The World Football Elo Ratings is a ranking system for men's national association football teams that is published by the website eloratings.net. It is based on the Elo 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. The FIFA World Rankings, not based on the Elo method, but changing soon[1], is the official national teams rating system used by the international governing body of football and is therefore more prevalent.
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.[2] Ratings for teams with fewer than 30 matches are considered provisional.
The FIFA Women's World Rankings system uses a modified version of the Elo formula whereas the FIFA men's ranking system uses a non-Elo formula. 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 performed poorly.[3]
Top 100
The following table shows the top 100 teams in the World Football Elo Ratings as they were on 3 July 2018 (23:40 FET), using data from the World Football Elo Ratings web site.[4]
Each national team's FIFA World Ranking is shown as per the latest release on 7 June 2018.[5]
^Northern Cyprus are not a member of FIFA and are not included in the FIFA Rankings. Also, they have played only 17 matches against other Elo-ranked teams, so their Elo rating is provisional.
^Martinique are also not members of FIFA, so are not included in the FIFA Rankings.
^Kuwait is ranked much lower in the FIFA Ranking because they were inactive from October 2015 to December 2017 due to their suspension from FIFA. While this caused their FIFA Ranking to fall dramatically, their Elo rating remained the same. The same applies to Guatemala but to a lesser extent.
List of number one teams
The following is the list of nations who have achieved the number one position in the World Football Elo Ratings since 1872:[6]
The following is a list of national football teams ranked by their highest Elo score ever reached.[8] The team in each confederation that has achieved the highest rank is shown in color.
The biggest point gap between 1st and 2nd national team was between 14 march and 21 March 1885, when Scotland (at 2094) led by 205 points over 2nd ranked England (at 1889).[9]
Average ratings
Time averaged Elo or Elo-like scores are routinely used to compare chess player strengths.[10][11][12] The following is a list of the national teams with the highest average Elo score from 1 January 1970 to 1 January 2018. 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.
This is a list of matches with the biggest point exchange.[13] Since the importance of the match, the goal differential and the perceived home team advantage are factored in the exchange, these are not necessarily the most surprising wins as expressed by the difference in Elo rating.[x] The nations' points before the matches are given.
*The initial ratings may be partially responsible for the high point exchange. The national teams of China, Egypt, Russia, and South Korea had played only 18, 3, 2, and 18 international matches before their respective upsets. China had only yet played against East Asian teams.
The Elo 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.
Overview
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:
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.
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 rankings, 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:
or
Where;
= 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
The number of Points Change is rounded to the nearest integer before updating the team rating.
Status of match
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 given in the table below:
Tournament or Match type
Index (K)
World Cup, Olympic Games (1908-1980)
60
Continental Championship and Intercontinental Tournaments
50
World Cup and Continental qualifiers and major tournaments
40
All other tournaments
30
Friendly matches
20
Number of goals
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
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)
0
1
+1
1
+2
1.5
+3
1.75
+4
1.875
+5
2
+6
2.125
+7
2.25
+8
2.375
+9
2.5
+10
2.625
Result of match
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 on 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
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 (add 100 points for the home team). 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.
Examples
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.
Team
Points
A
630
B
500
C
480
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
20
20
20
20
20
20
1.5
1.5
1.5
1.5
1
1
1
0
0
1
0.5
0.5
0.679
0.321
0.679
0.321
0.679
0.321
Total (P)
+9.63
-9.63
-20.37
+20.37
-3.58
+3.58
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
20
20
20
20
20
20
1.5
1.5
1.5
1.5
1
1
1
0
0
1
0.5
0.5
0.529
0.471
0.529
0.471
0.529
0.471
Total (P)
+14.13
-14.13
-15.87
+15.87
-0.58
+0.58
Note that Team B drops more ranking points by losing to Team C, which is approximately the same strength, than by losing to Team A, which is considerably better than Team B.
^Wales was in 3rd place from its first match in 1876 to 1902, in a period that only 3 to 4 teams were in the rankings
^ abThe combined Ireland national football team was in 4th place from its first match in 1882 to 1902, in a period that only 4 teams were in the rankings
^Trinidad and Tobago were in 11th place after their first match in July 1905, but had slipped to 32nd place before their second match in 1923.
^Guyana was in 15th and last place after their first match in July 1905, but was in 22nd place (out of 26) before their second match in 1915.
^In the 1940s, most national teams did not play games until after the end of World War II, making comparison of countries for this decade weak. For example, Mexico did not play any matches between Feb 1938 and July 1947, so that the average over the decade mostly reflects the single Elo rating achieved in February 1938
^In those terms, most surprising may have been the 2:1 win of Luxembourg (Elo rating 1036) over Switzerland (ER 1794) in a World Cup qualification match in September 2008 (a 758 point difference). In another World Cup qualifier in October 2004 Liechtenstein (ER 1049) held the 853 points higher rated Portuguese team (ER 1902) to a 2:2 draw.
England
Argentina
Brazil
Scotland
Germany [c]
Spain
Italy
Hungary
France
Uruguay
Soviet Union [d]
Netherlands
Denmark
Austria
Czech Republic
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Hungary
Bern
Johannesburg
Stockholm
Brazil
Brazil
Brazil
Santiago
Mexico City
Poland
Belgium
Italy
Spain
Turkey
China *
Walthamstow
Norway
Egypt *
Hungary
Fiji
New Zealand
Nouméa
Ghana
Germany
Russia *
South Korea *
Trinidad and Tobago
Port-au-Prince
Kazan
Paraguay
Guayaquil
Croatia
Germany
Costa Rica
Guatemala
United States
Venezuela
Bolivia
Montserrat
British Virgin Islands
Fort-de-France
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