# World Football Elo Ratings: Wikis

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# Encyclopedia

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

## Top 60 ranking

Current table, as of January 14, 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 16 December 2009.[2]

Elo Rank Nation Points Confederation FIFA Rank
1  Brazil 2081 CONMEBOL 2
2  Spain 2067 UEFA 1
3  Netherlands 2002 UEFA 3
4  England 1957 UEFA 9
5  Germany 1933 UEFA 6
6  Italy 1928 UEFA 4
7  Argentina 1876 CONMEBOL 8
8  Mexico 1875 CONCACAF 17
9  France 1863 UEFA 7
10  Croatia 1861 UEFA 10
11  Chile 1858 CONMEBOL 15
12  Portugal 1843 UEFA 5
13  Russia 1822 UEFA 12
14  Serbia 1805 UEFA 19
15  Uruguay 1793 CONMEBOL 20
16  United States 1784 CONCACAF 14
17  Côte d'Ivoire 1781 CAF 16
18  Japan 1777 AFC 43
19  Denmark 1774 UEFA 28
20  Switzerland 1764 UEFA 18
21  Australia 1762 AFC 21
22  Greece 1757 UEFA 13
Turkey 1757 UEFA 41
24  Ukraine 1756 UEFA 22
25  Romania 1743 UEFA 36
Sweden 1743 UEFA 42
27  Egypt 1739 CAF 24
Paraguay 1739 CONMEBOL 29
29  Colombia 1738 CONMEBOL 39
30  Republic of Ireland 1735 UEFA 35
Elo rank Nation Points Federation FIFA rank
31  Cameroon 1732 CAF 11
32  Honduras 1729 CONCACAF 37
33  Bulgaria 1721 UEFA 30
Norway 1721 UEFA 32
35  Czech Republic 1718 UEFA 25
36  Korea Republic 1709 AFC 52
37  Venezuela 1702 CONMEBOL 50
39  Nigeria 1693 CAF 22
40  Israel 1689 UEFA 26
41  Costa Rica 1685 CONCACAF 44
42  Saudi Arabia 1672 AFC 63
43  Iran 1653 AFC 64
44  Finland 1651 UEFA 55
45  Ghana 1646 CAF 34
46  Scotland 1642 UEFA 46
47  Slovenia 1641 UEFA 31
48  Slovakia 1636 UEFA 33
49  Bosnia and Herzegovina 1615 UEFA 51
50  Bahrain 1611 AFC 60
51  Montenegro 1607 UEFA 74
52  Jamaica 1606 CONCACAF 81
53  Poland 1605 UEFA 58
54  Tunisia 1596 CAF 53
55  Oman 1590 AFC 79
57  Bolivia 1579 CONMEBOL 56
58  Hungary 1578 UEFA 54
59  Wales 1577 UEFA 77
60  Morocco 1567 CAF 67
Peru 1567 CONMEBOL 68
Locations of top 60 teams as of June 24, 2009.

## Top 10 since 1970

The following is a list of the national teams with the highest average Elo score from January 1, 1970 to January 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 2007.1
2  Germany[3] 1970.8
3  Italy 1929.2
4  England 1923.1
5  Netherlands 1914.4
6  Argentina 1897.4
7  Spain 1889.1
8  France 1888.3
9  Russia[4] 1856.6
10  Czechoslovakia[5] 1844.4

## 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 in the last five years:

Start Date Nation # of days
August 18, 2004  Argentina 290
June 04, 2005  Czech Republic 4
June 08, 2005  Argentina 21
June 29, 2005  Brazil 102
October 09, 2005  Netherlands 3
October 12, 2005  Brazil 265
July 04, 2006  Italy 43
August 16, 2006  France 52
October 07, 2006  Brazil 122
February 06, 2007  France 1
February 07, 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 -

Complete list since 1872: see World Football Elo Ratings leaders.

## Ranking by days as leader since January 1, 2000

Nation # of days Last Date as Leader
Brazil 1505 [6] 14 June 2008
France 1115 10 July 2007
Spain 372 June 24 2009
Argentina 316 14 July 2007
Netherlands 104 20 June 2008
Italy 43 15 August 2006
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.

Rank Nation Points Date
1  Hungary 2166 30 June 1954
2  Brazil 2153 17 June 1962
3  Argentina 2117 3 April 1957
4  France 2106 15 August 2001
5  Spain 2104 20 June 2009
6  Germany 2099 4 September 1974 (as West Germany)
7  Italy 2079 20 July 1939
8  Netherlands 2067 3 June 1978
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

## 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.

## 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

A large difference here is that FIFA ranks the Confederations Cup third highest while the Elo system ranks it joint second (treating Continental and World Cup qualifiers separately for the purposes of comparison, because FIFA does).

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:

Rn = Ro + KG(WWe)

or

P = KG(WWe)

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

### 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 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 We 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 We 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

1. ^ The World Football Elo Rating System
2. ^ FIFA (16 Dec 2009). "FIFA/Coca-Cola World Ranking". Press release. Retrieved 2009-12-29.
3. ^ Includes the record of West Germany (1949-1990)
4. ^ Includes the record of USSR
5. ^ Includes the record of the Czechoslovakia
6. ^ Does not include current period as rankings leader