World Football Elo Ratings

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The World Football Elo Ratings is a ranking system for men's national teams in association football. The method used to rank teams is based upon the Elo rating system method but modified to take various football-specific variables into account. These ratings should not be confused with the FIFA World Rankings, which is more prevalent because it is the official rating system used by the international governing body of football to rank national teams.

The ratings consider 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.[1] Ratings for teams with fewer than 30 matches should be 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.[2]

Top 60 ranking[edit]

The following table shows World Football Elo Ratings on 23 November 2014, using data from the World Football Elo Ratings web site.[3]

Each national team's FIFA World Rankings are shown as they were on 27 November 2014.[4]

Strongest teams since the mid to late 1960s[edit]

Time averaged Elo or Elo-like scores are routinely used to compare chess player strengths.[5][6][7] The following is a list of the national teams with the highest average Elo score from 1 January 1970 to 1 December 2014. 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. Since Elo scores reflect past accomplishments, the table represents the relative strength of national teams since the mid to late 1960s.

Rank Country Avg Elo
1  Brazil 2013.1
2  (West) Germany[8] 1978.3
3  Netherlands 1926.4
4  Italy 1922.6
5  England 1922.3
6  Spain 1911.3
7  Argentina 1904.6
8  France 1882.1
9  Soviet Union → Russia[9] 1852.0
10  Czechoslovakia/Czech Rep.[10] 1831.2
11  Portugal 1818.6
12  Yugoslavia → Serbia[11] 1816.2
13  Sweden 1799.1
14  Romania 1780.6
15  Mexico 1776.1
16  Uruguay 1773.7
17  Poland 1771.0
Rank Country Avg Elo
18  Belgium 1763.0
19  Denmark 1756.9
20  Scotland 1738.2
21  Paraguay 1726.5
22  Republic of Ireland 1720.7
23  Chile 1720.1
24  Bulgaria 1706.7
25  Australia 1700.9
26  Austria 1688.6
27  Switzerland 1688.4
28  Colombia 1686.6
29  Hungary 1685.0
30  Iran 1676.1
31  South Korea 1665.9
32  Greece 1657.6
33  Egypt 1655.2
34  Nigeria 1655.1
Rank Country Avg Elo
35  Wales 1652.9
36  Peru 1645.1
37  Israel 1644.1
38  Morocco 1643.7
39  Ivory Coast 1639.8
40  Cameroon 1637.5
41  Norway 1636.9
42  Turkey 1635.6
43  Ghana 1613.3
44  United States 1607.5
45  Northern Ireland 1605.7
46  Tunisia 1602.6
47  Costa Rica 1599.4
48  Iraq 1595.7
49  Japan 1593.2
50  Ecuador 1585.4
51  Algeria 1571.3

List of number one teams[edit]

The following is the list of nations who have achieved the number one position on the World Football Elo Ratings since 2000:

Ranking by days as leader since 1 January 2000[edit]

Nation # of days Last Date as Leader
 Brazil 2464 8 July 2014
 Spain 1523 12 October 2013
 France 1115 10 July 2007
 Argentina 316 14 July 2007
 Germany 170 Current
 Netherlands 114 4 July 2014
 Italy 43 15 August 2006
 Czech Republic 8 7 June 2005

All-time highest ratings[edit]

The following is a list of national football teams ranked by their highest Elo score ever reached.

Averages by decade[edit]

The table below shows the teams with the best average Elo score per decade (Jan 1 19X0 - Dec 31 19X9). Because the Elö scores take into account past achievements with an inercy of months, the averaging over a decade is more representative of the teams' strengths for a decade starting a few years earlier and ending with the latest results of the decade relatively underweighted. For instance, this partially explains England claiming #3 spot despite missing two WCs in the 70s, boosted by results legacy from the late 60s. Or conversely the surging of France in the late 90s and Spain in the late 00s not being fully reflected in that decade but rather on the subsequent one.

Rank 1920s 1930s 1940s [12] 1950s 1960s
1 1911

 Uruguay

1976

 Argentina

2036

 Argentina

2025

 Argentina

1962

 Brazil

2 1873

 Spain

1970

 Italy

2018

 Italy

1998

 Hungary

1928

 England

3 1859

 Argentina

1899

 Uruguay

1892

 England

1996

 Brazil

1924

 Hungary

4 1843

 Scotland

1868

 Spain

1876

 Brazil

1917

 England

1923

 Argentina

5 1820

 Czechoslovakia

1867

 England

1858

 Spain

1870

 West Germany

1917

 Soviet Union

6 1795

 Denmark

1859

 Austria

1852

 Uruguay

1856

 Uruguay

1887

 West Germany

7 1771

 Brazil

1841

 Scotland

1841

 Scotland

1853

 Italy

1867

 Czechoslovakia

8 1768

 England

1814

 Czechoslovakia

1832

 Germany

1850

 Yugoslavia

1852

 Italy

9 1761

 Hungary

1810

 Brazil

1815

 Hungary

1817

 Austria

1844

 Spain

10 1760

 Austria

1785

 Hungary

1783

 Mexico

1815

 Spain

1840

 Uruguay

11 1739

 Netherlands

1767

 Costa Rica

1768

 Czechoslovakia

1799

 Paraguay

1811

 Yugoslavia

12 1712

 Sweden

1759

 Germany

1766

 Austria

1796

 Sweden

1801

 Scotland

13 1701

 Belgium

1685

 Denmark

1746

 Wales

1791

 Scotland

1796

 Sweden

14 1693

 Italy

1682

 Sweden

1734

 Sweden

1753

 France

1783

 Mexico

15 1676

 Portugal

1678

 United States

1719

 Paraguay

1728

 Peru

1741

 Austria

Rank 1970s 1980s 1990s 2000s 2010s [13]
1 2059

 Brazil

1975

 Brazil

1998

 Brazil

1999

 Brazil

2090

 Spain

2 2040

 West Germany

1964

 West Germany

1988

 Germany

1984

 France

2057

 Brazil

3 1948

 England

1951

 Soviet Union

1952

 Italy

1966

 Netherlands

2038

 Germany

4 1933

 Italy

1927

 England

1928

 France

1964

 Argentina

2023

 Netherlands

5 1888

 Netherlands

1897

 Argentina

1920

 Netherlands

1955

 Spain

1960

 Argentina

6 1883

 Poland

1890

 Italy

1904

 Spain

1942

 Italy

1916

 England

7 1878

 Soviet Union

1884

 Netherlands

1901

 Yugoslavia[14]

1916

 England

1877

 Uruguay

8 1869

 East Germany

1884

 France

1901

 England

1891

 Germany

1876

 Portugal

9 1861

 Argentina

1847

 Spain

1869

 Argentina

1887

 Portugal

1869

 Italy

10 1851

 Spain

1840

 Poland

1869

 Denmark

1872

 Czechia

1865

 Chile

11 1838

 Czechoslovakia

1820

 Czechoslovakia

1843

 Czechia[15]

1838

 Croatia

1845

 Mexico

12 1831

 Hungary

1819

 Belgium

1836

 Sweden

1825

 Mexico

1844

 Croatia

13 1830

 Yugoslavia

1818

 Yugoslavia

1829

 Croatia

1821

 Denmark

1837

 France

14 1809

 Scotland

1803

 East Germany

1826

 Russia[16]

1807

 Sweden

1822

 Colombia

15 1803

 Portugal

1784

 Uruguay

1825

 Mexico

1800

 Romania

1813

 Sweden

16 1793

 Belgium

1784

 Romania

1813

 Romania

1791

 United States

1812

 Russia

17 1771

 Sweden

1783

 Scotland

1810

 Portugal

1787

 Ireland

1788

 Ivory Coast

18 1766

 Austria

1776

 Sweden

1784

 Colombia

1786

 Turkey

1769

 Ecuador

19 1766

 Romania

1775

 Austria

1777

 Ireland

1783

 Uruguay

1768

 Switzerland

20 1755

 France

1774

 Denmark

1773

 Belgium

1775

 Australia

1767

 Japan

Highest rated matches[edit]

A list of the 15 matches between teams with the highest combined Elo ratings (the nation's points before the matches are given).

Rank Combined
points
Nation 1 Elo 1 Nation 2 Elo 2 Score Date Occasion Location
1 4240  Germany 2180  Argentina 2060 1 : 0 aet 2014-07-13 World Cup F Brazil Rio de Janeiro
 Germany 2200  Argentina 2040 2 : 4 2014-09-03 Friendly[17] Germany Düsseldorf
3 4213  Netherlands 2101  Spain 2112 0 : 1 aet 2010-07-11 World Cup F South Africa Johannesburg
4 4198  Brazil 2100  Germany 2098 1 : 7 2014-07-08 World Cup SF Brazil Belo Horizonte
5 4192  Brazil 2064  Spain 2128 3 : 0 2013-06-30 Confederations Cup F Brazil Rio de Janeiro
6 4161  West Germany 1995  Hungary 2166 3 : 2 1954-07-04 World Cup F Switzerland Bern
7 4159  Netherlands 2051  Brazil 2108 2 : 1 2010-07-02 World Cup QF South Africa Port Elizabeth
8 4151  Brazil 2061  Netherlands 2090 0 : 0 2011-06-04 Friendly Brazil Goiânia
9 4149  West Germany 2069  Brazil 2080 0 : 1 1973-06-16 Friendly West Germany Berlin
10 4135  Netherlands 2075  Argentina 2060 0 : 0 2014-07-09 World Cup SF Brazil São Paulo
11 4130  Spain 2086  Germany 2044 1 : 0 2010-07-07 World Cup SF South Africa Durban
12 4121  Brazil 2051  West Germany 2070 1 : 0 1982-03-21 Friendly Brazil Rio de Janeiro
13 4118  Hungary 2108  Brazil 2010 4 : 2 1954-06-27 World Cup QF Switzerland Bern
14 4116  Hungary 2141  Uruguay 1975 4 : 2 1954-06-30 World Cup SF Switzerland Lausanne
15 4113  West Germany 2079  Netherlands 2034 2 : 1 1974-07-07 World Cup F West Germany Munich

History[edit]

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[edit]

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 single difference is Elo giving a special treatment for minor tournaments, while FIFA consider them as friendly matches.

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. Match data are primarily from International Football 1872 – present web site.

Basic calculation principles[edit]

The basic principle behind the Elo ratings is only in its simplest form similar to that of a league, unlike the FIFA tables 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:

R_n = R_o + K G (W - W_e)

or

P = K G (W - W_e)

Where;

R_n = The new team rating
R_o = The old team rating
K = Weight index regarding the tournament of the match
G = A number from the index of goal differences
W = The result of the match
W_e = The expected result
P = Points Change

The number of Points Change is rounded to the nearest integer before updating the team rating.

Status of match[edit]

The status of the match is incorporated by the use of a weight constant. The weight is a constant regarding the "weight" or importance of a match, defined by which tournament the match is in, they are as follows;

Tournament or Match type Index (K)
World Cup 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[edit]

The number of goals is taken into account by use of a goal difference index. G is increased by half if a game is won by two goals, and if the game is won by three or more goals by a number decided through the appropriate calculation shown below;

If the game is a draw or is won by one goal

G = 1

If the game is won by two goals

G = \frac{3}{2}

If the game is won by three or more goals

  • Where N is the goal difference
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
+7 2.25
+8 2.375
+9 2.5
+10 2.625

Result of match[edit]

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[edit]

We is the expected result (win expectancy with a draw counting as 0.5) from the following formula:

W_e = \frac{1}{10^{-dr/400} + 1}

where dr equals the difference in ratings plus 100 points for a team playing at home. 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[edit]

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[edit]

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
K 20 20 20 20 20 20
G 1.5 1.5 1.5 1.5 1 1
W 1 0 0 1 0.5 0.5
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

Example 2[edit]

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
K 20 20 20 20 20 20
G 1.5 1.5 1.5 1.5 1 1
W 1 0 0 1 0.5 0.5
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

Note that Team B loses more ranking points by losing to Team C than by losing to Team A.

See also[edit]

Notes and references[edit]

  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. ^ World Football Elo Ratings Elo.net. Retrieved: 2014-10-11.
  4. ^ "FIFA/Coca-Cola World Ranking" (Press release). FIFA. 17 July 2014. Retrieved 1 September 2014. 
  5. ^ Arpad E. Elo, The Rating of Chessplayers, Past and Present, Arco, 1978. ISBN 0-668-04721-6.
  6. ^ Arpad Elo, Chess Life, 1962.
  7. ^ About the Chessmetrics Rating System, by Jeff Sonas
  8. ^ Representing West Germany from 1949 to 1990
  9. ^ Combined record of the USSR (1970-1992), the CIS (1992), and Russia national football teams (1992-present)
  10. ^ Combined record of Czechoslovakia (1970-1992) and Czech Republic national football teams (1993-present)
  11. ^ Combined record of Yugoslavia (1970-1992), Serbia and Montenegro (1994-2006) and Serbia national football teams (2006-present)
  12. ^ 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
  13. ^ (up to December 1, 2014)
  14. ^ Combined record of Yugoslavia (1990-1992) and FR of Yugoslavia (1994-1999)
  15. ^ Combined record of Czechoslovakia (1990-1992) and Czech national football teams (1993-1999)
  16. ^ Combined record of the USSR (1990-1992), the CIS (1992), and Russia national football teams (1992-1999)
  17. ^ "Germany to play Argentina in September friendly". The Star. 21 March 2014. Retrieved 15 July 2014. 

External links[edit]