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 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 31 January 2012, of the World Football Elo rankings, compiled by the World Football Elo Ratings web site.

Each national team's FIFA World Rankings as of 18 January 2012.[2]

Elo Rank Nation Points Confederation FIFA Rank
1  Spain 2093 UEFA 1
2  Germany 2057 UEFA 3
3  Netherlands 2042 UEFA 2
4  Brazil 2039 CONMEBOL 6
5  Uruguay 1968 CONMEBOL 4
6  England 1926 UEFA 5
7  Argentina 1893 CONMEBOL 10
8  Portugal 1874 UEFA 7
9  Croatia 1865 UEFA 8
10  Chile 1862 CONMEBOL 13
11  Italy 1861 UEFA 9
12  Mexico 1853 CONCACAF 21
13  Sweden 1836 UEFA 18
14  Côte d'Ivoire 1831 CAF 16
15  France 1811 UEFA 15
16  Australia 1803 AFC 23
17  Denmark 1800 UEFA 11
18  Japan 1789 AFC 19
19  Russia 1788 UEFA 12
20  Ghana 1780 CAF 29
21  Republic of Ireland 1775 UEFA 22
22  Czech Republic 1765 UEFA 33
23  Paraguay 1763 CONMEBOL 24
24  Greece 1759 UEFA 14
25  Ecuador 1758 CONMEBOL 42
26  South Korea 1755 AFC 32
27  Colombia 1746 CONMEBOL 36
28  Ukraine 1740 UEFA 55
29  Switzerland 1737 UEFA 17
30  Iran 1733 AFC 45
Elo Rank Nation Points Confederation FIFA Rank
31  Norway 1732 UEFA 25
 Peru 1732 CONMEBOL 35
33  Turkey 1718 UEFA 28
34  Egypt 1716 CAF 31
35  United States 1711 CONCACAF 34
36  Serbia 1696 UEFA 27
37  Romania 1683 UEFA 56
38  Poland 1682 UEFA 66
39  Venezuela 1680 CONMEBOL 39
40  Scotland 1674 UEFA 47
41  Bosnia and Herzegovina 1666 UEFA 20
42  Belgium 1656 UEFA 41
43  Nigeria 1653 CAF 43
44  Israel 1647 UEFA 37
45  Hungary 1645 UEFA 37
46  Costa Rica 1644 CONCACAF 65
47  Cameroon 1642 CAF 50
48  Panama 1639 CONCACAF 49
49  Honduras 1636 CONCACAF 53
50  Jamaica 1626 CONCACAF 54
51  Slovenia 1625 UEFA 26
52  Wales 1618 UEFA 48
53  China PR 1603 AFC 71
54  Bulgaria 1595 UEFA 84
55  Montenegro 1594 UEFA 51
56  Uzbekistan 1588 AFC 75
57  South Africa 1585 CAF 52
 Tunisia 1585 CAF 59
59  Finland 1584 UEFA 85
60  Canada 1578 CONCACAF 74

[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 January 1, 2012. 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 2010.0
2  Germany[3] 1972.3
3  Italy 1925.1
4  England 1922.5
5  Netherlands 1921.2
6  Argentina 1898.8
7  Spain 1898.7
8  France 1883.2
9  Russia[4] 1853.4
10  Czech Republic[5] 1836.9

[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
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 335

[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 [6] 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 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  Russia 2022 9 October 1983 (as Soviet Union)
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  Mexico 1936 19 June 2005
22  Paraguay 1932 21 February 1954
23  Chile 1918 12 July 2011
24  Belgium 1916 9 September 1981
25  Norway 1913 13 June 2000

[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 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 Goiania
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

[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:

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 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

[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/Coca-Cola World Ranking" (Press release). FIFA. 18 January 2012. http://www.fifa.com/worldfootball/ranking/lastranking/gender=m/fullranking.html. Retrieved 2011-10-20. 
  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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