October 1966|
|11||Uruguay||2035||13 June 1928|
|12||Soviet Union||2022||9 October 1983|
|13||Czech Republic||1999||27 June 2004|
|14||Austria||1998||31 May 1934|
|15||Portugal||1982||15 November 2000|
|16||Croatia||1967||11 July 1998|
|17||Serbia||1961||25 June 1998 (as FR Yugoslavia)|
|18||Denmark||1960||13 June 1986|
|19||Scotland||1953||10 March 1888|
|20||Sweden||1950||25 June 1950|
|21||East Germany||1949||22 June 1974|
|22||Mexico||1936||19 June 2005|
|23||Paraguay||1932||21 February 1954|
|24||Chile||1918||12 July 2011|
|25||Belgium||1916||9 September 1981|
|26||Norway||1913||13 June 2000|
|27||Colombia||1912||5 June 1994|
|28||Romania||1908||9 June 1990|
|29||Greece||1896||18 August 2004|
|30||Republic of Ireland||1889||21 August 2002|
Highest rated matches 
A list of the 10 matches between teams with the highest combined Elo ratings (the nation's points before the matches are given).
|Nation 1||Elo 1||Nation 2||Elo 2||Score||Date||Occasion||Location|
|1||4211||Netherlands||2100||Spain||2111||0 : 1||2010-07-10||World Cup F||Johannesburg|
|2||4161||West Germany||1995||Hungary||2166||3 : 2||1954-07-04||World Cup F||Bern|
|3||4158||Netherlands||2050||Brazil||2108||2 : 1||2010-07-02||World Cup QF||Port Elizabeth|
|4||4150||Brazil||2061||Netherlands||2089||0 : 0||2011-06-04||Friendly||Goiânia|
|5||4148||West Germany||2068||Brazil||2080||0 : 1||1973-06-16||Friendly||Berlin|
|6||4129||Spain||2085||Germany||2044||1 : 0||2010-07-07||World Cup SF||Durban|
|7||4119||Brazil||2050||West Germany||2069||1 : 0||1982-03-21||Friendly||Rio de Janeiro|
|8||4118||Hungary||2108||Brazil||2010||4 : 2||1954-06-27||World Cup QF||Bern|
|9||4116||Hungary||2141||Uruguay||1975||4 : 2||1954-06-30||World Cup SF||Lausanne|
|10||4113||West Germany||2079||Netherlands||2034||2 : 1||1974-07-07||World Cup F||Munich|
This system, developed by Hungarian-American mathematician Dr. Árpád Élő, is used by FIDE, the international chess federation, to rate chess players, and by the European Go Federation, to rate Go players. In 1997 Bob Runyan adapted the Elo rating system to international football and posted the results on the Internet. He was also the first maintainer of the World Football Elo Ratings web site, now maintained by Kirill Bulygin.
The Elo system was adapted for football by adding a weighting for the kind of match, an adjustment for the home team advantage, and an adjustment for goal difference in the match result.
The factors taken into consideration when calculating a team's new rating are:
- The team's old rating
- The considered weight of the tournament
- The goal difference of the match
- The result of the match
- The expected result of the match
The different weights of competitions in descending order are:
- World Cup Finals
- Continental championships finals and Intercontinental tournaments
- World Cup and Continental championship qualifiers
- All other tournaments
- Friendly matches
The single difference is Elo giving a special treatment for minor tournaments, while FIFA consider them as friendly matches.
These ratings take into account all international "A" matches for which results could be found. Ratings tend to converge on a team's true strength relative to its competitors after about 30 matches. Ratings for teams with fewer than 30 matches should be considered provisional. Match data are primarily from International Football 1872 – present web site.
Basic calculation principles 
The basic principle behind the Elo ratings is only in its simplest form similar to that of a league, unlike the FIFA tables who effectively run their table as a normal league table, but with weightings to take into account the other factors, the Elo system has its one formula which takes into account the factors mentioned above. There is no first step as in the FIFA system where a team immediately receives points for the result, there is just one calculation in the Elo system.
The ratings are based on the following formulae:
|= The new team rating
|= The old team rating
|= Weight index regarding the tournament of the match
|= A number from the index of goal differences
|= The result of the match
|= The expected result
|= Points Change
Status of match 
The status of the match is incorporated by the use of a weight constant. The weight is a constant regarding the "weight" or importance of a match, defined by which tournament the match is in, they are as follows;
|Tournament or Match type||Index (K)|
|World Cup Finals||60|
|Continental Championship and Intercontinental Tournaments||50|
|World Cup and Continental qualifiers and major tournaments||40|
|All other tournaments||30|
Number of goals 
The number of goals is taken into account by use of a goal difference index. G is increased by half if a game is won by two goals, and if the game is won by three or more goals by a number decided through the appropriate calculation shown below;
If the game is a draw or is won by one goal
If the game is won by two goals
If the game is won by three or more goals
- Where N is the goal difference
Table of examples:
|Goal Difference||Coefficient of K (G)|
Result of match 
W is the result of the game (1 for a win, 0.5 for a draw, and 0 for a loss).
Expected result of match 
We is the expected result (win expectancy with a draw counting as 0.5) from the following formula:
where dr equals the difference in ratings plus 100 points for a team playing at home. So dr of 0 gives 0.5, of 120 gives 0.666 to the higher-ranked team and 0.334 to the lower, and of 800 gives 0.99 to the higher-ranked team and 0.01 to the lower.
The same examples have been used on the FIFA World Rankings for a fair comparison. Some actual examples should help to make the methods of calculation clear. In this instance it is assumed that three teams of different strengths are involved in a small friendly tournament on neutral territory.
Before the tournament the three teams have the following point totals.
Thus, team A is by some distance the highest ranked of the three: The following table shows the points allocations based on three possible outcomes of the match between the strongest team A, and the somewhat weaker team B:
Example 1 
Team A versus Team B (Team A stronger than Team B)
|Team A||Team B||Team A||Team B||Team A||Team B|
|Score||3 : 1||1 : 3||2 : 2|
Example 2 
Team B versus Team C (both teams approximately the same strength)
When the difference in strength between the two teams is less, so also will be the difference in points allocation. The following table illustrates how the points would be divided following the same results as above, but with two roughly equally ranked teams, B and C, being involved:
|Team B||Team C||Team B||Team C||Team B||Team C|
|Score||3 : 1||1 : 3||2 : 2|
Note that Team B loses more ranking points by losing to Team C than by losing to Team A.
See also 
- FIFA World Rankings
- FIFA Women's World Rankings
- Elo rating system
- Unofficial Football World Championships
- Statistical association football predictions
- "The World Football Elo Rating System". Eloratings.net. Retrieved 26 February 2012.
- "FIFA/Coca-Cola World Ranking" (Press release). FIFA. 7 November 2012. Retrieved 7 November 2012.
- Arpad E. Elo, The Rating of Chessplayers, Past and Present, Arco, 1978. ISBN 0-668-04721-6.
- Arpad Elo, Chess Life, 1962.
- About the Chessmetrics Rating System, by Jeff Sonas
- Representing West Germany from 1949 to 1990
- Combined record of the USSR (1970-1992), the CIS (1992), and Russia national football teams (1992-present)
- Combined record of Czechoslovakia (1970-1992) and Czech national football teams (1993-present)
- Combined record of Yugoslavia (1970-1992), Serbia and Montenegro (1994-2006) and Serbia national football teams (2006-present)
- Including current leader period up to 1 August 2012
- World Football Elo ratings
- How the rankings are calculated
- Interactive Map of World Football Elo ratings
- FootballDatabase's World Club Ratings (using Elo Formula)
- Excel implementation of World Football Elo rating, very useful for amateur fussball (kicker) championships