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Elo Rating System for football

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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. 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.

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.

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. 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 20 ratings as of 3 July 2018
Elo
Rank
1 Year
Change
Team Elo
Rating
FIFA
Rank*
1 Steady  Brazil 2156 2
2 Increase 4  France 2029 7
3 Increase 8  Belgium 2010 3
Increase 1  Spain 2010 10
5 Increase 13  Uruguay 1986 14
6 Decrease 4  Germany 1964 1
7 Increase 9  Croatia 1950 20
8 Increase 2  England 1944 12
9 Decrease 4  Portugal 1940 4
10 Decrease 3  Colombia 1939 16
11 Increase 6  Netherlands 1908 17
12 Increase 7  Sweden 1906 24
13 Decrease 10  Argentina 1896 5
Increase 20  Denmark 1896 12
15 Decrease 7  Italy 1891 19
16 Decrease 1  Peru 1890 11
17 Decrease 3   Switzerland 1879 6
18 Decrease 9  Chile 1869 9
19 Decrease 7  Mexico 1829 15
20 Increase 3  Iran 1816 37
*FIFA rankings per 7 June 2018
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:

R n = R o + K G ( W W e ) {\displaystyle R_{n}=R_{o}+KG(W-W_{e})}

or

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

Where;

R n {\displaystyle R_{n}} = The new team rating
R o {\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
W e {\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

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.

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

G = 1 {\displaystyle G=1}

If the game is won by two goals

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

If the game is won by three or more goals

  • Where N is the goal difference
G = 11 + N 8 {\displaystyle G={\frac {11+N}{8}}}

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:

W e = 1 10 d r / 400 + 1 {\displaystyle W_{e}={\frac {1}{10^{-dr/400}+1}}}

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.

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
K {\displaystyle K} 20 20 20 20 20 20
G {\displaystyle G} 1.5 1.5 1.5 1.5 1 1
W {\displaystyle W} 1 0 0 1 0.5 0.5
W e {\displaystyle W_{e}} 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
K {\displaystyle K} 20 20 20 20 20 20
G {\displaystyle G} 1.5 1.5 1.5 1.5 1 1
W {\displaystyle W} 1 0 0 1 0.5 0.5
W e {\displaystyle W_{e}} 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.

All-time highest ratings

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

Rank Nation High
(rank)
High date High rank
(first,last year)
Low
(rank)
Low date
1  Hungary 2230 (1) 1954-06-30 1 (1952,1960) 1528 (74) 2003-11-19
2  Germany 2223 (1) 2014-07-13 1 (1966,2017) 1639 (19) 1920-09-26
3  England 2216 (1) 1912-09-09 1 (1872,1988) 1790 (13) 1928-03-31
4  Brazil 2194 (1) 1962-06-17 1 (1958,2018) 1813 (13) 1922-09-24
5  Spain 2165 (1) 2013-06-23 1 (1920,2013) 1800 (19) 1969-06-25
6  Argentina 2159 (1) 1957-04-03 1 (1929,2016) 1751 (26) 1990-06-08
7  Netherlands 2154 (2) 2014-07-12 1 (1978,2014) 1550 (49) 1954-10-24
8  France 2137 (1) 2001-05-30 1 (1984,2007) 1507 (40) 1930-05-18
9  Italy 2132 (1) 1939-06-11 1 (1952,2006) 1605 (21) 1920-08-29
10  Uruguay 2108 (1) 1928-06-13 1 (1920,1929) 1635 (44) 1979-09-05
11  Scotland 2104 (1) 1888-03-10 1 (1876,1926) 1600 (63) 2005-03-26
12  Soviet Union 1449 (1) 1966-07-23 1 (1963,1988) 1449 (22) 1913-09-14
13  Poland 2083 (2) 1974-09-01 2 (1974,1975) 1525 (55) 1956-08-26
14  Denmark 2077 (1) 1916-06-25 1 (1914,1916) 1536 (59) 1967-05-24
15  Austria 2068 (1) 1934-05-31 1 (1934) 1550 (73) 2011-09-02
16  Chile 2041 (3) 2016-06-26 2 (2016) 1384 (24) 1916-07-06
17  Czech Republic 2038 (1) 2004-06-27 1 (2004,2005) 1670 (46) 2017-09-04
18  Colombia 2035 (5) 2014-06-28 3 (2016) 1304 (94) 1957-03-13
19  Portugal 2022 (3) 1966-07-28 2 (2006) 1619 (41) 1962-11-07
20  Sweden 2012 (3) 1949-06-02 2 (1950) 1577 (28) 1922-05-28
21  Belgium 2010 (3) 2018-07-02 3 (2018) 1497 (44) 1936-03-29
22  Yugoslavia 1515 (3) 1962-06-10 2 (1962) 1515 (39) 1927-04-10
23  Croatia 2005 (5) 1998-07-11 5 (1998) 1781 (21) 2015-09-06
24  East Germany 1993 (5) 1974-06-22 4 (1974,1977) 1419 (74) 1954-10-24
25  Mexico 1986 (6) 2016-06-09 4 (2016) 1495 (41) 1930-07-19
26  Paraguay 1954 (5) 1954-02-21 5 (1954) 1617 (42) 1962-08-12
27  Romania 1946 (6) 1990-06-09 5 (1990) 1503 (43) 1935-09-01
28  Greece 1931 (7) 2004-08-18 7 (2004) 1277 (65) 1936-06-19
29   Switzerland 1930 (9) 2018-06-22 9 (1930) 1490 (23) 1920-02-29
30  Norway 1929 (8) 2000-06-13 8 (2000) 1364 (26) 1916-07-02
31  Rep. of Ireland 1920 (8) 1994-06-18 8 (1991,2002) 1538 (62) 1971-10-10
32  Peru 1916 (10) 2018-06-13 10 (2018) 1486 (45) 1935-01-20
33  Ecuador 1915 (12) 2015-11-17 12 (2013) 1184 (92) 1949-04-25
34  Wales 1905 (13) 1981-05-20 3 (1876,1902) 1403 (3) 1900-02-03
35  Turkey 1899 (12) 2003-06-19 10 (2002,2003) 1381 (55) 1937-08-01
Rank Nation High
(rank)
High date High rank
(first,last year)
Low
(rank)
Low date
36  Bulgaria 1896 (9) 1969-06-15 7 (1969) 1320 (56) 1931-05-10
 Japan 1896 (10) 2001-08-15 8 (2001) 1214 (59) 1927-08-27
38  United States 1891 (11) 2005-09-03 9 (2009) 1417 (88) 1975-08-24
 Egypt 1891 (12) 1965-03-25 10 (1965) 1526 (51) 1953-01-16
40  Australia 1880 (12) 1997-12-14 11 (2001) 1472 (76) 1965-11-29
41  Algeria 1875 (12) 1963-01-04 10 (1959,1960) 1392 (108) 2007-09-09
42  Ghana 1872 (10) 1966-10-30 10 (1966,1967) 1427 (100) 2004-06-14
43  Costa Rica 1868 (15) 2014-11-13 9 (1932,1934) 1495 (72) 1983-03-22
 Ivory Coast 1868 (15) 2013-01-26 15 (2013) 1497 (73) 1983-01-09
45  Cameroon 1852 (14) 2003-06-26 14 (2003) 1453 (81) 1964-01-31
46  Northern Ireland 1850 (17) 1986-04-23 14 (1986) 1397 (108) 2013-10-11
47  Ukraine 1846 (17) 2013-11-15 15 (2010) 1536 (69) 1995-03-29
48  North Korea 1844 (15) 1966-07-19 10 (1969,1970) 1415 (104) 2004-03-31
 South Korea 1844 (17) 2002-06-22 15 (1948,1953) 1446 (79) 1967-08-07
50  Iceland 1841 (19) 2017-10-09 18 (2017) 1256 (123) 1973-08-29
51  Iran 1836 (18) 2005-04-12 18 (2005) 1461 (75) 1959-12-11
52  Nigeria 1828 (18) 2004-06-05 16 (2004) 1500 (72) 1964-12-27
53  Morocco 1823 (21) 1976-06-11 18 (1999) 1512 (86) 2013-03-24
54 South Africa 1817 (10) 1906-07-09 8 (1907,1908) 1452 (95) 2006-09-02
55  Senegal 1812 (21) 2002-06-16 21 (2002,2018) 1392 (105) 1994-10-28
56  Bosnia Herzegovina 1807 (21) 2013-06-07 20 (2013) 1499 (75) 2002-09-07
57  Venezuela 1806 (19) 2011-07-20 19 (2011) 1212 (76) 1938-08-19
58  Guinea 1799 (24) 1977-06-05 20 (1977) 1306 (128) 1996-06-01
59  Bolivia 1793 (21) 1997-06-25 21 (1997) 1244 (61) 1930-07-20
60  Honduras 1790 (25) 2001-09-05 19 (2001 1332 (108) 1965-03-17
61  DR Congo 1789 (19) 1969-12-14 19 (1969) 1392 (111) 2010-09-05
62  Slovakia 1776 (28) 2017-09-01 17 (1939,1941) 1578 (66) 2011-10-07
63  Uzbekistan 1772 (27) 1994-10-16 23 (1994) 1435 (91) 2001-02-12
64  Israel 1771 (25) 1976-04-11 23 (1976) 1426 (75) 1954-05-01
65  Tunisia 1761 (32) 2006-01-26 24 (1978) 1437 (83) 1987-09-23
66  Slovenia 1758 (28) 2001-11-14 27 (2001) 1516 (70) 1998-08-19
67  China 1755 (28) 2001-10-13 21 (1934) 1444 (90) 1992-08-29
 Panama 1755 (29) 2013-07-24 28 (2013) 1152 (141) 1971-04-22
69  Iraq 1753 (24) 1982-12-03 24 (1982) 1452 (97) 2016-10-06
70  Finland 1747 (29) 2002-03-27 14 (1912) 1245 (116) 1961-06-16

  1. at present as Russia
  2. at present as Serbia
  3. Switzerland reached a low of 1485 after its second match in March 1908.
  4. ^ 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.
  5. 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
  6. On 1 January 2006, Football Federation Australia moved from the OFC to the AFC
  7. Algeria had only played 4 matches to reach their highest ranking and 8 matches to reach their highest ratings.
  8. South Africa had only played 1 match when they reached their highest ratings and ranking between 1906 and 1908
  9. Slovakia's highest rank of 17 was after their first match in August 1939
  10. Finland reached their highest ranking after their 4th match, after beating Italy and Russia in the 1912 Olympic Games

See also

External links

References

  1. "The World Football Elo Rating System". Eloratings.net. Retrieved 26 February 2012.
  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.
  3. FIFA Council, 2026 FIFA World Cup™: FIFA Council designates bids for final voting by the FIFA Congress, 10 Jun 2018
  4. ^ FIFA council, Revision of the FIFA / Coca-Cola World Ranking
  5. "World Football Elo Ratings". Elo ratings. Retrieved 30 June 2018.
  6. "FIFA/Coca-Cola World Ranking" (Press release). FIFA. 7 June 2018. Retrieved 17 May 2018.
  7. World Football Elo Ratings; under the columns tab choose "Highest Rank / Rating" as well as "Lowest Rank / Rating"
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