World Football Elo Ratings

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.

Since being developed, the Elo rankings have been found to have the highest predictive capability for football matches.[1] FIFA's official rankings, both the FIFA World Rankings for men and the FIFA Women's World Rankings are based on a modified version of the Elo formula, the men's rankings having switched away from FIFA's own system for matches played since June 2018.[2]

Top 100

The following table shows the top 100 teams in the World Football Elo Ratings as they were on 17 December 2019, using data from the World Football Elo Ratings web site.[3]

Each national team's FIFA World Ranking is shown as per the latest release on 28 November 2019.[4]

AFC CAF CONCACAF CONIFA CONMEBOL OFC UEFA
  1. Guatemala is ranked much lower in the FIFA Ranking because they were inactive from September 2016 to August 2018 due to their suspension from FIFA. While this caused their FIFA Ranking to fall dramatically under the former system, their Elo rating remained the same.
  2. Northern Cyprus is not a member of FIFA and is not included in the FIFA Rankings. Also, the team has played only 17 matches against other Elo-ranked teams, so its Elo rating is provisional.
  3. Martinique are also not members of FIFA, so are not included in the FIFA Rankings.
  4. Iraqi Kurdistan is not a member of FIFA and is not included in the FIFA Rankings. Also, the team has played only 4 matches against other Elo-ranked teams, so its Elo rating is provisional.

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 the first international match in 1872:[5]

  1. Number-one position reached at / after first match

Ranking by matches played as leader

NationGames[lower-alpha 1]Days as
leader[lower-alpha 2]
First date
as leader
Last date
as leader
 Brazil3158,49612 Jun 195815 Nov 2019
 England15410,60530 Nov 187211 Jun 1988
 Germany [lower-alpha 3]1394,70425 Jul 19669 Nov 2017
 Argentina1239,16520 Jul 19029 Nov 2016
 Spain782,86928 Aug 192011 Oct 2013
 France732,02212 Sep 198410 Oct 2018
 Hungary571,89720 Sep 195212 Mar 1960
 Scotland425,9664 Mar 187619 Oct 1926
 Italy412,6947 Jun 193415 Aug 2006
 Soviet Union [lower-alpha 4]411,36721 Mar 196324 Jun 1988
 Uruguay371,79429 Aug 192015 Jun 1929
 Netherlands321,0391 Jun 19783 Jul 2014
 Denmark66765 Jun 19147 Oct 1916
 Austria31127 May 19346 Jun 1934
 Czech Republic2827 Jun 20047 Jun 2005
 Belgium13116 Nov 2019current
  1. Number of games played (started) with the highest Elo rating amongst nations
  2. Days spent as co-leaders are counted as a ½ day
  3. Combined record of the Germany (1908–1950 & 1990–present) and West Germany (1950–1990) national football teams.
  4. So far, only the Soviet Union national football team (1924–1992) has reached the #1 position, but any future efforts by the Russia national football team (1992–present) will be included.[6]

All-time team highs and lows

The following is a list of national football teams ranked by the highest Elo rating they ever reached.[7] The table also includes the highest ranking as well as the lowest rating and ranking reached by each nation. The team that has achieved the highest rank in each confederation is shown in color.

  1. The ranking in parentheses is that at the time the highest rating was reached.
  2. The date given is when the highest or lowest rating was first reached.
  3. The team's indicated lowest ratings and rank may not have coincided in time.
  4. at present as Russia
  5. at present as Serbia
  6. Formally, Switzerland reached a low of 1485 after its second match, in March 1908.
  7. The 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. It reached a low ratings of 1237 on 29 March 1890.
  8. 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.
  9. On 1 January 2006, Football Federation Australia moved from the OFC to the AFC
  10. Algeria's highest ranking and ratings were reached after the first 5 and 8 matches, respectively.
  11. Cameroon possibly reached a lower ratings after their 4th or 5th match, sometimes in 1956.
  12. South Africa had only played 1 match when reaching its highest ratings and ranking.
  13. at present as DR Congo
  14. Slovakia was ranked highest (17th) for their first six matches.
  15. Finland reached its highest ranking (14th) after 4 games, following wins over Italy and Russia in the 1912 Olympic Games.

Average ratings

Time averaged Elo or Elo-like scores are routinely used to compare chess player strengths.[8][9][10]

Highest average ratings since 1970

This table is a list of the national teams with the highest average Elo score since 1 January 1970, i.e. over approximately the last half century.[11] 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. Only those teams are displayed that started playing before 1970 and played the entire period without a 5 year or longer interruption. Some excluded strong national football teams, like East-Germany and Croatia, appear in the decades tables below.

  1. Representing West Germany from 1949 to 1990
  2. Combined record of the USSR (1970-1992), the CIS (1992), and Russia national football teams (1992-present)
  3. Combined record of the Czechoslovakian (1970-1992) and Czech national football teams (1993-present)
  4. Combined record of Yugoslavia (1970-1992), Serbia and Montenegro (1994-2006) and Serbia national football teams (2006-present)

Averages by decade

The tables below shows the teams with the best average Elo score per decade (1 Jan XXX0 - 31 Dec XXX9). Only those teams are displayed that had played before the start of the decade and played at least ten games in the decade.

  1. Includes the record of the Great Britain Olympic football team in the 1908, 1912 and 1920 Olympics
  2. First game played on 15 May 1910
  3. First game played on 27 May 1910
  4. 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.
  5. Average over the period from 2 April 1940 to 8 April 1945
  6. Combined record of Yugoslavia (1990–1992) and FR of Yugoslavia (1994–1999)
  7. Combined record of Czechoslovakia (1990–1992) and Czech national football teams (1993–1999)
  8. Combined record of the USSR (1990–1992), the CIS (1992), and Russia national football teams (1992–1999)
  9. 2010s averages up to 24 June 2019

Highest average over entire team history

The eloratings.net website presents the average ratings since the first international match of each team. Such averages can not really be compared to each other, as they represent strengths over different periods and in different pools. For example, they represent 147 years of matches for Scotland (34 years of which in a pool of 3 or 4 British nations only), 99 years for Spain, 27 years for Ukraine, and 12 years for Montenegro. For Croatia and Slovakia the average is dominated by the single rating during the 50 years between the few games played between 1940 and 1943 and the rebirth of the countries in the 1990s. Likewise, South Africa's average is mostly determined by the 44 matches (of a 417 total in 2018) played in the 86 years before it rejoined FIFA in 1992.

Highest rated matches

A list of the 25 matches between teams with the highest combined Elo ratings (the nations' points before the matches are given).

RankCombined
points
Nation 1Elo 1Nation 2Elo 2ScoreDateOccasionLocation
1 4287  Germany 2203  Argentina 2084 1–0 aet 2014-07-13 World Cup Final Rio de Janeiro
 Germany 2223  Argentina 2064 2–4 2014-09-03 Friendly Düsseldorf
3 4278  Hungary 2230  West Germany 2048 2–3 1954-07-04 World Cup Final Bern
4 4263  Spain 2136  Netherlands 2127 1–0 aet 2010-07-11 World Cup Final Johannesburg
5 4245  Great Britain 2184  Denmark 2061 4–2 1912-07-04 Olympic Games Final Stockholm
6 4242  Brazil 2120  Germany 2122 1–7 2014-07-08 World Cup SF Belo Horizonte
7 4238  West Germany 2114  Brazil 2124 0–1 1973-06-16 Friendly Berlin
8 4236  Brazil 2086  Spain 2150 3–0 2013-06-30 Confederations Cup Final Rio de Janeiro
9 4224  Hungary 2208  Uruguay 2016 4–2 1954-06-30 World Cup SF Lausanne
10 4223  Germany 2104  Brazil 2119 0–1 2018-03-27 Friendly Berlin
11 4218  Hungary 2180  Brazil 2038 4–2 1954-06-27 World Cup QF Bern
12 4207  Netherlands 2077  Brazil 2130 2–1 2010-07-02 World Cup QF Port Elizabeth
13 4200  Brazil 2083  Netherlands 2117 0–0 2011-06-04 Friendly Goiânia
14 4199  Brazil 2088  West Germany 2111 1–0 1982-03-21 Friendly Rio de Janeiro
15 4198  Brazil 2060  West Germany 2138 1–1 1977-06-12 Friendly Rio de Janeiro
16 4197  West Germany 2123  Netherlands 2074 2–1 1974-07-07 World Cup Final Munich
17 4191  Brazil 2166  Czechoslovakia 2025 3–1 1962-06-17 World Cup Final Santiago
 West Germany 2135  Brazil 2056 0–1 1978-04-05 Friendly Hamburg
19 4187  Brazil 2132  Italy 2055 4–1 1970-06-21 World Cup Final Mexico City
20 4179  Spain 2110  Germany 2069 1–0 2010-07-07 World Cup SF Durban
 Netherlands 2096  Argentina 2083 0–0 2014-07-09 World Cup SF São Paulo
22 4177  Germany 2076  Brazil 2101 1–2 1998-03-25 Friendly Stuttgart
23 4173  West Germany 2097  Netherlands 2076 1–1 1975-05-17 Friendly Frankfurt
24 4172  West Germany 2104  Poland 2068 1–0 1974-07-03 World Cup 2nd round Frankfurt
25 4168  England 2141  Denmark 2017 3–0 1911-10-21 Friendly London

Biggest upsets

This is a list of matches with the biggest point exchange.[23] 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.[lower-alpha 2]
The nations' points before the matches are given.

RankPoint
exchange
Nation 1Elo 1Nation 2Elo 2ScoreDateOccasionLocation
1 98  Sweden 1676  Belgium 1845 8–1 1924-05-29 Olympic Games Paris
2 92  Italy 1824  Spain 1991 7–1 1928-06-04 Olympic Games Amsterdam
 Turkey 1397  China * 1655 4–0 1948-08-02 Olympic Games Walthamstow
4 87  Norway 1478  Great Britain 2041 3–1 1920-08-28 Olympic Games Antwerp
5 84  Egypt * 1677  Hungary 1919 3–0 1924-05-29 Olympic Games Paris
 Czechoslovakia 1855  Argentina 2003 6–1 1958-06-15 World Cup Helsingborg
7 83  Fiji 1171  New Zealand 1523 4–0 1980-02-23 OFC Nations Cup Nouméa
8 82  Ghana 1606  Czech Republic 2005 2–0 2006-06-17 World Cup Cologne
9 81  Brazil 2120  Germany 2122 1–7 2014-07-08 World Cup Belo Horizonte
10 80  Germany 1642  Russia * 1567 16–0 1912-07-01 Olympic Games Solna
 Turkey 1604  South Korea * 1668 7–0 1954-06-20 World Cup Geneva
 Trinidad & Tobago 1481  Mexico 1783 4–0 1973-12-14 CONCACAF Championship Port-au-Prince
 South Korea 1677  Germany 2044 2–0 2018-06-27 World Cup Kazan
14 78  Paraguay 1685  Uruguay 2054 3–0 1929-11-01 Copa América Buenos Aires
 Chile 1587  Uruguay 1957 3–0 1937-01-10 Copa América Buenos Aires
16 77  Uruguay 1813  Brazil 2162 3–0 1959-12-12 Copa América Guayaquil
 Croatia 1912  Germany 2090 3–0 1998-07-04 World Cup Lyon
18 76  Germany 1906  Norway 1714 0–2 1936-08-07 Olympic Games Berlin
 Costa Rica 1717  Guatemala 1491 1–4 1946-03-10 CCCF Championship San José
 United States 1888  Mexico 1788 0–5 2009-07-26 CONCACAF Gold Cup East Rutherford
21 75  Denmark 1759  Italy 2044 5–3 1948-08-05 Olympic Games London
 Venezuela 1336  Bolivia 1646 3–0 1967-01-28 Copa América Montevideo
 Netherlands 1986  Spain 2109 5–1 2014-06-13 World Cup Salvador
24 74  Chile 1800  Brazil 2032 4–0 1987-07-03 Copa América Córdoba
25 73  Montserrat 511  British Virgin Islands 758 7–0 2012-09-09 Caribbean Cup qualifier Fort-de-France

*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.

Elo Ratings before each World Championship

History and overview

The Elo system, developed by Hungarian-American mathematician 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.[45] 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 [1] but the Runyan system is the best known.

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:

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.[46] Ratings for teams with fewer than 30 matches are considered provisional.

Comparison with other systems

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.[1]

The FIFA World Rankings is the official national teams rating system used by the international governing body of football. The FIFA 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.[47] 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 a penalty shoot-out as a win/loss rather than a draw; thus, a 7:0 blowout is considered equal to a 7:6 penalty shoot-out win (neither method distinguishes a win in extra time from a win in regular time). The FIFA method is also less sensitive to the difference in ratings and more sensitive to match status.[48] Finally, World Football Elo Ratings considers all official international matches for which results are available, including those involving "unaffiliated" teams that are not a member of FIFA.

Calculation principles

The ratings are based on the following formulae:

where

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

"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:

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 will feature 8 weights, with the knockout stages in the World Cup weighing 12x more than some friendly matches.[48]

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 ( N ≥ 3)

Table of examples:

Goal Difference 0+1+2+3+4+5+6+7+8+9+10
G 111.51.751.87522.1252.252.3752.52.625

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.

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.[48]

Examples for clarification

The same example of a three-team friendly tournament on neutral territory is used as on the FIFA 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
Score 3 : 11 : 32 : 2
202020202020
1.51.51.51.511
10010.50.5
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
Score 3–11–32–2
202020202020
1.51.51.51.511
10010.50.5
0.5290.4710.5290.4710.5290.471
Total (P) +14.13-14.13-15.87+15.87-0.58+0.58

Team B drops more points by losing to Team C, which has shown about the same strength, than by losing to Team A, which has been considerably better than Team B.

See also

Notes

  1. The Israel Football Association was a member of the AFC from 1954 until 1974. In 1992, the IFA was admitted to UEFA as an associate member
  2. 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.

References

  1. J. Lasek, Z. Szlávik and S. Bhulai (2013), The predictive power of ranking systems in association football, Int. J. Applied Pattern Recognition1: 27-46.
  2. "2026 FIFA World Cup™: FIFA Council designates bids for final voting by the FIFA Congress". fifa.com. FIFA. 10 June 2018. Retrieved 2 July 2018.
  3. "World Football Elo Ratings". Elo ratings. Retrieved 17 December 2019.
  4. "FIFA/Coca-Cola World Ranking" (Press release). FIFA. 28 November 2019. Retrieved 28 November 2019.
  5. Graph of rankings at eloratings.net. Yearly graphs, like this one for 2018, give enough resolution. For individual dates, the Elo ratings table is also a good source.
  6. "History of the Football Union of Russia". Rfs.ru. Retrieved 4 June 2016.
  7. World Football Elo Ratings; under the columns tab choose "Highest Rank / Rating" as well as "Lowest Rank / Rating"
  8. Arpad E. Elo, The Rating of Chessplayers, Past and Present, Arco, 1978. ISBN 0-668-04721-6.
  9. Arpad Elo, Chess Life, 1962.
  10. About the Chessmetrics Rating System, by Jeff Sonas
  11. "Average Elo ratings from January 1st 1970 to June 29th 2019" at international-football.net
  12. "Average Elo ratings from January 1st 1910 to December 31st 1919" at international-football.net
  13. "Average Elo ratings from January 1st 1920 to December 31st 1929" at international-football.net
  14. "Average Elo ratings from January 1st 1930 to December 31st 1939" at international-football.net
  15. "Average Elo ratings from January 1st 1940 to December 31st 1949" at international-football.net
  16. "Average Elo ratings from January 1st 1950 to December 31st 1959" at international-football.net
  17. "Average Elo ratings from January 1st 1960 to December 31st 1969" at international-football.net
  18. "Average Elo ratings from January 1st 1970 to December 31st 1979" at international-football.net
  19. "Average Elo ratings from January 1st 1980 to December 31st 1989" at international-football.net
  20. "Average Elo ratings from January 1st 1990 to December 31st 1999" at international-football.net
  21. "Average Elo ratings from January 1st 2000 to December 31st 2009" at international-football.net
  22. "Average Elo ratings from January 1st 2010 to June 24th 2019" at international-football.net
  23. Upsets at eloratings.net (per June 2018 this page is under reconstruction)
  24. As the Great Britain national amateur team
  25. Starting Ratings 1930 World Cup at eloratings.net
  26. Starting Ratings 1934 World Cup at eloratings.net
  27. Starting Ratings 1938 World Cup at eloratings.net
  28. Starting Ratings 1950 World Cup at eloratings.net
  29. Starting Ratings 1954 World Cup at eloratings.net
  30. Starting Ratings 1958 World Cup at eloratings.net
  31. Starting Ratings 1962 World Cup at eloratings.net
  32. Starting Ratings 1966 World Cup at eloratings.net
  33. Starting Ratings 1970 World Cup at eloratings.net
  34. Starting Ratings 1974 World Cup at eloratings.net
  35. Starting Ratings 1978 World Cup at eloratings.net
  36. Starting Ratings 1982 World Cup at eloratings.net
  37. Starting Ratings 1986 World Cup at eloratings.net
  38. Starting Ratings 1990 World Cup at eloratings.net
  39. Starting Ratings 1994 World Cup at eloratings.net
  40. Starting Ratings 1998 World Cup at eloratings.net
  41. Starting Ratings 2002 World Cup at eloratings.net
  42. Starting Ratings 2006 World Cup at eloratings.net
  43. Starting Ratings 2010 World Cup at eloratings.net
  44. Starting Ratings 2014 World Cup at eloratings.net
  45. Lyons, Kieth. "What are the World Football Elo Ratings?". The Conversation. Retrieved 16 July 2018.
  46. "The World Football Elo Rating System". Eloratings.net. Retrieved 26 February 2012.
  47. FIFA Council, 2026 FIFA World Cup™: FIFA Council designates bids for final voting by the FIFA Congress, 10 Jun 2018
  48. FIFA council, Revision of the FIFA / Coca-Cola World Ranking
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