# World Football Elo Ratings

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

The following table shows World Football Elo Ratings on 13 July 2014, using data from the World Football Elo Ratings web site[3] and updated with recent results.[4]

Each national team's FIFA World Rankings are shown as they were on 17 July 2014.[5] Cell color indicates confederation.

## Strongest teams since the mid to late 1960s

Time averaged Elo or Elo-like scores are routinely used to compare chess player strengths.[6][7][8] The following is a list of the national teams with the highest average Elo score from 1 January 1970 to 1 July 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 2013.3
2  (West) Germany[9] 1976.2
3  Netherlands 1924.9
4  Italy 1923.2
5  England 1922.7
6  Spain 1910.5
7  Argentina 1903.0
8  France 1881.5
9  Soviet Union → Russia[10] 1852.5
10  Czechoslovakia/Czechia[11] 1831.8
11  Portugal 1817.9
12  Yugoslavia → Serbia[12] 1816.8
13  Sweden 1799.0
14  Romania 1780.9
15  Mexico 1774.8
16  Uruguay 1772.7
17  Poland 1771.8
Rank Country Avg Elo
18  Belgium 1761.8
19  Denmark 1756.8
20  Scotland 1738.7
21  Paraguay 1726.8
22  Republic of Ireland 1721.1
23  Chile 1718.1
24  Bulgaria 1708.3
25  Australia 1696.5
26  Austria 1688.6
27   Switzerland 1687.2
28  Hungary 1685.6
29  Colombia 1683.8
30  Iran 1676.2
31  South Korea 1666.5
32  Greece 1656.4
33  Egypt 1654.7
34  Nigeria 1654.6
Rank Country Avg Elo
35  Wales 1653.4
36  Peru 1644.4
37  Morocco 1644.3
38  Israel 1644.1
39  Ivory Coast 1638.9
40  Cameroon 1637.8
41  Norway 1637.3
42  Turkey 1634.7
43  Ghana 1612.2
44  Northern Ireland 1607.4
45  United States 1604.8
46  Tunisia 1602.5
47  Costa Rica 1597.1
48  Iraq 1595.3
49  Japan 1591.2
51  Algeria 1569.9

## List of number one teams

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

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
Netherlands 114 4 July 2014
Italy 43 15 August 2006
Germany 15 Current
Czech Republic 8 7 June 2005

## All-time highest ratings

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

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 1950s 1960s
1 1911 1976 2036 2025 1962
2 1873 1970 2018 1997 1928
3 1859 1899 1892 1996 1924
4 1843 1868 1876 1917 1923
5 1820 1866 1858 1870 1917
6 1795 1859 1852 1856 1887
7 1771 1841 1841 1853 1867
8 1768 1814 1832 1850 1852
9 1761 1810 1814 1817 1843
10 1760 1785 1768 1815 1840
11 1739 1759 1766 1799 1810
12 1712 1685 1746 1796 1800
13 1734 1790 1796
14 1753 1783
15 1728 1741

Rank 1970s 1980s 1990s 2000s 2010s [13]
1 2060 1975 1998 1998 2101
2 2040 1964 1988 1984 2063
3 1948 1951 1952 1966 2027
4 1933 1927 1928 1964 2018
5 1888 1897 1920 1955 1951
6 1883 1890 1904 1941 1922
7 1877 1884 1901 1916 1878
8 1869 1884 1901 1891 1875
9 1861 1847 1869 1887 1871
10 1851 1839 1869 1872 1857
11 1838 1820 1842 1838 1850
12 1831 1819 1834 1825 1841
13 1830 1818 1828 1821 1828
14 1809 1803 1825 1807 1817
15 1803 1785 1825 1799 1816
16 1793 1784 1813 1790 1806
17 1771 1784 1810 1787 1793
18 1766 1776 1784 1786 1772
19 1766 1775 1777 1782 1766
20 1755 1773 1773 1774 1764

## Highest rated matches

A list of the 10 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 Rio de Janeiro
Germany 2200  Argentina 2040 2014-09-03 Friendly[17] Düsseldorf
3 4212  Netherlands 2101  Spain 2111 0 : 1 aet 2010-07-11 World Cup F Johannesburg
4 4197  Brazil 2099  Germany 2098 1 : 7 2014-07-08 World Cup SF Belo Horizonte
5 4190  Brazil 2063  Spain 2127 3 : 0 2013-06-30 Confederations Cup F Rio de Janeiro
6 4161  West Germany 1995  Hungary 2166 3 : 2 1954-07-04 World Cup F Bern
7 4159  Netherlands 2051  Brazil 2108 2 : 1 2010-07-02 World Cup QF Port Elizabeth
8 4151  Brazil 2061  Netherlands 2090 0 : 0 2011-06-04 Friendly Goiânia
9 4149  West Germany 2068  Brazil 2081 0 : 1 1973-06-16 Friendly Berlin
10 4133  Netherlands 2074  Argentina 2059 0 : 0 2014-07-09 World Cup SF São Paulo

## History

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

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

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

### Status of match

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 Finals 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

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

W is the result of the game (1 for a win, 0.5 for a draw, and 0 for a loss).

### Expected result of match

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

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

Team A versus Team B (Team A stronger than Team B)

 Score $K$ $G$ $W$ $W_e$ Total (P) Team A Team B Team A Team B Team A Team B 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 +9.63 -9.63 -20.37 +20.37 -3.58 +3.58

#### Example 2

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:

 Score $K$ $G$ $W$ $W_e$ Total (P) Team B Team C Team B Team C Team B Team C 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 +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.

## Notes and 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. ^ World Football Elo Ratings Elo.net. Retrieved: 2014-06-05.
4. ^ See this site for spelled-out results between June 28 and July 15 as well as a complete ranking per July 16.
5. ^ "FIFA/Coca-Cola World Ranking" (Press release). FIFA. 17 July 2014. Retrieved 17 July 2014.
6. ^ Arpad E. Elo, The Rating of Chessplayers, Past and Present, Arco, 1978. ISBN 0-668-04721-6.
7. ^ Arpad Elo, Chess Life, 1962.
8. ^ About the Chessmetrics Rating System, by Jeff Sonas
9. ^ Representing West Germany from 1949 to 1990
10. ^ Combined record of the USSR (1970-1992), the CIS (1992), and Russia national football teams (1992-present)
11. ^ Combined record of Czechoslovakia (1970-1992) and Czech national football teams (1993-present)
12. ^ Combined record of Yugoslavia (1970-1992), Serbia and Montenegro (1994-2006) and Serbia national football teams (2006-present)
13. ^ (up to July 1st, 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.