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. Elo 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 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.[1] Ratings for teams with fewer than 30 matches should be considered provisional.

The FIFA Women's World Rankings uses a modified version of the Elo formula. The FIFA men's ranking, however, uses a non-Elo formula.

Contents

Top 100 ranking [edit]

Current table, as of 28 April 2013, of the World Football Elo rankings, compiled by the World Football Elo Ratings web site.

Each national team's FIFA World Rankings as of 9 May 2013.[2]

Elo Rank Nation Points Confederation FIFA Rank
1  Spain 2125 UEFA 1
2  Germany 2037 UEFA 2
3  Brazil 2017 CONMEBOL 19
4  Argentina 1991 CONMEBOL 3
5  Netherlands 1977 UEFA 9
6  England 1924 UEFA 7
7  Italy 1896 UEFA 8
8  Croatia 1885 UEFA 4
9  Russia 1868 UEFA 11
10  Colombia 1867 CONMEBOL 6
11  Ecuador 1862 CONMEBOL 10
12  Portugal 1860 UEFA 5
13  Mexico 1851 CONCACAF 16
 Sweden 1851 UEFA 24
15  France 1846 UEFA 18
16  Ivory Coast 1823 CAF 12
17  Chile 1796 CONMEBOL 23
18  Uruguay 1790 CONMEBOL 17
19  Switzerland 1789 UEFA 14
20  Belgium 1785 UEFA 15
21  Japan 1782 AFC 30
22  Denmark 1770 UEFA 20
23  Greece 1769 UEFA 13
24  Bosnia and Herzegovina 1762 UEFA 21
25  United States 1747 CONCACAF 29
26  Ukraine 1741 UEFA 37
27  South Korea 1740 AFC 42
28  Czech Republic 1739 UEFA 25
29  Australia 1732 AFC 47
30  Peru 1729 CONMEBOL 32
31  Republic of Ireland 1712 UEFA 39
32  Romania 1711 UEFA 34
33  Venezuela 1710 CONMEBOL 36
34  Nigeria 1701 CAF 28
 Paraguay 1701 CONMEBOL 44
36  Panama 1698 CONCACAF 38
37  Norway 1683 UEFA 31
38  Serbia 1674 UEFA 40
 Costa Rica 1674 CONCACAF 48
40  Ghana 1670 CAF 22
41  Hungary 1663 UEFA 33
42  Montenegro 1659 UEFA 27
43  Egypt 1658 CAF 68
44  Turkey 1655 UEFA 44
45  Iran 1651 AFC 57
46  Honduras 1650 CONCACAF 50
 Poland 1650 UEFA 63
48  Bulgaria 1645 UEFA 52
49  Israel 1632 UEFA 59
50  Finland 1622 UEFA 83
Elo Rank Nation Points Confederation FIFA Rank
51  Mali 1621 CAF 26
52  Uzbekistan 1608 AFC 66
 New Zealand 1608 OFC 87
54  Bolivia 1607 CONMEBOL 58
55  United Arab Emirates 1604 AFC 89
56  China PR 1600 AFC 98
57  North Korea 1588 AFC 115
58  Austria 1587 UEFA 71
59  Iraq 1586 AFC 97
60  Scotland 1585 UEFA 78
61  Tunisia 1584 CAF 41
62  Cameroon 1580 CAF 62
63  Wales 1578 UEFA 49
64  Belarus 1574 UEFA 69
65  Slovakia 1565 UEFA 54
66  South Africa 1562 CAF 56
67  Jamaica 1549 CONCACAF 53
68  Libya 1546 CAF 65
 Canada 1546 CONCACAF 80
70  Kuwait 1545 AFC 113
71  Zambia 1543 CAF 46
72  Burkina Faso 1539 CAF 50
73  Jordan 1533 AFC 76
74  Slovenia 1527 UEFA 55
75  El Salvador 1522 CONCACAF 85
 Uganda 1522 CAF 91
77  Senegal 1521 CAF 76
78  Algeria 1520 CAF 35
 Oman 1520 AFC 102
80  Morocco 1508 CAF 74
 Syria 1508 AFC 138
82  Albania 1507 UEFA 43
83  Macedonia 1504 UEFA 84
 Saudi Arabia 1504 AFC 108
85  Guinea 1500 CAF 70
86  Gabon 1490 CAF 80
87  Georgia 1489 UEFA 96
88  Iceland 1483 UEFA 73
89  Guatemala 1480 CONCACAF 94
90  Armenia 1474 UEFA 90
91  Latvia 1472 UEFA 110
92  Estonia 1468 UEFA 92
 Qatar 1468 AFC 102
94  Angola 1462 CAF 93
95  Bahrain 1456 AFC 117
96  Congo DR 1454 CAF 77
97  Cape Verde 1442 CAF 75
 Lithuania 1442 UEFA 111
99  Togo 1430 CAF 72
100  Cuba 1422 CONCACAF 87

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

Time averaged Elo or Elo-like scores are routinely used to compare chess player strengths.[3][4][5] The following is a list of the national teams with the highest average Elo score from 1 January 1970 to 1 May 2013. 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 2010.7
2  (West) Germany[6] 1974.2
3  Italy 1923.5
4  Netherlands 1923.2
5  England 1922.8
6  Spain 1905.4
7  Argentina 1900.4
8  France 1881.8
9  USSR → Russia[7] 1852.8
10  Czechoslovakia/Czechia[8] 1834.4
11  Yugoslavia → Serbia[9] 1819.4
12  Portugal 1815.4
13  Sweden 1798.2
14  Romania 1782.9
15  Poland 1775.4
16  Mexico 1774.4
17  Uruguay 1769.9
18  Belgium 1760.3
Rank Country Avg Elo
19  Denmark 1757.4
20  Scotland 1740.7
21  Paraguay 1727.8
22  Republic of Ireland 1721.0
23  Chile 1713.7
24  Bulgaria 1710.3
25  Australia 1695.6
26  Austria 1689.6
27  Hungary 1686.2
28  Switzerland 1683.3
29  Colombia 1677.7
30  Iran 1675.8
31  South Korea 1665.2
32  Wales 1655.7
33  Egypt 1654.4
34  Greece 1652.4
35  Nigeria 1650.6
Rank Country Avg Elo
36  Morocco 1647.1
37  Israel 1644.3
38  Peru 1642.2
39  Cameroon 1639.2
40  Norway 1637.9
41  Ivory Coast 1633.9
42  Turkey 1633.3
43  Northern Ireland 1613.3
44  Ghana 1609.2
45  Tunisia 1603.7
46  United States 1598.6
47  Iraq 1597.4
48  Costa Rica 1593.9
49  Japan 1587.0
50  Ecuador 1576.8
51  Algeria 1569.1
52  Zambia 1561.2

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:

Start Date Nation # of days
5 Jun 1999  Brazil 389
28 Jun 2000  France 708
6 Jun 2002  Argentina 1
7 Jun 2002  France 4
11 Jun 2002  Netherlands 1
12 Jun 2002  Spain 4
16 Jun 2002  Netherlands 5
21 Jun 2002  Brazil 351
7 Jun 2003  Netherlands 4
11 Jun 2003  Brazil 8
19 Jun 2003  Netherlands 83
10 Sep 2003  France 291
27 Jun 2004  Czech Republic 4
Start Date Nation # of days
1 Jul 2004  France 10
11 Jul 2004  Brazil 3
14 Jul 2004  France 35
18 Aug 2004  Argentina 290
4 Jun 2005  Czech Republic 4
8 Jun 2005  Argentina 21
29 Jun 2005  Brazil 102
9 Oct 2005  Netherlands 3
12 Oct 2005  Brazil 265
4 Jul 2006  Italy 43
16 Aug 2006  France 52
7 Oct 2006  Brazil 122
6 Feb 2007  France 1
Start Date Nation # of days
7 Feb 2007  Brazil 140
27 Jun 2007  France 14
11 Jul 2007  Argentina 4
15 Jul 2007  Brazil 334
13 Jun 2008  Brazil /  Netherlands 2
15 Jun 2008  Netherlands 6
21 Jun 2008  Spain 368
24 Jun 2009  Brazil 373
2 Jul 2010  Netherlands 1
3 Jul 2010  Netherlands /  Spain 3
6 Jul 2010  Netherlands 1
7 Jul 2010  Spain Current

Ranking by days as leader since 1 January 2000 (as of 1 August 2012) [edit]

Nation # of days Last Date as Leader
 Brazil 1878 1 July 2010
 Spain 1131 [10] Current
 France 1115 10 July 2007
 Argentina 316 14 July 2007
 Netherlands 109 6 July 2010
 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.

Rank Nation Points Date
1  Hungary 2166 30 June 1954
2  Brazil 2153 17 June 1962
3  Spain 2140 11 July 2010
4  Argentina 2117 3 April 1957
5  France 2105 15 August 2001
6  Netherlands 2100 6 July 2010
7  Germany 2099 4 September 1974 (as West Germany)
8  Italy 2079 20 July 1939
9  Poland 2046 1 September 1974
10  England 2041 22 October 1966
11  Uruguay 2035 13 June 1928
12  Soviet Union 2022 9 October 1983
13  Czech Republic 1999 27 June 2004
14  Austria 1998 31 May 1934
15  Portugal 1982 15 November 2000
16  Croatia 1967 11 July 1998
17  Serbia 1961 25 June 1998 (as FR Yugoslavia)
18  Denmark 1960 13 June 1986
19  Scotland 1953 10 March 1888
20  Sweden 1950 25 June 1950
21  East Germany 1949 22 June 1974
22  Mexico 1936 19 June 2005
23  Paraguay 1932 21 February 1954
24  Chile 1918 12 July 2011
25  Belgium 1916 9 September 1981
26  Norway 1913 13 June 2000
27  Colombia 1912 5 June 1994
28  Romania 1908 9 June 1990
29  Greece 1896 18 August 2004
30  Republic of Ireland 1889 21 August 2002

Highest rated matches [edit]

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 4211  Netherlands 2100  Spain 2111 0 : 1 2010-07-10 World Cup F South Africa Johannesburg
2 4161  West Germany 1995  Hungary 2166 3 : 2 1954-07-04 World Cup F Switzerland Bern
3 4158  Netherlands 2050  Brazil 2108 2 : 1 2010-07-02 World Cup QF South Africa Port Elizabeth
4 4150  Brazil 2061  Netherlands 2089 0 : 0 2011-06-04 Friendly Brazil Goiânia
5 4148  West Germany 2068  Brazil 2080 0 : 1 1973-06-16 Friendly West Germany Berlin
6 4129  Spain 2085  Germany 2044 1 : 0 2010-07-07 World Cup SF South Africa Durban
7 4119  Brazil 2050  West Germany 2069 1 : 0 1982-03-21 Friendly Brazil Rio de Janeiro
8 4118  Hungary 2108  Brazil 2010 4 : 2 1954-06-27 World Cup QF Switzerland Bern
9 4116  Hungary 2141  Uruguay 1975 4 : 2 1954-06-30 World Cup SF Switzerland Lausanne
10 4113  West Germany 2079  Netherlands 2034 2 : 1 1974-07-07 World Cup F West Germany Munich

History [edit]

This 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

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 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 [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).

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 [edit]

  1. ^ "The World Football Elo Rating System". Eloratings.net. Retrieved 26 February 2012. 
  2. ^ "FIFA/Coca-Cola World Ranking" (Press release). FIFA. 7 November 2012. Retrieved 7 November 2012. 
  3. ^ Arpad E. Elo, The Rating of Chessplayers, Past and Present, Arco, 1978. ISBN 0-668-04721-6.
  4. ^ Arpad Elo, Chess Life, 1962.
  5. ^ About the Chessmetrics Rating System, by Jeff Sonas
  6. ^ Representing West Germany from 1949 to 1990
  7. ^ Combined record of the USSR (1970-1992), the CIS (1992), and Russia national football teams (1992-present)
  8. ^ Combined record of Czechoslovakia (1970-1992) and Czech national football teams (1993-present)
  9. ^ Combined record of Yugoslavia (1970-1992), Serbia and Montenegro (1994-2006) and Serbia national football teams (2006-present)
  10. ^ Including current leader period up to 1 August 2012

External links [edit]