World Football Elo Ratings

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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. 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 40 ranking
2 Top 10 since 1970
3 List of number one teams
4 Ranking by Days as Leader since January 1, 2000
5 All-time highest ratings
6 History
7 Overview
8 Basic calculation principles
9 Notes
10 See also
11 External links

Top 40 ranking

Current table, as of October 15, 2008, 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	Federation	FIFA rank
1	Spain	2068	UEFA	1
2	Netherlands	1996	UEFA	5
3	Brazil	1988	CONMEBOL	4
4	Italy	1980	UEFA	2
5	Germany	1951	UEFA	3
6	Argentina	1946	CONMEBOL	7
6	England	1946	UEFA	14
8	France	1869	UEFA	11
9	Croatia	1855	UEFA	6
10	Russia	1853	UEFA	9
11	Mexico	1831	CONCACAF	24
11	Paraguay	1831	CONMEBOL	22
13	Czech Republic	1816	UEFA	8
14	Uruguay	1805	CONMEBOL	20
15	Denmark	1803	UEFA	31
16	Romania	1801	UEFA	18
17	Portugal	1799	UEFA	10
18	Turkey	1793	UEFA	13
19	United States	1784	CONCACAF	21
20	Chile	1781	CONMEBOL	36

Elo rank	Nation	Points	Federation	FIFA rank
21	Iran	1776	AFC	48
22	Bulgaria	1767	UEFA	15
23	Cameroon	1760	CAF	12
24	Switzerland	1759	UEFA	45
25	Republic of Ireland	1755	UEFA	38
26	Egypt	1754	CAF	22
27	Greece	1746	UEFA	17
28	Ukraine	1745	UEFA	19
29	Nigeria	1741	CAF	27
29	Serbia	1741	UEFA	40
31	Sweden	1735	UEFA	28
32	Japan	1734	AFC	32
33	Australia	1729	AFC	34
34	Israel	1720	UEFA	16
35	Colombia	1717	CONMEBOL	33
36	Côte d'Ivoire	1710	CAF	29
37	Poland	1699	UEFA	30
38	Scotland	1697	UEFA	26
39	Ecuador	1695	CONMEBOL	42
39	Saudi Arabia	1695	AFC	51

Each national team's FIFA World Ranking is of October 8, 2008. [1]

Top 10 since 1970

The following is a list of the national teams with the highest average Elo score from Jan 1, 1970 to Oct 1, 2008. 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	2005.1
2	Germany^[1]	1971.3
3	Italy	1927.9
4	England	1921.1
5	Netherlands	1910.6
6	Argentina	1895.8
7	France	1888.3
8	Spain	1882.7
9	Russia^[2]	1855.7
10	Czech Republic^[3]	1845.6

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	Italy	2079	20 July 1939
7	Spain	2068	15 October 2008
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	Serbia	1962	25 June 1998 (as Federal Republic of Yugoslavia)
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:

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.

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

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

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.

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
$K$	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

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