Elo Rating System for football
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. Ratings tend to converge on a team's true strength relative to its competitors after about 30 matches.[1] Ratings for teams with fewer than 30 matches are considered provisional.
Other implementations of the Elo rating system are possible. 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 in place until July 2018 performed poorly.[2]
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. Following the 2018 World Cup, the FIFA ranking will switch to an Elo-based ranking as well, starting from the current FIFA rating points.[3]
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.[4] 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.
Top 80 ratings as of 3 July 2018[5] | ||||
Elo Rank |
1 Year Change |
Team | Elo Rating |
FIFA Rank* |
---|---|---|---|---|
1 | Brazil | 2156 | 2 | |
2 | 4 | France | 2029 | 7 |
3 | 8 | Belgium | 2010 | 3 |
1 | Spain | 2010 | 10 | |
5 | 13 | Uruguay | 1986 | 14 |
6 | 4 | Germany | 1964 | 1 |
7 | 9 | Croatia | 1950 | 20 |
8 | 2 | England | 1944 | 12 |
9 | 4 | Portugal | 1940 | 4 |
10 | 3 | Colombia | 1939 | 16 |
11 | 6 | Netherlands | 1908 | 17 |
12 | 7 | Sweden | 1906 | 24 |
13 | 10 | Argentina | 1896 | 5 |
20 | Denmark | 1896 | 12 | |
15 | 7 | Italy | 1891 | 19 |
16 | 1 | Peru | 1890 | 11 |
17 | 3 | Switzerland | 1879 | 6 |
18 | 9 | Chile | 1869 | 9 |
19 | 7 | Mexico | 1829 | 15 |
20 | 3 | Iran | 1816 | 37 |
21 | 8 | Poland | 1783 | 8 |
22 | 3 | Wales | 1777 | 18 |
23 | 9 | Serbia | 1772 | 34 |
24 | 2 | United States | 1764 | 25 |
25 | 11 | Senegal | 1763 | 27 |
26 | 8 | South Korea | 1757 | 57 |
27 | Slovakia | 1752 | 28 | |
28 | 2 | Ukraine | 1750 | 35 |
29 | 9 | Ecuador | 1747 | 60 |
30 | Bosnia & Herzegovina | 1745 | 40 | |
31 | 8 | Austria | 1742 | 26 |
32 | 8 | Venezuela | 1739 | 33 |
33 | 9 | Republic of Ireland | 1729 | 31 |
34 | 3 | Paraguay | 1728 | 32 |
12 | Turkey | 1728 | 38 | |
36 | 8 | Romania | 1727 | 30 |
37 | 8 | Costa Rica | 1726 | 23 |
38 | 22 | Morocco | 1720 | 41 |
39 | 4 | Australia | 1713 | 36 |
1 | Czech Republic | 1713 | 46 | |
41 | 2 | Russia | 1710 | 70 |
42 | 1 | Scotland | 1709 | 42 |
43 | 23 | Iceland | 1708 | 22 |
44 | 9 | Nigeria | 1702 | 48 |
45 | 17 | Japan | 1699 | 61 |
46 | 1 | Northern Ireland | 1676 | 29 |
47 | 19 | Tunisia | 1662 | 21 |
48 | 7 | Bolivia | 1661 | 59 |
49 | 3 | Greece | 1646 | 44 |
50 | 3 | Cameroon | 1645 | 49 |
17 | Ghana | 1645 | 47 | |
52 | 17 | Norway | 1640 | 53 |
53 | 2 | Slovenia | 1626 | 56 |
54 | 1 | Bulgaria | 1615 | 49 |
55 | 13 | Syria | 1606 | 73 |
56 | 20 | Finland | 1605 | 63 |
57 | 8 | Ivory Coast | 1602 | 68 |
58 | 6 | Uzbekistan | 1599 | 95 |
59 | 1 | Burkina Faso | 1597 | 52 |
3 | Montenegro | 1597 | 43 | |
61 | 11 | Panama | 1596 | 55 |
62 | 1 | Honduras | 1590 | 62 |
63 | 2 | DR Congo | 1589 | 38 |
64 | 7 | Saudi Arabia | 1588 | 67 |
65 | 11 | Hungary | 1576 | 51 |
66 | 18 | Egypt | 1575 | 45 |
67 | 18 | Jamaica | 1574 | 54 |
68 | 4 | South Africa | 1565 | 74 |
69 | 10 | Albania | 1560 | 58 |
70 | 8 | Iraq | 1550 | 89 |
71 | 24 | Oman | 1539 | 84 |
72 | 9 | Canada | 1534 | 79 |
1 | China | 1534 | 75 | |
74 | 2 | United Arab Emirates | 1532 | 77 |
75 | 5 | Israel | 1527 | 93 |
76 | 11 | Belarus | 1522 | 78 |
77 | 2 | Mali | 1519 | 64 |
78 | 15 | North Macedonia | 1518 | 71 |
79 | 1 | Guatemala | 1511 | 146 |
80 | 25 | Algeria | 1508 | 66 |
*FIFA rankings per 7 June 2018 [6] | ||||
Complete rankings at eloratings.net |
AFC | CAF | CONCACAF | CONIFA |
CONMEBOL | OFC | UEFA |
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. He was also the first maintainer of the World Football Elo Ratings web site, currently 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
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.
Calculation principles
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 |
"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 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 |
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.[4]
- 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 |
- 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.[4]
- 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 600 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 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 |
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 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 |
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.
List of number one teams
The following is the list of nations who reached a first rank in ratings since 1872.[7]
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All-time highest ratings
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.
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- ^ at present as Russia
- ^ at present as Serbia
- ^ Switzerland reached a low of 1485 after its second match in March 1908.
- ^ a b 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.
- ^ Wales was in 3 place from its first match in 1876 to 1902, in a period that only 3 to 4 teams were in the rankings
- ^ On 1 January 2006, Football Federation Australia moved from the OFC to the AFC
- ^ Algeria had only played 4 matches to reach their highest ranking and 8 matches to reach their highest ratings.
- ^ South Africa had only played 1 match when they reached their highest ratings and ranking between 1906 and 1908
- ^ Slovakia's highest rank of 17 was after their first match in August 1939
- ^ Finland reached their highest ranking after their 4th match, after beating 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.[9][10][11] The first 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.
- Highest average ratings since 1970
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- ^ 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 the Czechoslovakian (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)
- Averages by decade
The table below shows the teams with the best average Elo score each decade since the 1920s (Jan 1 XXX0 - Dec 31 XXX9).
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- ^ Includes the record of the Great Britain Olympic football team in the 1908, 1912 and 1920 Olympics
- ^ 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
- ^ Combined record of Yugoslavia (1990-1992) and FR of Yugoslavia (1994-1999)
- ^ Combined record of Czechoslovakia (1990-1992) and Czech national football teams (1993-1999)
- ^ Combined record of the USSR (1990-1992), the CIS (1992), and Russia national football teams (1992-1999)
- ^ 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.
Rank | Combined points |
Nation 1 | Elo 1 | Nation 2 | Elo 2 | Score | Date | Occasion | Location |
---|---|---|---|---|---|---|---|---|---|
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 | England | 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.[12] 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.[a]
The nations' points before the matches are given.
Rank | Point exchange |
Nation 1 | Elo 1 | Nation 2 | Elo 2 | Score | Date | Occasion | Location |
---|---|---|---|---|---|---|---|---|---|
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 and Tobago | 1481 | Mexico | 1783 | 4–0 | 1973-12-14 | CONCACAF Championship | Port-au-Prince | ||
South Korea | 1677 | Germany | 2044 | 2–0 | 2018-06-28 | 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.
- ^ 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.
See also
External links
- World Football Elo ratings
- How the rankings are calculated
- FootballDatabase's World Club Ratings (using Elo Formula)
References
- ^ "The World Football Elo Rating System". Eloratings.net. Retrieved 26 February 2012.
- ^ J. Lasek, Z. Szlávik and S. Bhulai (2013), The predictive power of ranking systems in association football, Int. J. Applied Pattern Recognition1: 27-46.
- ^ FIFA Council, 2026 FIFA World Cup™: FIFA Council designates bids for final voting by the FIFA Congress, 10 Jun 2018
- ^ a b c FIFA council, Revision of the FIFA / Coca-Cola World Ranking
- ^ "World Football Elo Ratings". Elo ratings. Retrieved 30 June 2018.
- ^ "FIFA/Coca-Cola World Ranking" (Press release). FIFA. 7 June 2018. Retrieved 17 May 2018.
- ^ 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.
- ^ World Football Elo Ratings; under the columns tab choose "Highest Rank / Rating" as well as "Lowest Rank / Rating"
- ^ 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
- ^ Upsets at eloratings.net (per June 2018 this page is under reconstruction)