World Football Elo Ratings

The World Football Elo Ratings (Elo is often pronounced E-L-O despite not being an initialism) 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 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. Ratings for teams with fewer than 30 matches should be considered provisional.

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

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World Football Elo Ratings

The World Football Elo Ratings (Elo is often pronounced E-L-O despite not being an initialism) 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 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. Ratings for teams with fewer than 30 matches should be considered provisional.

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

Contents

[edit] Top 60 ranking

Current table, as of 5 September 2010, of the World Football Elo rankings, compiled by the World Football Elo Ratings web site.

Each national team's FIFA World Ranking as of 11 August 2010.

Elo Rank Nation Points Confederation FIFA Rank
1  Spain 2135 UEFA 1
2  Brazil 2079 CONMEBOL 3
3  Netherlands 2066 UEFA 2
4  Germany 2035 UEFA 4
5  Argentina 1947 CONMEBOL 5
6  England 1903 UEFA 7
7  Croatia 1878 UEFA 14
8  Uruguay 1864 CONMEBOL 6
9  Chile 1858 CONMEBOL 10
10  Portugal 1842 UEFA 8
11  Mexico 1829 CONCACAF 25
12  Russia 1823 UEFA 16
13  Italy 1819 UEFA 11
14  Egypt 1810 CAF 9
15  Turkey 1791 UEFA 28
16  Sweden 1787 UEFA 35
17  Ukraine 1783 UEFA 24
18  Côte d'Ivoire 1773 CAF 26
19  Serbia 1770 UEFA 13
20  Switzerland 1761 UEFA 17
21  Paraguay 1760 CONMEBOL 15
22  Australia 1755 AFC 20
23  Japan 1754 AFC 32
24  Ghana 1752 CAF 23
25  Republic of Ireland 1743 UEFA 36
26  United States 1742 CONCACAF 18
27  Norway 1741 UEFA 22
 Colombia 1741 CONMEBOL 36
29  Korea Republic 1734 AFC 44
30  Czech Republic 1728 UEFA 31
Elo Rank Nation Points Confederation FIFA Rank
31  France 1711 UEFA 21
32  Ecuador 1710 CONMEBOL 58
33  Denmark 1705 UEFA 29
34  Israel 1697 UEFA 38
35  Romania 1696 UEFA 42
36  Greece 1684 UEFA 12
 Iran 1684 AFC 65
38  Bulgaria 1680 UEFA 43
39  Saudi Arabia 1679 AFC 70
40  Honduras 1672 CONCACAF 46
41  Venezuela 1669 CONMEBOL 47
42  Nigeria 1663 CAF 30
43  Slovakia 1662 UEFA 27
44  Costa Rica 1660 CONCACAF 53
45  Slovenia 1654 UEFA 19
46  Cameroon 1651 CAF 40
47  Scotland 1643 UEFA 41
48  Poland 1628 UEFA 56
49  China PR 1622 AFC 77
50  South Africa 1620 CAF 66
 Belarus 1620 UEFA 78
52  Jamaica 1617 CONCACAF 82
53  Bosnia and Herzegovina 1615 UEFA 57
54  Montenegro 1600 UEFA 73
55  Finland 1590 UEFA 51
56  Peru 1587 CONMEBOL 39
57  New Zealand 1586 OFC 54
58  Tunisia 1577 CAF 64
59  Bolivia 1574 CONMEBOL 50
60  Senegal 1572 CAF 91

[edit] Top 10 since 1970

The following is a list of the national teams with the highest average Elo score from January 1, 1970 to September 1, 2010. See Strongest football nations by Elo Ratings for a top 50 and for tables of the Strongest teams per decade since 1910.

Rank Country Average Elo rating
1  Brazil 2008.4
2  Germany 1970.5
3  Italy 1928.6
4  England 1923.4
5  Netherlands 1916.2
6  Argentina 1897.6
7  Spain 1892.3
8  France 1887.2
9  Russia 1856.0
10  Czech Republic 1842.3

[edit] List of number one teams

Main article: World Football Elo Ratings leaders

The following is the list of nations who have achieved the number one position on the World Football Elo Ratings in the last five years:

Start Date Nation # of days
June 29, 2005  Brazil 102
October 9, 2005  Netherlands 3
October 12, 2005  Brazil 265
July 4, 2006  Italy 43
August 16, 2006  France 52
October 7, 2006  Brazil 122
February 6, 2007  France 1
February 7, 2007  Brazil 140
June 27, 2007  France 14
July 11, 2007  Argentina 4
July 15, 2007  Brazil 334
June 13, 2008  Brazil /  Netherlands 2
June 15, 2008  Netherlands 6
June 21, 2008  Spain 368
June 24, 2009  Brazil 373
July 2, 2010  Netherlands 1
July 3, 2010  Netherlands /  Spain 3
July 6, 2010  Netherlands 1
July 7, 2010  Spain -

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

Nation # of days Last Date as Leader
 Brazil 1878 1 July 2010
 France 1115 10 July 2007
 Spain 375 Current
 Argentina 316 14 July 2007
 Netherlands 109 6 July 2010
 Italy 43 15 August 2006
 Czech Republic 8 7 June 2005

[edit] All-time highest ratings

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 2106 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  Russia 2023 9 October 1983 (as Soviet Union)
13  Czech Republic 1999 27 June 2004
14  Austria 1998 31 May 1934
15  Portugal 1983 15 November 2000
16  Croatia 1967 11 July 1998
17  Serbia 1962 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  Mexico 1936 19 June 2005
22  Paraguay 1932 21 February 1954
23  Belgium 1916 9 September 1981
24  Norway 1914 13 June 2000
=25  Colombia 1911 20 February 1994 & 5 June 1994
=25  Romania 1911 9 June 1990

[edit] 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 4211  Netherlands 2100  Spain 2111 0 : 1 2010-07-11 World Cup F South Africa Johannesburg
2 4161  West Germany 1995  Hungary 2166 3 : 2 1954-07-04 World Cup F Switzerland Bern
3 4157  Netherlands 2050  Brazil 2107 2 : 1 2010-07-02 World Cup QF South Africa Cape Town
4 4148  West Germany 2068  Brazil 2080 0 : 1 1973-06-16 Friendly West Germany Berlin
5 4129  Spain 2085  Germany 2044 1 : 0 2010-07-10 World Cup SF South Africa Durban
6 4119  Brazil 2050  West Germany 2069 1 : 0 1982-03-21 Friendly Brazil Rio de Janeiro
7 4118  Hungary 2108  Brazil 2010 4 : 2 1954-06-27 World Cup QF Switzerland Bern
8 4116  Hungary 2141  Uruguay 1975 4 : 2 1954-06-30 World Cup SF Switzerland Lausanne
9 4113  West Germany 2079  Netherlands 2034 2 : 1 1974-07-07 World Cup F West Germany Munich
10 4108  Brazil 2015  West Germany 2093 1 : 1 1977-06-12 Friendly Brazil Rio de Janeiro

[edit] History

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.

[edit] 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:

  • World Cup Finals
  • Continental championships finals and Intercontinental tournaments
  • World Cup and Continental championship qualifiers
  • All other tournaments
  • Friendly matches

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.

[edit] 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:

Rn = Ro + KG(W − We)

or

P = KG(W − We)

Where;

Rn = The new team rating
Ro = 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
We = The expected result
P = Points Change

[edit] 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

[edit] 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 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

[edit] Result of match

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

[edit] 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.

[edit] 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:

[edit] Example 1

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
We 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

[edit] 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:

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
We 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.

[edit] Notes

  1. The World Football Elo Rating System
  2. FIFA (14 July 2010). "FIFA/Coca-Cola World Ranking". Press release. http://www.fifa.com/worldfootball/ranking/lastranking/gender=m/fullranking.html. Retrieved 2010-07-14. 
  3. Includes the record of West Germany (1949-1990)
  4. Includes the record of USSR
  5. Includes the record of Czechoslovakia
  6. Does not include current period as rankings leader

[edit] See also

[edit] External links

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