World Football Elo Ratings

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. 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 9 March 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 7 March 2012.

Elo Rank	Change	Nation	Points	Confederation	FIFA Rank
1		Spain	2095	UEFA	1
2		Netherlands	2052	UEFA	2
3		Brazil	2041	CONMEBOL	5
4		Germany	2039	UEFA	3
5		Uruguay	1963	CONMEBOL	4
6		England	1916	UEFA	6
7		Argentina	1906	CONMEBOL	8
8		Portugal	1871	UEFA	7
9		Sweden	1856	UEFA	17
10		Croatia	1845	UEFA	10
		Italy	1845	UEFA	9
12		Chile	1843	CONMEBOL	14
13		Mexico	1834	CONCACAF	22
14		France	1829	UEFA	16
15		Côte d'Ivoire	1825	CAF	15
16		Australia	1810	AFC	20
17		Russia	1808	UEFA	12
18		Paraguay	1784	CONMEBOL	25
19		Denmark	1780	UEFA	11
20		Republic of Ireland	1772	UEFA	19
21		Czech Republic	1768	UEFA	29
		South Korea	1768	AFC	30
23		Colombia	1765	CONMEBOL	31
		Ecuador	1765	CONMEBOL	39
25		Japan	1757	AFC	33
26		Greece	1754	UEFA	13
27		Ukraine	1750	UEFA	49
28		Norway	1740	UEFA	24
29		Peru	1730	CONMEBOL	34
30		United States	1727	CONCACAF	27

Elo Rank	Change	Nation	Points	Confederation	FIFA Rank
31		Switzerland	1724	UEFA	18
32		Iran	1713	AFC	51
33		Egypt	1711	CAF	64
34		Turkey	1702	UEFA	31
35		Serbia	1698	UEFA	26
36		Romania	1688	UEFA	53
37		Ghana	1686	CAF	23
38		Poland	1685	UEFA	75
39		Venezuela	1678	CONMEBOL	46
40		Scotland	1675	UEFA	51
41		Bosnia and Herzegovina	1664	UEFA	21
42		Belgium	1661	UEFA	40
43		Costa Rica	1656	CONCACAF	59
44		Cameroon	1647	CAF	66
45		Nigeria	1645	CAF	57
46		Jamaica	1643	CONCACAF	54
47		Hungary	1641	UEFA	37
		Zambia	1641	CAF	41
49		Israel	1637	UEFA	38
50		Panama	1635	CONCACAF	50
51		Honduras	1629	CONCACAF	63
		China PR	1629	AFC	68
53		Slovenia	1624	UEFA	28
54		Uzbekistan	1617	AFC	67
55		Wales	1606	UEFA	48
56		Bulgaria	1599	UEFA	85
57		Montenegro	1597	UEFA	44
58		Mali	1588	CAF	42
59		South Africa	1581	CAF	60
60		Iraq	1576	AFC	76

Top 10 since 1970

The following is a list of the national teams with the highest average Elo score from 1 January 1970 to 1 March 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	2010.1
2	Germany	1972.7
3	Italy	1924.8
4	England	1922.5
5	Netherlands	1921.6
6	Spain	1899.5
7	Argentina	1898.8
8	France	1882.9
9	Russia	1853.2
10	Czech Republic	1836.6

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
7 February 2007	Brazil	140
27 June 2007	France	14
11 July 2007	Argentina	4
15 July 2007	Brazil	334
13 June 2008	Brazil / Netherlands	2
15 June 2008	Netherlands	6
21 June 2008	Spain	368
24 June 2009	Brazil	373
2 July 2010	Netherlands	1
3 July 2010	Netherlands / Spain	3
6 July 2010	Netherlands	1
7 July 2010	Spain	Current

Ranking by days as leader since 1 January 2000

Nation	# of days	Last Date as Leader
Brazil	1878	1 July 2010
France	1115	10 July 2007
Spain	375	Current
Argentina	316	14 July 2007
Netherlands	109	6 July 2010
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	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

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	Johannesburg
2	4161	West Germany	1995	Hungary	2166	3 : 2	1954-07-04	World Cup F	Bern
3	4158	Netherlands	2050	Brazil	2108	2 : 1	2010-07-02	World Cup QF	Port Elizabeth
4	4150	Brazil	2061	Netherlands	2089	0 : 0	2011-06-04	Friendly	Goiania
5	4148	West Germany	2068	Brazil	2080	0 : 1	1973-06-16	Friendly	Berlin
6	4129	Spain	2085	Germany	2044	1 : 0	2010-07-07	World Cup SF	Durban
7	4119	Brazil	2050	West Germany	2069	1 : 0	1982-03-21	Friendly	Rio de Janeiro
8	4118	Hungary	2108	Brazil	2010	4 : 2	1954-06-27	World Cup QF	Bern
9	4116	Hungary	2141	Uruguay	1975	4 : 2	1954-06-30	World Cup SF	Lausanne
10	4113	West Germany	2079	Netherlands	2034	2 : 1	1974-07-07	World Cup F	Munich

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.

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

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.

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:

$R_n = R_o + K G (W - W_e)$

or

$P = K G (W - W_e)$

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 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

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

Note that Team B loses more ranking points by losing to Team C than by losing to Team A.

See also

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

External links

• World Football Elo ratings
• How the rankings are calculated
• Interactive Map of World Football Elo ratings
• FootballDatabase's World Club Ratings (using Elo Formula)