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 modified version of the Elo formula. The FIFA men's ranking, however, uses a non-Elo formula.

Top 100 ranking

Current table, as of 28 April 2013, of the World Football Elo rankings, compiled by the World Football Elo Ratings web site.

Each national team's FIFA World Rankings as of 9 May 2013.

Elo Rank	Nation	Points	Confederation	FIFA Rank
1	Spain	2125	UEFA	1
2	Germany	2037	UEFA	2
3	Brazil	2017	CONMEBOL	19
4	Argentina	1991	CONMEBOL	3
5	Netherlands	1977	UEFA	9
6	England	1924	UEFA	7
7	Italy	1896	UEFA	8
8	Croatia	1885	UEFA	4
9	Russia	1868	UEFA	11
10	Colombia	1867	CONMEBOL	6
11	Ecuador	1862	CONMEBOL	10
12	Portugal	1860	UEFA	5
13	Mexico	1851	CONCACAF	16
	Sweden	1851	UEFA	24
15	France	1846	UEFA	18
16	Ivory Coast	1823	CAF	12
17	Chile	1796	CONMEBOL	23
18	Uruguay	1790	CONMEBOL	17
19	Switzerland	1789	UEFA	14
20	Belgium	1785	UEFA	15
21	Japan	1782	AFC	30
22	Denmark	1770	UEFA	20
23	Greece	1769	UEFA	13
24	Bosnia and Herzegovina	1762	UEFA	21
25	United States	1747	CONCACAF	29
26	Ukraine	1741	UEFA	37
27	South Korea	1740	AFC	42
28	Czech Republic	1739	UEFA	25
29	Australia	1732	AFC	47
30	Peru	1729	CONMEBOL	32
31	Republic of Ireland	1712	UEFA	39
32	Romania	1711	UEFA	34
33	Venezuela	1710	CONMEBOL	36
34	Nigeria	1701	CAF	28
	Paraguay	1701	CONMEBOL	44
36	Panama	1698	CONCACAF	38
37	Norway	1683	UEFA	31
38	Serbia	1674	UEFA	40
	Costa Rica	1674	CONCACAF	48
40	Ghana	1670	CAF	22
41	Hungary	1663	UEFA	33
42	Montenegro	1659	UEFA	27
43	Egypt	1658	CAF	68
44	Turkey	1655	UEFA	44
45	Iran	1651	AFC	57
46	Honduras	1650	CONCACAF	50
	Poland	1650	UEFA	63
48	Bulgaria	1645	UEFA	52
49	Israel	1632	UEFA	59
50	Finland	1622	UEFA	83

Elo Rank	Nation	Points	Confederation	FIFA Rank
51	Mali	1621	CAF	26
52	Uzbekistan	1608	AFC	66
	New Zealand	1608	OFC	87
54	Bolivia	1607	CONMEBOL	58
55	United Arab Emirates	1604	AFC	89
56	China PR	1600	AFC	98
57	North Korea	1588	AFC	115
58	Austria	1587	UEFA	71
59	Iraq	1586	AFC	97
60	Scotland	1585	UEFA	78
61	Tunisia	1584	CAF	41
62	Cameroon	1580	CAF	62
63	Wales	1578	UEFA	49
64	Belarus	1574	UEFA	69
65	Slovakia	1565	UEFA	54
66	South Africa	1562	CAF	56
67	Jamaica	1549	CONCACAF	53
68	Libya	1546	CAF	65
	Canada	1546	CONCACAF	80
70	Kuwait	1545	AFC	113
71	Zambia	1543	CAF	46
72	Burkina Faso	1539	CAF	50
73	Jordan	1533	AFC	76
74	Slovenia	1527	UEFA	55
75	El Salvador	1522	CONCACAF	85
	Uganda	1522	CAF	91
77	Senegal	1521	CAF	76
78	Algeria	1520	CAF	35
	Oman	1520	AFC	102
80	Morocco	1508	CAF	74
	Syria	1508	AFC	138
82	Albania	1507	UEFA	43
83	Macedonia	1504	UEFA	84
	Saudi Arabia	1504	AFC	108
85	Guinea	1500	CAF	70
86	Gabon	1490	CAF	80
87	Georgia	1489	UEFA	96
88	Iceland	1483	UEFA	73
89	Guatemala	1480	CONCACAF	94
90	Armenia	1474	UEFA	90
91	Latvia	1472	UEFA	110
92	Estonia	1468	UEFA	92
	Qatar	1468	AFC	102
94	Angola	1462	CAF	93
95	Bahrain	1456	AFC	117
96	Congo DR	1454	CAF	77
97	Cape Verde	1442	CAF	75
	Lithuania	1442	UEFA	111
99	Togo	1430	CAF	72
100	Cuba	1422	CONCACAF	87

Strongest teams since the mid to late 1960s

Time averaged Elo or Elo-like scores are routinely used to compare chess player strengths. The following is a list of the national teams with the highest average Elo score from 1 January 1970 to 1 May 2013. Before this time intercontinental play was fairly limited and many nations in Africa, North America, and Asia had played too few games yet to create a representative Elo score. Since Elo scores reflect past accomplishments, the table represents the relative strength of national teams since the mid to late 1960s.

Rank Country Avg Elo 1 Brazil 2010.7 2 (West) Germany 1974.2 3 Italy 1923.5 4 Netherlands 1923.2 5 England 1922.8 6 Spain 1905.4 7 Argentina 1900.4 8 France 1881.8 9 USSR → Russia 1852.8 10 Czechoslovakia/Czechia 1834.4 11 Yugoslavia → Serbia 1819.4 12 Portugal 1815.4 13 Sweden 1798.2 14 Romania 1782.9 15 Poland 1775.4 16 Mexico 1774.4 17 Uruguay 1769.9 18 Belgium 1760.3

Rank Country Avg Elo 19 Denmark 1757.4 20 Scotland 1740.7 21 Paraguay 1727.8 22 Republic of Ireland 1721.0 23 Chile 1713.7 24 Bulgaria 1710.3 25 Australia 1695.6 26 Austria 1689.6 27 Hungary 1686.2 28 Switzerland 1683.3 29 Colombia 1677.7 30 Iran 1675.8 31 South Korea 1665.2 32 Wales 1655.7 33 Egypt 1654.4 34 Greece 1652.4 35 Nigeria 1650.6

Rank Country Avg Elo 36 Morocco 1647.1 37 Israel 1644.3 38 Peru 1642.2 39 Cameroon 1639.2 40 Norway 1637.9 41 Ivory Coast 1633.9 42 Turkey 1633.3 43 Northern Ireland 1613.3 44 Ghana 1609.2 45 Tunisia 1603.7 46 United States 1598.6 47 Iraq 1597.4 48 Costa Rica 1593.9 49 Japan 1587.0 50 Ecuador 1576.8 51 Algeria 1569.1 52 Zambia 1561.2

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
5 Jun 1999	Brazil	389
28 Jun 2000	France	708
6 Jun 2002	Argentina	1
7 Jun 2002	France	4
11 Jun 2002	Netherlands	1
12 Jun 2002	Spain	4
16 Jun 2002	Netherlands	5
21 Jun 2002	Brazil	351
7 Jun 2003	Netherlands	4
11 Jun 2003	Brazil	8
19 Jun 2003	Netherlands	83
10 Sep 2003	France	291
27 Jun 2004	Czech Republic	4

Start Date	Nation	# of days
1 Jul 2004	France	10
11 Jul 2004	Brazil	3
14 Jul 2004	France	35
18 Aug 2004	Argentina	290
4 Jun 2005	Czech Republic	4
8 Jun 2005	Argentina	21
29 Jun 2005	Brazil	102
9 Oct 2005	Netherlands	3
12 Oct 2005	Brazil	265
4 Jul 2006	Italy	43
16 Aug 2006	France	52
7 Oct 2006	Brazil	122
6 Feb 2007	France	1

Start Date	Nation	# of days
7 Feb 2007	Brazil	140
27 Jun 2007	France	14
11 Jul 2007	Argentina	4
15 Jul 2007	Brazil	334
13 Jun 2008	Brazil / Netherlands	2
15 Jun 2008	Netherlands	6
21 Jun 2008	Spain	368
24 Jun 2009	Brazil	373
2 Jul 2010	Netherlands	1
3 Jul 2010	Netherlands / Spain	3
6 Jul 2010	Netherlands	1
7 Jul 2010	Spain	Current

Ranking by days as leader since 1 January 2000 (as of 1 August 2012)

Nation	# of days	Last Date as Leader
Brazil	1878	1 July 2010
Spain	1131	Current
France	1115	10 July 2007
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	Soviet Union	2022	9 October 1983
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	East Germany	1949	22 June 1974
22	Mexico	1936	19 June 2005
23	Paraguay	1932	21 February 1954
24	Chile	1918	12 July 2011
25	Belgium	1916	9 September 1981
26	Norway	1913	13 June 2000
27	Colombia	1912	5 June 1994
28	Romania	1908	9 June 1990
29	Greece	1896	18 August 2004
30	Republic of Ireland	1889	21 August 2002

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	2010-07-10	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	Goiânia
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, now maintained by Kirill Bulygin.

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
• Elo rating system
• Unofficial Football World Championships
• Statistical association 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)
• Excel implementation of World Football Elo rating, very useful for amateur fussball (kicker) championships