Elo Rating System for football

The World Football Elo Ratings is a ranking system for men's national teams in association football published by the website eloratings.net. The method used to rank teams is based upon the Elo rating system method but modified to take various football-specific variables into account. These ratings 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. Also this website uses specific numbers and factors in its implementation of the general Elo system. Other Elo rankings are of course possible, thus there is not the Elo ranking for a national team.

The ratings consider 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 system uses a modified version of the Elo formula whereas the FIFA men's ranking system uses a non-Elo formula. A 2009 comparative study of eight methods found that the implementation of the Elo rating system described below had the highest predictive capability for football matches, while the men's FIFA ranking method performed poorly.

Top 60 ranking

The following table shows World Football Elo Ratings on 2 May 2016, using data from the World Football Elo Ratings web site.

Each national team's FIFA World Rankings are shown as they were on 7 April 2016.

	AFC
	CAF
	CONCACAF
	CONMEBOL
	UEFA

Elo Rank	1 Year Change	Team	Points	FIFA Rank
1		Germany	2037	5
2		Argentina	2032	1
3		Brazil	1993	7
4	2	Spain	1977	6
5	1	Colombia	1960	4
6	1	France	1947	21
7	1	Chile	1946	3
8	2	Uruguay	1945	9
9		England	1934	10
10	2	Mexico	1905	16
11		Belgium	1896	2
12	1	Portugal	1885	8
13	8	Netherlands	1880	17
14	3	Ecuador	1863	12
15	1	Italy	1844	15
16	3	Ukraine	1797	22
	25	Turkey	1797	13
18	2	Croatia	1794	23
19	11	South Korea	1783	56
20	5	Costa Rica	1769	25

Elo Rank	1 Year Change	Team	Points	FIFA Rank
21	18	Austria	1766	11
22	11	Poland	1762	27
23	2	Switzerland	1753	14
24	12	Republic of Ireland	1751	31
25	3	Japan	1749	57
26	11	Peru	1748	46
27	2	Russia	1747	27
28	5	Romania	1738	19
29	9	Sweden	1735	36
30	13	Paraguay	1732	39
31	7	Czech Republic	1728	29
32	7	Bosnia and Herzegovina	1727	20
33	3	Iran	1721	42
34	7	Ivory Coast	1720	34
35	7	Slovakia	1715	32
	17	United States	1715	29
37	5	Australia	1707	50
38	12	Denmark	1703	41
39	4	Serbia	1701	55
40	3	Scotland	1696	40

Elo Rank	1 Year Change	Team	Points	FIFA Rank
41	10	Hungary	1671	18
42	8	Panama	1670	52
43	2	Senegal	1661	43
44	10	Uzbekistan	1652	66
45	3	Algeria	1651	33
46	2	Iceland	1647	35
47	3	Wales	1638	24
48	4	Egypt	1637	44
49	20	Ghana	1634	38
50	4	United Arab Emirates	1618	68
51	8	Norway	1608	49
52	4	Nigeria	1606	67
53	2	Cameroon	1603	63
54	2	Bolivia	1592	79
55	11	Venezuela	1591	74
56	3	Bulgaria	1590	69
57	4	Slovenia	1589	61
58	12	Greece	1580	37
59	24	Northern Ireland	1578	26
	7	Albania	1578	45

Highest average ratings since 1970

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 2016. 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.

Rank Country Avg Elo 1 Brazil 2013.4 2 Germany 1981.6 3 Netherlands 1927.1 4 England 1922.1 5 Italy 1920.7 6 Spain 1912.7 7 Argentina 1908.4 8 France 1883.5 9 Russia 1848.8 10 Czech Republic 1828.8 11 Portugal 1820.7 12 Serbia 1813.0 13 Sweden 1798.0 14 Romania 1779.4 15 Mexico 1779.1 16 Uruguay 1777.4 17 Poland 1769.9

Rank Country Avg Elo 18 Belgium 1766.9 19 Denmark 1757.3 20 Scotland 1736.7 21 Chile 1727.1 22 Paraguay 1725.2 23 Republic of Ireland 1720.7 24 Bulgaria 1702.6 25 Australia 1700.4 26 Colombia 1695.5 27 Switzerland 1691.1 28 Austria 1690.0 29 Hungary 1683.8 30 Iran 1676.6 31 South Korea 1667.8 32 Greece 1656.3 33 Nigeria 1654.7 34 Egypt 1654.2

Rank Country Avg Elo 35 Wales 1652.5 36 Peru 1648.3 37 Israel 1642.6 38 Ivory Coast 1642.5 39 Morocco 1640.6 40 Turkey 1638.2 41 Cameroon 1636.7 42 Norway 1635.9 43 Ghana 1615.0 44 United States 1612.6 45 Costa Rica 1605.4 46 Northern Ireland 1603.2 47 Tunisia 1601.6 48 Japan 1597.2 49 Ecuador 1593.1 50 Iraq 1590.6 51 Algeria 1574.2

List of number one teams

The following is the list of nations who have achieved the number one position in the World Football Elo Ratings since 1990:

Start Date	Nation	# of days
25 June 1988	Netherlands	717
12 June 1990	West Germany	7
19 June 1990	Brazil	5
24 June 1990	West Germany	725
18 June 1992	Netherlands	3
21 June 1992	Germany	5
26 June 1992	Netherlands	75
9 September 1992	Brazil	37
16 October 1992	Argentina	247
20 June 1993	Germany	49
8 August 1993	Argentina	7
15 August 1993	Germany	313
24 June 1994	Brazil	3
27 June 1994	Germany	12
9 July 1994	Brazil	708
16 June 1996	Germany	3
19 June 1996	Brazil	4
23 June 1996	Germany	311
30 April 1997	Brazil	30
30 May 1997	Germany	11
10 June 1997	Brazil	380
25 June 1998	Brazil  Germany	2
27 June 1998	Brazil	15

Start Date	Nation	# of days
12 July 1998	France	328
5 June 1999	Brazil	389
28 June 2000	France	708
6 June 2002	Argentina	1
7 June 2002	France	4
11 June 2002	Netherlands	1
12 June 2002	Spain	4
16 June 2002	Netherlands	5
21 June 2002	Brazil	351
7 June 2003	Netherlands	4
11 June 2003	Brazil	8
19 June 2003	Netherlands	83
10 September 2003	France	291
27 June 2004	Czech Republic	4
1 July 2004	France	10
11 July 2004	Brazil	3
14 July 2004	France	35
18 August 2004	Argentina	290
4 June 2005	Czech Republic	4
8 June 2005	Argentina	21
29 June 2005	Brazil	102
9 October 2005	Netherlands	3
12 October 2005	Brazil	265

Start Date	Nation	# of days
4 July 2006	Italy	43
16 August 2006	France	52
7 October 2006	Brazil	122
6 February 2007	France	1
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	1089
30 June 2013	Brazil	45
14 August 2013	Spain	59
12 October 2013	Brazil	260
29 June 2014	Netherlands	5
4 July 2014	Brazil	4
8 July 2014	Germany	3790

Ranking by days as leader since 1 January 1990

Nation	days	Last Date as Leader
Brazil	3,582	8 July 2014
Germany		Current
Spain	1,523	12 October 2013
France	1,443	10 July 2007
Argentina	570	14 July 2007
Netherlands	354	4 July 2014
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	Germany	2200	13 July 2014
2	Hungary	2166	30 June 1954
3	Brazil	2153	17 June 1962
4	Spain	2143	23 June 2013
5	Netherlands	2133	12 July 2014
6	Argentina	2117	3 April 1957
7	France	2106	15 August 2001
8	Italy	2079	20 July 1939
9	Poland	2047	1 September 1974
10	England	2042	22 October 1966
11	Uruguay	2035	13 June 1928
12	Russia	2023	9 October 1983
13	Colombia	2016	28 June 2014
14	Czech Republic	1999	27 June 2004
15	Austria	1998	31 May 1934
16	Chile	1997	13 October 2015
17	Portugal	1983	28 February 2001
18	Croatia	1968	11 July 1998
19	Serbia	1962	25 June 1998
20	Denmark	1961	13 June 1986

Rank	Nation	Points	Date
21	Scotland	1953	10 March 1888
22	East Germany	1951	22 June 1974
23	Sweden	1950	25 June 1950
24	Mexico	1936	19 June 2005
25	Paraguay	1932	21 February 1954
26	Belgium	1916	9 September 1981
27	Norway	1914	13 June 2000
28	Romania	1910	9 June 1990
29	Greece	1896	18 August 2004
30	Ecuador	1894	17 November 2015
31	Republic of Ireland	1889	21 August 2002
32	Ivory Coast	1881	26 January 2013
33	Switzerland	1877	22 June 1994
34	Australia	1873	14 December 1997
35	United States	1872	8 July 2009
36	Turkey	1868	19 June 2003
37	Japan	1867	15 August 2001
38	Wales	1859	20 May 1981
39	Bulgaria	1856	15 June 1969
	Peru	1856	11 June 1978

Rank	Nation	Points	Date
41	Cameroon	1849	26 June 2003
42	Costa Rica	1846	13 November 2014
43	Egypt	1835	31 January 2010
44	Iran	1824	8 June 2005
45	Ukraine	1821	15 November 2013
46	South Korea	1818	22 June 2002
47	Nigeria	1816	5 June 2004
48	Northern Ireland	1809	23 April 1986
49	Senegal	1803	16 June 2002
50	Ghana	1798	3 February 2008
51	Morocco	1794	24 December 1998
52	Venezuela	1786	20 July 2011
53	Bosnia and Herzegovina	1783	7 June 2013
54	Algeria	1768	17 December 1990
55	Bolivia	1767	25 June 1997
56	South Africa	1764	18 September 1996
57	DR Congo	1759	14 March 1974
58	Guinea	1758	5 June 1977
59	Tunisia	1756	26 January 2006
60	Israel	1751	11 April 1976

Averages by decade

The table below shows the teams with the best average Elo score per decade (Jan 1 19X0 - Dec 31 19X9).

Rank	1920s		1930s		1940s		1950s		1960s
1	1911	Uruguay	1976	Argentina	2036	Argentina	2025	Argentina	1962	Brazil
2	1873	Spain	1970	Italy	2018	Italy	1998	Hungary	1928	England
3	1859	Argentina	1899	Uruguay	1892	England	1996	Brazil	1924	Hungary
4	1843	Scotland	1868	Spain	1876	Brazil	1917	England	1923	Argentina
5	1820	Czechoslovakia	1867	England	1858	Spain	1870	West Germany	1918	Soviet Union
6	1795	Denmark	1859	Austria	1852	Uruguay	1856	Uruguay	1887	West Germany
7	1771	Brazil	1841	Scotland	1841	Scotland	1853	Italy	1867	Czechoslovakia
8	1768	England	1814	Czechoslovakia	1832	Germany	1850	Yugoslavia	1852	Italy
9	1761	Hungary	1810	Brazil	1815	Hungary	1817	Austria	1844	Spain
10	1760	Austria	1785	Hungary	1783	Mexico	1815	Spain	1840	Uruguay
11	1739	Netherlands	1767	Costa Rica	1768	Czechoslovakia	1799	Paraguay	1811	Yugoslavia
12	1712	Sweden	1759	Germany	1766	Austria	1796	Sweden	1801	Scotland
13	1701	Belgium	1685	Denmark	1746	Wales	1791	Scotland	1796	Sweden
14	1693	Italy	1682	Sweden	1734	Sweden	1753	France	1783	Mexico
15	1676	Portugal	1678	United States	1719	Paraguay	1728	Peru	1741	Austria

Rank	1970s		1980s		1990s		2000s		2010s
1	2060	Brazil	1975	Brazil	1999	Brazil	1998	Brazil	2059	Spain
2	2041	West Germany	1964	West Germany	1988	Germany	1984	France	2048	Germany
3	1948	England	1951	Soviet Union	1952	Italy	1966	Netherlands	2047	Brazil
4	1933	Italy	1927	England	1928	France	1964	Argentina	2006	Netherlands
5	1888	Netherlands	1897	Argentina	1920	Netherlands	1955	Spain	1975	Argentina
6	1884	Poland	1890	Italy	1904	Spain	1942	Italy	1916	England
7	1878	Soviet Union	1884	Netherlands	1902	FR Yugosalvia	1916	England	1884	Chile
8	1869	East Germany	1884	France	1901	England	1891	Germany	1882	Uruguay
9	1861	Argentina	1847	Spain	1874	Denmark	1887	Portugal	1878	Portugal
10	1851	Spain	1840	Poland	1869	Argentina	1873	Czech Republic	1866	Italy
11	1838	Czechoslovakia	1820	Czechoslovakia	1843	Czech Republic	1838	Croatia	1858	France
12	1831	Hungary	1819	Belgium	1836	Sweden	1825	Mexico	1856	Colombia
13	1830	Yugoslavia	1818	Yugoslavia	1829	Croatia	1822	Denmark	1852	Mexico
14	1809	Scotland	1803	East Germany	1826	Russia	1808	Sweden	1833	Croatia
15	1803	Portugal	1785	Uruguay	1825	Mexico	1800	Romania	1799	Sweden
16	1793	Belgium	1784	Romania	1813	Romania	1790	United States	1798	Russia
17	1771	Sweden	1783	Scotland	1810	Portugal	1787	Ireland	1785	Ecuador
18	1767	Austria	1776	Sweden	1784	Colombia	1786	Turkey	1774	Ivory Coast
19	1766	Romania	1775	Austria	1777	Ireland	1782	Uruguay	1769	Switzerland
20	1755	France	1774	Denmark	1773	Belgium	1774	Australia	1768	Ukraine

Highest rated matches

A list of the 15 matches between teams with the highest combined Elo ratings (the nations' points before the matches are given).

Rank	Combined points	Nation 1	Elo 1	Nation 2	Elo 2	Score	Date	Occasion	Location
1	4240	Germany	2180	Argentina	2060	1 : 0 aet	2014-07-13	World Cup F	Rio de Janeiro
		Germany	2200	Argentina	2040	2 : 4	2014-09-03	Friendly	Düsseldorf
3	4213	Netherlands	2101	Spain	2112	0 : 1 aet	2010-07-11	World Cup F	Johannesburg
4	4198	Brazil	2100	Germany	2098	1 : 7	2014-07-08	World Cup SF	Belo Horizonte
5	4192	Brazil	2064	Spain	2128	3 : 0	2013-06-30	Confederations Cup F	Rio de Janeiro
6	4161	West Germany	1995	Hungary	2166	3 : 2	1954-07-04	World Cup F	Bern
7	4160	Netherlands	2051	Brazil	2109	2 : 1	2010-07-02	World Cup QF	Port Elizabeth
8	4152	Brazil	2062	Netherlands	2090	0 : 0	2011-06-04	Friendly	Goiânia
9	4150	West Germany	2069	Brazil	2081	0 : 1	1973-06-16	Friendly	Berlin
10	4135	Netherlands	2075	Argentina	2060	0 : 0	2014-07-09	World Cup SF	São Paulo
11	4130	Spain	2086	Germany	2044	1 : 0	2010-07-07	World Cup SF	Durban
12	4121	Brazil	2051	West Germany	2070	1 : 0	1982-03-21	Friendly	Rio de Janeiro
13	4118	Hungary	2108	Brazil	2010	4 : 2	1954-06-27	World Cup QF	Bern
14	4116	Hungary	2141	Uruguay	1975	4 : 2	1954-06-30	World Cup SF	Lausanne
15	4114	West Germany	2080	Netherlands	2034	2 : 1	1974-07-07	World Cup F	Munich

Biggest upsets

A list of the 15 matches with the biggest point exchange. Since the importance of the match, the goal differential and the perceived home team advantage are factored in the point exchange, these are not necessarily the most surprising wins as expressed by the difference in Elo rating. The nations' points before the matches are given.

Rank	Point exchange	Nation 1	Elo 1	Nation 2	Elo 2	Score	Date	Occasion	Location
1	95	Sweden	1621	Belgium	1772	8 : 1	1924-05-29	Olympic Games	Paris
2	85	Fiji	1148	New Zealand	1534	4 : 0	1980-02-23	OFC Nations Cup	Nouméa
		Czechoslovakia	1809	Argentina	1964	6 : 1	1958-06-15	World Cup	Helsingborg
4	84	Poland	1583	Hungary	1823	3 : 0	1936-08-05	Olympic Games	Berlin
5	82	Brazil	2100	Germany	2098	1 : 7	2014-07-08	World Cup	Belo Horizonte
6	81	Ghana	1598	Czech Republic	1975	2 : 0	2006-06-17	World Cup	Cologne
7	80	Khmer Republic	1200	Kuwait	1510	4 : 0	1972-05-14	Asian Cup	Bangkok
8	79	Paraguay	1596	Uruguay	1986	3 : 0	1929-11-01	Copa América	Buenos Aires
9	78	Croatia	1873	Germany	2054	3 : 0	1998-07-04	World Cup	Lyon
		Norway	1535	Great Britain	1865	3 : 1	1920-08-28	Olympic Games	Antwerp
11	77	Uruguay	1785	Brazil	2125	3 : 0	1959-12-12	Copa América	Guayaquil
		Chile	1540	Uruguay	1893	3 : 0	1937-01-10	Copa América	Buenos Aires
13	76	Netherlands	1962	Spain	2088	5 : 1	2014-06-13	World Cup	Salvador
		United States	1869	Mexico	1772	0 : 5	2009-07-26	Concacaf Gold Cup	East Rutherford
		Germany	1851	Norway	1650	0 : 2	1936-08-07	Olympic Games	Berlin

History

The Elo 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

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.

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;

$R_{n}$	= 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

The number of Points Change is rounded to the nearest integer before updating the team rating.

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	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). This also holds when a game is won or lost on extra time. If the match is decided on penalties, however, the result of the game is considered a draw (W = 0.5).

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 (add 100 points for the home team). 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

• 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)