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 13 October 2018, 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 20 September 2018.[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 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.
  3. ↑ Martinique are also not members of FIFA, so are not included in the FIFA Rankings.
  4. ↑ Kuwait is ranked 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 under the former system, their Elo rating remained the same.

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:[5]

Ranking by days as leader

NationDays[lower-alpha 2]First Date as LeaderLast Date as Leader
 England10,60530 November 187211 June 1988
 Argentina9,04429 July 19089 November 2016
 Brazil8,53412 June 1958current
 Scotland6,0594 March 187619 Oct 1926
 Germany [lower-alpha 3]4,63125 July 19669 November 2017
 Spain2,77128 August 192011 October 2013
 Italy2,6947 June 193415 August 2006
 France2,03712 September 198410 October 2018
 Hungary1,96420 September 195212 March 1960
 Uruguay1,77529 August 192015 June 1929
 Soviet Union [lower-alpha 4]1,41421 March 196324 June 1988
 Netherlands1,0421 June 19783 July 2014
 Denmark6765 June 19147 Oct 1916
 Austria1127 May 19346 June 1934
 Czech Republic827 June 20047 June 2005
  1. 1 2 3 Number one position reached at / after first match
  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]

Elo all-time records

All-time highest ratings

The following is a list of national football teams ranked by their highest Elo score ever reached.[7] The team in each confederation that has achieved the highest rank is shown in color.

  1. ↑ at present as Russia
  2. ↑ at present as Serbia
  3. ↑ On 1 January 2006, Football Federation Australia moved from the OFC to the AFC
  4. ↑ Algeria had only played 8 matches to this point.
  5. ↑ South Africa had only played 1 match to this point.

All-time highest ranking

The following is a list of national football teams ranked by their highest Elo ranking ever reached.[7]

  1. ↑ as Soviet Union
  2. ↑ as FR of Yugoslavia
  3. ↑ 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
  4. 1 2 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
  5. ↑ 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.
  6. ↑ 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.
The biggest point gap

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).[8]

Average ratings

Time averaged Elo or Elo-like scores are routinely used to compare chess player strengths.[9][10][11] 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.

Overall average ratings

Time averaged Elo or Elo-like scores are routinely used to compare chess player strengths.[12][13][14]

Highest average over entire team history

This table is directly extracted from the eloratings.net website. The numbers represent may not be directly comparable. For England and Scotland they represent 146 years of matches (in 2018), for Ukraine 26 years, and for Montenegro 11 years. 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 average ratings since 1970

This table is a list of the national teams with the highest average Elo score over approximately the last half century, 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. Only teams playing over the entire period are included. Short-lived or recently originated strong football teams, like East-Germany and Croatia, appear in the decades table 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 table below shows the teams with the best average Elo score per decade (Jan 1 XXX0 - Dec 31 XXX9).

  1. ↑ Includes the record of the Great Britain Olympic football team in the 1908, 1912 and 1920 Olympics
  2. ↑ 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
  3. ↑ Combined record of Yugoslavia (1990–1992) and FR of Yugoslavia (1994–1999)
  4. ↑ Combined record of Czechoslovakia (1990–1992) and Czech national football teams (1993–1999)
  5. ↑ Combined record of the USSR (1990–1992), the CIS (1992), and Russia national football teams (1992–1999)
  6. ↑ up to 1 January 2018

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

Biggest upsets

This is a list of matches with the biggest point exchange.[15] 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 1]
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 France Paris
2 92  Italy 1824  Spain 1991 7–1 1928-06-04 Olympic Games Netherlands Amsterdam
 Turkey 1397  China * 1655 4–0 1948-08-02 Olympic Games United Kingdom Walthamstow
4 87  Norway 1478  Great Britain 2041 3–1 1920-08-28 Olympic Games Belgium Antwerp
5 84  Egypt * 1677  Hungary 1919 3–0 1924-05-29 Olympic Games France Paris
 Czechoslovakia 1855  Argentina 2003 6–1 1958-06-15 World Cup Sweden Helsingborg
7 83  Fiji 1171  New Zealand 1523 4–0 1980-02-23 OFC Nations Cup New Caledonia Nouméa
8 82  Ghana 1606  Czech Republic 2005 2–0 2006-06-17 World Cup Germany Cologne
9 81  Brazil 2120  Germany 2122 1–7 2014-07-08 World Cup Brazil Belo Horizonte
10 80  Germany 1642  Russia * 1567 16–0 1912-07-01 Olympic Games Sweden Solna
 Turkey 1604  South Korea * 1668 7–0 1954-06-20 World Cup Switzerland Geneva
 Trinidad and Tobago 1481  Mexico 1783 4–0 1973-12-14 CONCACAF Championship Haiti Port-au-Prince
 South Korea 1677  Germany 2044 2–0 2018-06-28 World Cup Russia Kazan
14 78  Paraguay 1685  Uruguay 2054 3–0 1929-11-01 Copa América Argentina Buenos Aires
 Chile 1587  Uruguay 1957 3–0 1937-01-10 Copa América Argentina Buenos Aires
16 77  Uruguay 1813  Brazil 2162 3–0 1959-12-12 Copa América Ecuador Guayaquil
 Croatia 1912  Germany 2090 3–0 1998-07-04 World Cup France Lyon
18 76  Germany 1906  Norway 1714 0–2 1936-08-07 Olympic Games Germany Berlin
 Costa Rica 1717  Guatemala 1491 1–4 1946-03-10 CCCF Championship Costa Rica San José
 United States 1888  Mexico 1788 0–5 2009-07-26 CONCACAF Gold Cup United States East Rutherford
21 75  Denmark 1759  Italy 2044 5–3 1948-08-05 Olympic Games United Kingdom London
 Venezuela 1336  Bolivia 1646 3–0 1967-01-28 Copa América Uruguay Montevideo
 Netherlands 1986  Spain 2109 5–1 2014-06-13 World Cup Brazil Salvador
24 74  Chile 1800  Brazil 2032 4–0 1987-07-03 Copa América Argentina Córdoba
25 73  Montserrat 511  British Virgin Islands 758 7–0 2012-09-09 Caribbean Cup qualifier Martinique 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.[37] 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 [38] 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.[39] 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.

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. [38]

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.[40] The major difference between the World Football Elo Rating and the future men's FIFA rating system is that the latter will not consider goal differential and will count a penalty shoot-out as a win/loss rather than a draw; thus, a 7:0 blowout will be 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 will further be less sensitive to the difference in ratings and more sensitive to match status.[41] 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 typeIndex (K)
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.[41]

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 DifferenceCoefficient of K (G)
01
+11
+21.5
+31.75
+41.875
+52
+62.125

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 will not incorporate a home team advantage and will have a larger divisor in the formula (600 vs 400), making the points exchange less sensitive to the rating difference of two teams.[41]

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. ↑ 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 13 October 2018.
  4. ↑ "FIFA/Coca-Cola World Ranking" (Press release). FIFA. 20 September 2018. Retrieved 20 September 2018.
  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 2016-06-04.
  7. 1 2 World Football Elo Ratings; under the columns tab choose "Highest Rank / Rating"
  8. ↑ Elorating evolution up to the year 1902 at eloratings.net
  9. ↑ Arpad E. Elo, The Rating of Chessplayers, Past and Present, Arco, 1978. ISBN 0-668-04721-6.
  10. ↑ Arpad Elo, Chess Life, 1962.
  11. ↑ About the Chessmetrics Rating System, by Jeff Sonas
  12. ↑ Arpad E. Elo, The Rating of Chessplayers, Past and Present, Arco, 1978. ISBN 0-668-04721-6.
  13. ↑ Arpad Elo, Chess Life, 1962.
  14. ↑ About the Chessmetrics Rating System, by Jeff Sonas
  15. ↑ Upsets at eloratings.net (per June 2018 this page is under reconstruction)
  16. 1 2 3 As the Great Britain national amateur team
  17. ↑ Starting Ratings 1930 World Cup at eloratings.net
  18. ↑ Starting Ratings 1934 World Cup at eloratings.net
  19. ↑ Starting Ratings 1938 World Cup at eloratings.net
  20. ↑ Starting Ratings 1950 World Cup at eloratings.net
  21. ↑ Starting Ratings 1954 World Cup at eloratings.net
  22. ↑ Starting Ratings 1958 World Cup at eloratings.net
  23. ↑ Starting Ratings 1962 World Cup at eloratings.net
  24. ↑ Starting Ratings 1966 World Cup at eloratings.net
  25. ↑ Starting Ratings 1970 World Cup at eloratings.net
  26. ↑ Starting Ratings 1974 World Cup at eloratings.net
  27. ↑ Starting Ratings 1978 World Cup at eloratings.net
  28. ↑ Starting Ratings 1982 World Cup at eloratings.net
  29. ↑ Starting Ratings 1986 World Cup at eloratings.net
  30. ↑ Starting Ratings 1990 World Cup at eloratings.net
  31. ↑ Starting Ratings 1994 World Cup at eloratings.net
  32. ↑ Starting Ratings 1998 World Cup at eloratings.net
  33. ↑ Starting Ratings 2002 World Cup at eloratings.net
  34. ↑ Starting Ratings 2006 World Cup at eloratings.net
  35. ↑ Starting Ratings 2010 World Cup at eloratings.net
  36. ↑ Starting Ratings 2014 World Cup at eloratings.net
  37. ↑ Lyons, Kieth. "What are the World Football Elo Ratings?". The Conversation. Retrieved 16 July 2018.
  38. 1 2 J. Lasek, Z. Szlávik and S. Bhulai (2013), The predictive power of ranking systems in association football, Int. J. Applied Pattern Recognition1: 27-46.
  39. ↑ "The World Football Elo Rating System". Eloratings.net. Retrieved 26 February 2012.
  40. ↑ FIFA Council, 2026 FIFA World Cup™: FIFA Council designates bids for final voting by the FIFA Congress, 10 Jun 2018
  41. 1 2 3 FIFA council, Revision of the FIFA / Coca-Cola World Ranking
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