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 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 November 1, 2009, 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 October 2009.^[2]

Elo Rank Nation Points Confederation FIFA Rank 1  Brazil 2072 CONMEBOL 1 2  Spain 2061 UEFA 2 3  Netherlands 2011 UEFA 3 4  England 1964 UEFA 7 5  Germany 1940 UEFA 5 6  Italy 1925 UEFA 4 7  Argentina 1879 CONMEBOL 6 8  Mexico 1875 CONCACAF 18 9  Croatia 1861 UEFA 8 10  France 1856 UEFA 9 11  Chile 1846 CONMEBOL 17 12  Russia 1845 UEFA 12 13  Portugal 1823 UEFA 10 14  United States 1808 CONCACAF 11 15  Serbia 1791 UEFA 20 16  Uruguay 1784 CONMEBOL 25 17  Ukraine 1781 UEFA 22 18  Switzerland 1779 UEFA 13 19  Japan 1772 AFC 40 20  Czech Republic 1769 UEFA 15 21  Denmark 1766 UEFA 27 22  Paraguay 1760 CONMEBOL 21 23  Turkey 1757 UEFA 39 24  Cameroon 1752 CAF 14 25  Australia 1750 AFC 24 26  Côte d'Ivoire 1748 CAF 19 27  Sweden 1746 UEFA 41 28  Republic of Ireland 1742 UEFA 34 29  Honduras 1741 CONCACAF 35 30  Colombia 1738 CONMEBOL 30

Elo rank Nation Points Federation FIFA rank 31  Korea Republic 1737 AFC 48 32  Romania 1734 UEFA 36  Nigeria 1734 CAF 32 34  Greece 1732 UEFA 16 35  Bulgaria 1718 UEFA 23 36  Egypt 1713 CAF 28 37  Norway 1706 UEFA 37 38  Venezuela 1702 CONMEBOL 51 39  Ecuador 1698 CONMEBOL 44 40  Ghana 1697 CAF 38 41  Costa Rica 1694 CONCACAF 43 42  Israel 1689 UEFA 26 43  Iran 1687 AFC 62 44  Saudi Arabia 1661 AFC 64 45  Tunisia 1660 CAF 54 46  Scotland 1659 UEFA 46 47  Finland 1651 UEFA 57 48  Bosnia and Herzegovina 1635 UEFA 42 49  Slovakia 1631 UEFA 33 50  Slovenia 1618 UEFA 49 51  Bahrain 1616 AFC 61 52  Canada 1608 CONCACAF 53 53  Poland 1607 UEFA 56 54  Jamaica 1606 CONCACAF 69 55  Montenegro 1601 UEFA 75 56  Hungary 1594 UEFA 50 57  Morocco 1592 CAF 63  Oman 1592 AFC 79 59  Bolivia 1579 CONMEBOL 60 60  Syria 1564 AFC 95

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 November 1, 2009. 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	2006.9
2	Germany[3]	1970.9
3	Italy	1929.2
4	England	1922.9
5	Netherlands	1914.1
6	Argentina	1897.5
7	France	1888.4
8	Spain	1888.3
9	Russia[4]	1856.7
10	Czechoslovakia[5]	1844.9

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 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:

• 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:

R_n = R_o + KG(W − W_e)

or

P = KG(W − W_e)

Where;

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;

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

If the game is won by three or more goals

• Where N is the goal difference

Table of examples:

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

W_e 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.

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)

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:

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 (02 Sep 2009). "FIFA/Coca-Cola World Ranking". Press release. http://www.fifa.com/worldfootball/ranking/lastranking/gender=m/fullranking.html. Retrieved 2009-10-16. 
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

See also

• FIFA World Rankings
• FIFA Women's World Rankings
• AQB Sports Ratings
• Aggregated Football World Ranking-List
• Elo rating system
• Unofficial World Champions (soccer)
• Strongest Football Nations by Elo Ratings

External links

• World Football Elo ratings
• How the rankings are calculated

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