World Football Elo Ratings

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The World Football Elo Ratings (Elo is pronounced E.L.O. despite not being an acronym) 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 more prevalent FIFA World Rankings, which is the rating system used by FIFA, the international governing body of football.

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.

1 Top 20 ranking
2 Top 10 since 1970
3 List of number one teams
4 History
5 Overview
6 Basic calculation principles
7 See also
8 External links

[edit] Top 20 ranking

Current table, as of March 28, 2007, of the World Football Elo rankings, compiled by the World Football Elo Ratings web site based on data provided by Advanced Satellite Consulting.

Elo rank	Nation	Points	FIFA rank
1	Brazil	2042	3
2	France	2025	4
3	Italy	1998	2
4	Argentina	1971	1
5	Germany	1960	5
6	Netherlands	1959	7
7	England	1910	6
8	Portugal	1894	8
9	Spain	1888	10
10	Croatia	1876	12
11	Denmark	1858	22
12	Romania	1850	14
13	Czech Republic	1847	9
14	Turkey	1832	27
15	Uruguay	1831	26
16	Mexico	1811	21
17	Switzerland	1800	17
18	Ukraine	1784	11
19	USA	1782	30
20	Côte d'Ivoire	1778	20

[edit] Top 10 since 1970

The following is a list of the national teams with the highest average Elo score since Jan 1, 1970. 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]
1	Brazil	2003.7
2	Germany^[2]	1972.3
3	Italy	1925.2
4	England	1922.0
5	Netherlands	1908.7
6	Argentina	1891.9
7	France	1884.6
8	Spain	1880.2
9	USSR^[3]	1859.0
10	Czechoslovakia^[4]	1844.8

^ updated to April 1 2007
^ Includes the record of West Germany
^ Includes the record of Russia
^ Includes the record of the Czech Republic

[edit] 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 since 2000:

Start Date	Nation	# of days
June 28, 2000	France	708
June 06, 2002	Argentina	1
June 07, 2002	France	4
June 11, 2002	Netherlands	1
June 12, 2002	Spain	4
June 16, 2002	Netherlands	5
June 21, 2002	Brazil	351
June 07, 2003	Netherlands	4
June 11, 2003	Brazil	8
June 19, 2003	Netherlands	83
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	-

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

[edit] 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.

[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
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 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.

[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 formulas:

$R n = R o + K G (W - W e)$

$P = K G (W - W e)$

Where;


$R n$	= The new team rating
$R o$	= 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
$W e$	= 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

$G = \frac{1}{1}$

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

W_e 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
$W e$	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
$W e$	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] See also

[edit] External links

International football

v • d • e

Asia: AFC – Asian Cup

Africa: CAF – African Cup of Nations

North America: CONCACAF – Gold Cup

South America: CONMEBOL – Copa América

Oceania: OFC – Nations Cup

Europe: UEFA – European Championship

Non-FIFA: NF-Board – VIVA World Cup

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Categories: Football (soccer) rankings | Rating systems