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Elo Rating System for football

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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[citation needed]. 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 June 2, 2009, of the World Football Elo rankings, compiled by the World Football Elo Ratings web site.

Each national team's FIFA World Ranking is of May 6, 2009. [1]

Elo Rank Nation Points Confederation FIFA Rank
1  Spain 2092 UEFA 1
2  Netherlands 2001 UEFA 3
3  Brazil 2000 CONMEBOL 4
4  England 1961 UEFA 7
5  Italy 1958 UEFA 5
6  Germany 1929 UEFA 2
7  Argentina 1907 CONMEBOL 6
8  Croatia 1867 UEFA 8
9  Russia 1856 UEFA 9
10  France 1849 UEFA 10
11  Uruguay 1841 CONMEBOL 16
12  Paraguay 1816 CONMEBOL 17
13  United States 1813 CONCACAF 15
14  Denmark 1797 UEFA 29
15  Portugal 1794 UEFA 11
16  Turkey 1784 UEFA 14
17  Serbia 1783 UEFA 23
18   Switzerland 1776 UEFA 18
19  Mexico 1775 CONCACAF 25
 Japan 1775 AFC 35
21  Czech Republic 1771 UEFA 12
22  Ukraine 1769 UEFA 22
23  Bulgaria 1766 UEFA 20
24  Greece 1764 UEFA 13
25  Chile 1756 CONMEBOL 26
26  Republic of Ireland 1755 UEFA 34
27  Sweden 1747 UEFA 33
28  Egypt 1746 CAF 37
29  Romania 1737 UEFA 28
30  Nigeria 1736 CAF 30
Elo rank Nation Points Federation FIFA rank
31  Costa Rica 1724 CONCACAF 41
32  Ivory Coast 1722 CAF 36
33  Cameroon 1718 CAF 19
34  Honduras 1713 CONCACAF 39
 South Korea 1713 AFC 46
36  Colombia 1708 CONMEBOL 44
37  Australia 1707 AFC 32
38  Israel 1704 UEFA 21
 Iran 1704 AFC 53
40  Poland 1703 UEFA 40
41  Ghana 1699 CAF 31
42  Scotland 1689 UEFA 24
43  Norway 1688 UEFA 45
44  Ecuador 1668 CONMEBOL 42
45  Venezuela 1665 CONMEBOL 56
46  Saudi Arabia 1664 AFC 55
47  Finland 1659 UEFA 51
48  Morocco 1638 CAF 50
 Tunisia 1638 CAF 52
50  Bolivia 1632 CONMEBOL 58
51  Jamaica 1615 CONCACAF 70
52  Slovakia 1611 UEFA 47
53  Hungary 1607 UEFA 43
54  Bosnia and Herzegovina 1604 UEFA 38
55  Montenegro 1598 UEFA 117
56  Lithuania 1593 UEFA 59
57  Oman 1591 AFC 81
58  Bahrain 1587 AFC 71
59  Wales 1571 UEFA 73
60  Panama 1566 CONCACAF 60
Locations of top 60 teams as of May 12, 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 May 12, 2009. For a top 50, and top 20 lists per decade since the 1950s, see Strongest Football Nations by Elo Ratings

Rank Country Average Elo rating
1  Brazil 2005.0
2  Germany[1] 1970.7
3  Italy 1928.6
4  England 1921.7
5  Netherlands 1911.9
6  Argentina 1896.6
7  France 1887.9
8  Spain 1885.7
9  Russia[2] 1855.7
10  Czech Republic[3] 1845.0

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
September 10, 2003  France 291
June 27, 2004  Czech Republic 4
July 01, 2004  France 10
July 11, 2004  Brazil 3
July 14, 2004  France 35
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 -

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 14 June 2008
 France 1115 10 July 2007
 Argentina 316 14 July 2007
 Netherlands 104 20 June 2008
 Italy 43 15 August 2006
 Czech Republic 8 7 June 2005
 Spain 4 [4] Current

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 2165 30 June 1954
2  Brazil 2153 17 June 1962
3  Argentina 2117 3 April 1957
4  France 2106 15 August 2001
5  Germany 2098 4 September 1974 (as West Germany)
6  Spain 2092 1 April 2009
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 2022 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  FR Yugoslavia 1962 25 June 1998
18  Denmark 1960 13 June 1986
19  Scotland 1953 10 March 1888
20  Sweden 1950 25 June 1950

History

This system, developed by Hungarian mathematician Dr. Árpád Élő, is used by FIDE, the international chess federation, to rate chess 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:

A large difference here is that FIFA ranks the Confederations Cup third highest while the Elo system ranks it fifth (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:

or

Where;

= The new team rating
= The old team rating
= Weight index regarding the tournament of the match
= A number from the index of goal differences
= The result of the match
= The expected result
= 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

If the game is won by two goals

If the game is won by three or more goals

  • Where N is the goal difference

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:

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)

Team A Team B Team A Team B Team A Team B
Score 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
Total (P) +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:

Team B Team C Team B Team C Team B Team C
Score 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
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.

Notes

  1. ^ Includes the record of West Germany (1949-1990)
  2. ^ Includes the record of USSR
  3. ^ Includes the record of the Czechoslovakia
  4. ^ Does not include current period as rankings leader

See also

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