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World Football Elo Ratings

From Wikipedia, the free encyclopedia
Ranking system for men's national association football teams

Top 20 rankings as of 19 January 2026[1]
RankChangeTeamPoints
1Steady Spain2171
2Steady Argentina2113
3Steady France2063
4Steady England2042
5Increase 2 Colombia1998
6Decrease 1 Brazil1979
7Decrease 1 Portugal1976
8Increase 2 Netherlands1959
9Increase 5 Croatia1933
9Increase 3 Ecuador1933
11Increase 11 Norway1922
12Decrease 4 Germany1910
13Increase 6  Switzerland1897
14Decrease 5 Uruguay1890
15Increase 14 Turkey1880
16Decrease 3 Japan1879
17Increase 14 Senegal1869
18Decrease 2 Denmark1864
19Decrease 8 Italy1859
20Decrease 3 Belgium1849
*Change from one year ago
Complete rankings at eloratings.net

TheWorld Football Elo Ratings are a ranking system for men's nationalassociation football teams that is published by the website eloratings.net. It is based on theElo rating system but includes modifications to take various football-specific variables into account, like the margin of victory, importance of a match, and home field advantage. Other implementations of the Elo rating system are possible and there is no single nor any official Elo ranking for football teams. FIFA's official rankings (both theFIFA World Rankings for men and theFIFA Women's World Rankings) are based on a modified version of the Elo formula, the men's rankings having switched away from FIFA's custom system in 2018.[2] The Elo rankings have been found to have the highest predictive capability for football matches.[3]

History and overview

[edit]

The Elo system, developed by Hungarian-American mathematicianArpad Elo, is used byFIDE, the international chess federation, to ratechess players, and by theEuropean Go Federation, to rateGo players. In 1997, Bob Runyan adapted the Elo rating system to internationalfootball and posted the results on the Internet.[4] He was also the first maintainer of the World Football Elo Ratings web site, currently maintained by Kirill Bulygin. Other implementations of the Elo rating system are possible.[3]

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 ratings consider all official international matches for which results are available. 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 are considered provisional.[5]

Comparison with other systems

[edit]

A 2009 comparative study of eight methods found that the implementation of the Elo rating system described below had the highest predictive capability for football matches, while the men's FIFA ranking method (2006–2018 system) performed poorly.[3]

TheFIFA World Rankings is the official national teams rating system used by theinternational governing body of football. TheFIFA Women's World Rankings system has used a modified version of the Elo formula since 2003. In June 2018, the FIFA ranking switched to an Elo-based ranking as well, starting from the current FIFA rating points.[6] The major difference between the World Football Elo Rating and the new men's FIFA rating system is that the latter does not consider goal differential and counts apenalty shoot-out as a win/loss rather than a draw (neither method distinguishes a win inextra time from a win in regular time).[7]

Calculation principles

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The ratings are based on the following formula:

Rn=Ro+P{\displaystyle R_{n}=R_{o}+P}

where

P=KG(WWe){\displaystyle P=KG(W-W_{e})}

Where;

Rn{\displaystyle R_{n}}= The new team rating
Ro{\displaystyle R_{o}}= The old team rating
K{\displaystyle K}= Weight index regarding the tournament of the match
G{\displaystyle G}= A number from the index of goal differences
W{\displaystyle W}= The result of the match
We{\displaystyle W_{e}}= The expected result
P{\displaystyle P}= Points Change

"Points Change" is rounded to the nearest integer before updating the team rating.

Status of match

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The status of the match is incorporated by the use of a weight constant. The constant reflects the importance of a match, which, in turn, is determined entirely by which tournament the match is in; the weight constant for each major tournament is:

Tournament or Match typeK
World Cup,Olympic Games (1908–1980)60
Continental championship and intercontinental tournaments50
World Cup and Continental qualifiers and major tournaments40
All other tournaments30
Friendly matches20

The FIFA adaptation of the Elo rating features 8 weights, with the last knockout stages in the World Cup weighing 12 times more than some friendly matches.[7]

Number of goals

[edit]

The number of goals is taken into account by use of a goal difference index. If the game is a draw or is won by one goal

G=1{\displaystyle G=1}

If the game is won by two goals

G=32{\displaystyle G={\frac {3}{2}}}

If the game is won by three or more goals:

G=11+N8{\displaystyle G={\frac {11+N}{8}}}

Table of examples:

Goal Difference0+1+2+3+4+5+6+7+8+9+10
G111.51.751.87522.1252.252.3752.52.625

Result of match

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W is the result of the game (1 for a win, 0.5 for a draw, and 0 for a loss). This also holds when a game is won or lost in extra time. If the match is decided on penalties, however, the result of the game is considered a draw (W = 0.5).

Expected result of match

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We is the expected result (win expectancy with a draw counting as 0.5) from the following formula:

We=110dr/400+1{\displaystyle W_{e}={\frac {1}{10^{-dr/400}+1}}}

wheredr equals the difference in ratings (add 100 points for the home team). Sodr 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 FIFA adaptation of the Elo rating does not incorporate a home team advantage and has a larger divisor in the formula (600 vs. 400), making the points exchange less sensitive to the rating difference of two teams.[7]

Examples for clarification

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The same example of a three-team friendly tournament on neutral territory is used as on theFIFA World Rankings page. Beforehand team A had a rating of 630 points, team B 500 points, and teams C 480 points. The first table shows the points allocations based on three possible outcomes of the match between the strongest team A, and the somewhat weaker team B.

Team ATeam BTeam ATeam BTeam ATeam B
Score3–11–32–2
K{\displaystyle K}202020202020
G{\displaystyle G}1.51.51.51.511
W{\displaystyle W}10010.50.5
We{\displaystyle W_{e}}0.6790.3210.6790.3210.6790.321
Total (P)+9.63-9.63-20.37+20.37-3.58+3.58

When the difference in strength between the two teams is less, so also will be the difference in points allocation. The next 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 BTeam CTeam BTeam CTeam BTeam C
Score3–11–32–2
K{\displaystyle K}202020202020
G{\displaystyle G}1.51.51.51.511
W{\displaystyle W}10010.50.5
We{\displaystyle W_{e}}0.5290.4710.5290.4710.5290.471
Total (P)+14.13-14.13-15.87+15.87-0.58+0.58

See also

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References

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  1. ^Elo rankings change compared to one year ago."World Football Elo Ratings".eloratings.net. 19 January 2026. Retrieved19 January 2026.
  2. ^"2026 FIFA World Cup: FIFA Council designates bids for final voting by the FIFA Congress".fifa.com. FIFA. 10 June 2018. Archived fromthe original on 12 June 2018. Retrieved2 July 2018.
  3. ^abcJ. Lasek, Z. Szlávik and S. Bhulai (2013),The predictive power of ranking systems in association football,Archived 26 July 2014 at theWayback Machine, Int. J. Applied Pattern Recognition1: 27–46.
  4. ^Lyons, Keith."What are the World Football Elo Ratings?". The Conversation. Retrieved16 July 2018.
  5. ^"The World Football Elo Rating System". Eloratings.net. Retrieved26 February 2012.
  6. ^FIFA Council,2026 FIFA World Cup: FIFA Council designates bids for final voting by the FIFA Congress, 10 June 2018
  7. ^abcFIFA council,Revision of the FIFA / Coca-Cola World Ranking

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