World Football Elo Ratings

The World Football Elo Ratings is a ranking system for men's national association football teams that is published by the website eloratings.net. It is based on the Elo rating system but includes modifications to take various football-specific variables into account, like the margin of victory, importance of a match, and home field advantage. Other implementations of the Elo rating system are possible and there is no single nor any official Elo ranking for football teams. The FIFA World Rankings -not based on the Elo method- is the official national teams rating system used by the international governing body of football and is therefore more prevalent.

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.^[1] 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.^[2]

Top 100 ranking

The following table shows the top 100 teams in the World Football Elo Ratings on 4 December 2016, using data from the World Football Elo Ratings web site.^[3]

Each national team's FIFA World Rankings are shown as they were in the latest release on 24 November 2016.^[4]

	AFC
	CAF
	CONCACAF
	CONMEBOL
	OFC
	UEFA
	No confederation

Highest average ratings since 1970

Time averaged Elo or Elo-like scores are routinely used to compare chess player strengths.^[5][6][7] The following is a list of the national teams with the highest average Elo score from 1 January 1970 to 1 December 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 2017.9 2  Germany[lower-alpha 1] 1988.4 3  Netherlands 1932.4 4  England 1929.2 5  Italy 1926.3 6  Spain 1919.5 7  Argentina 1912.3 8  France 1893.0 9  Russia[lower-alpha 2] 1853.3 10  Czech Republic[lower-alpha 3] 1836.7 11  Portugal 1827.7 12  Serbia[lower-alpha 4] 1817.9 13  Sweden 1802.8 14  Mexico 1790.2 15  Romania 1789.8 16  Uruguay 1779.3 17  Belgium 1774.8

Rank Country Avg Elo 18  Poland 1773.7 19  Denmark 1771.7 20  Scotland 1744.2 21  Chile 1732.1 22  Paraguay 1729.2 23  Republic of Ireland 1729.1 24  Bulgaria 1709.9 25  Australia 1699.9 26   Switzerland 1699.4 27  Austria 1697.0 28  Colombia 1696.7 29  Hungary 1691.5 30  South Korea 1681.8 31  Iran 1673.6 32  Greece 1663.2 33  Wales 1661.8 34  Egypt 1660.9

Rank Country Avg Elo 35  Nigeria 1660.3 36  Peru 1647.8 37  Turkey 1647.3 38  Israel 1643.1 39  Norway 1642.8 40  Cameroon 1639.6 41  Morocco 1636.0 42  Ivory Coast 1630.9 43  United States 1619.7 44  Ghana 1616.0 45  Northern Ireland 1610.6 46  Iraq 1607.0 47  Costa Rica 1605.7 48  Japan 1604.3 49  Tunisia 1599.3 50  Ecuador 1599.2 51  China PR 1591.1

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 1872:

Ranking by days as leader

Nation	days	First Date as Leader	Last Date as Leader
England	13,177	30 November 1872	11 June 1988
Brazil	8,335	12 June 1958	Current
Argentina	7,449	16 June 1929	9 Nov 2016
Scotland	6,215	4 March 1876	23 Oct 1926
Germany [lower-alpha 5]	4,361	25 July 1966	28 May 2016
Spain	2,535	5 September 1920	11 October 2013
Italy	2,259	7 June 1934	15 August 2006
Uruguay	2,020	18 September 1920	31 October 1929
Hungary	2,001	2 August 1952	11 June 1958
France	1,868	12 September 1984	10 July 2007
Soviet Union [lower-alpha 6]	1,450	31 March 1963	24 June 1988
Netherlands	965	1 June 1978	3 July 2014
Denmark	105	25 June 1916	7 Oct 1916
Austria	11	27 May 1934	6 June 1934
Czech Republic [lower-alpha 7]	9	25 May 1924	7 June 2005

Elo all-time records

All-time highest ratings

The following is a list of national football teams ranked by their highest Elo score ever reached. The team in each confederation that has achieved the highest rank is shown in color.

All-time highest ranking

The following is a list of national football teams ranked by their highest Elo ranking ever reached. Note that for the highest ranking/rating of a national football team the Elo ratings website ignores the ranking/rating before 30 matches have been played.

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 [lower-alpha 16]		1950s		1960s
1	1908	Uruguay	1972	Argentina	2035	Argentina	2022	Argentina	1972	Brazil
2	1875	Scotland	1965	Italy	2005	Italy	2016	Hungary	1945	Soviet Union
3	1867	Spain	1893	Uruguay	1908	England	1997	Brazil	1933	England
4	1845	Argentina	1887	England	1876	Brazil	1927	England	1930	Hungary
5	1822	Czechoslovakia	1880	Austria	1870	Scotland	1878	West Germany	1922	Argentina
6	1814	England [lower-alpha 17]	1869	Scotland	1859	Spain	1860	Yugoslavia	1893	West Germany
7	1805	Denmark	1866	Spain	1845	Uruguay	1856	Uruguay	1876	Czechoslovakia
8	1781	Hungary	1819	Czechoslovakia	1838	Germany	1833	Austria	1856	Italy
9	1769	Brazil	1809	Brazil	1830	Hungary	1822	Italy	1849	Spain
10	1768	Austria	1805	Hungary	1813	Austria	1812	Spain	1841	Uruguay
11	1728	Netherlands	1769	Costa Rica	1788	Czechoslovakia	1807	Scotland	1826	Yugoslavia
12	1711	Sweden	1760	Germany	1782	Mexico	1803	Sweden	1808	Scotland
13	1693	Belgium	1686	Denmark	1765	Wales	1797	Paraguay	1794	Sweden
14	1686	Italy	1681	Sweden	1752	Sweden	1757	France	1785	Mexico
15	1677	Portugal	1681	Wales	1715	Paraguay	1729	Czechoslovakia	1742	Austria

Rank	1970s		1980s		1990s		2000s		2010s [lower-alpha 18]
1	2067	Brazil	1980	Brazil	2007	Brazil	2000	Brazil	2054	Spain
2	2046	West Germany	1971	West Germany	1998	Germany	1991	France	2048	Germany
3	1955	England	1953	Soviet Union	1962	Italy	1973	Netherlands	2044	Brazil
4	1936	Italy	1937	England	1940	France	1965	Argentina	2000	Netherlands
5	1890	Netherlands	1900	Argentina	1929	Netherlands	1960	Spain	1983	Argentina
6	1884	Poland	1899	Italy	1912	Spain	1946	Italy	1919	England
7	1879	East Germany	1895	France	1911	FR Yugoslavia[lower-alpha 19]	1922	England	1892	Chile
8	1878	Soviet Union	1890	Netherlands	1910	England	1897	Germany	1885	Portugal
9	1863	Argentina	1854	Spain	1882	Denmark	1893	Portugal	1885	Uruguay
10	1858	Spain	1839	Poland	1871	Argentina	1884	Czech Republic	1872	Italy
11	1846	Czechoslovakia	1830	Belgium	1852	Czech Republic[lower-alpha 20]	1844	Denmark	1870	France
12	1840	Hungary	1829	Czechoslovakia	1846	Russia[lower-alpha 21]	1843	Croatia	1864	Colombia
13	1837	Yugoslavia	1829	East Germany	1844	Sweden	1825	Mexico	1856	Mexico
14	1818	Scotland	1826	Yugoslavia	1830	Mexico	1812	Sweden	1837	Croatia
15	1811	Portugal	1792	Scotland	1829	Croatia	1809	Romania	1798	Sweden
16	1798	Belgium	1789	Romania	1828	Romania	1794	United States	1793	Russia
17	1783	Romania	1788	Denmark	1814	Portugal	1793	Republic of Ireland	1789	Ecuador
18	1777	Sweden	1785	Uruguay	1791	Republic of Ireland	1792	Turkey	1775	Switzerland
19	1772	Austria	1782	Austria	1788	Colombia	1780	Uruguay	1771	Ivory Coast
20	1762	France	1781	Sweden Wales	1780	Belgium Norway	1777	Russia	1769	Ukraine

Highest rated matches

A list of the 16 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	4247	Germany	2184	Argentina	2063	1 : 0 aet	2014-07-13	World Cup F	Rio de Janeiro
		Germany	2204	Argentina	2043	2 : 4	2014-09-03	Friendly	Düsseldorf
3	4223	Netherlands	2106	Spain	2117	0 : 1 aet	2010-07-11	World Cup F	Johannesburg
4	4203	Brazil	2102	Germany	2101	1 : 7	2014-07-08	World Cup SF	Belo Horizonte
5	4201	West Germany	2009	Hungary	2192	3 : 2	1954-07-04	World Cup F	Bern
6	4197	Brazil	2066	Spain	2131	3 : 0	2013-06-30	Confederations Cup F	Rio de Janeiro
7	4165	Netherlands	2056	Brazil	2109	2 : 1	2010-07-02	World Cup QF	Port Elizabeth
8	4162	West Germany	2074	Brazil	2088	0 : 1	1973-06-16	Friendly	Berlin
9	4156	Brazil	2062	Netherlands	2094	0 : 0	2011-06-04	Friendly	Goiânia
10	4149	Hungary	2169	Uruguay	1980	4 : 2	1954-06-30	World Cup SF	Lausanne
11	4148	Hungary	2141	Brazil	2007	4 : 2	1954-06-27	World Cup QF	Bern
12	4139	Spain	2091	Germany	2048	1 : 0	2010-07-07	World Cup SF	Durban
13	4138	Netherlands	2077	Argentina	2061	0 : 0	2014-07-09	World Cup SF	São Paulo
14	4130	Brazil	2056	West Germany	2074	1 : 0	1982-03-21	Friendly	Rio de Janeiro
15	4125	Germany	2047	Brazil	2078	1 : 2	1998-03-25	Friendly	Stuttgart
16	4124	Brazil	2025	West Germany	2099	1 : 1	1977-06-12	Friendly	Rio de Janeiro
17	4121	West Germany	2084	Netherlands	2037	2 : 1	1974-07-07	World Cup F	Munich
18	4116	West Germany	2096	Brazil	2020	0 : 1	1978-04-05	Friendly	Hamburg
19	4115	Argentina	2099	Chile	2016	0 : 0	2016-06-26	Copa América F	East Rutherford
20	4112	Brazil	2097	Italy	2015	4 : 1	1970-06-21	World Cup F	Mexico City

Biggest upsets

A list of the 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.^{[lower-alpha 22]}
The nations' points before the matches are given.

Rank	Point exchange	Nation 1	Elo 1	Nation 2	Elo 2	Score	Date	Occasion	Location
1	91	Sweden	1636	Belgium	1764	8 : 1	1924-05-29	Olympic Games	Paris
2	88	Italy	1761	Spain	1902	7 : 1	1928-06-04	Olympic Games	Amsterdam
3	84	Czechoslovakia	1816	Argentina	1963	6 : 1	1958-06-15	World Cup	Helsingborg
4	83	Norway	1530	Great Britain	1953	3 : 1	1920-08-28	Olympic Games	Antwerp
		Egypt *	1590	Hungary	1823	3 : 0	1924-05-29	Olympic Games	Paris
6	82	Brazil	2102	Germany	2101	1 : 7	2014-07-08	World Cup	Belo Horizonte
7	81	Ghana	1601	Czech Republic	1982	2 : 0	2006-06-17	World Cup	Cologne
8	80	Fiji	1208	New Zealand	1521	4 : 0	1980-02-23	OFC Nations Cup	Nouméa
		Trinidad and Tobago	1445	Mexico	1749	4 : 0	1973-12-14	CONCACAF Championship	Port-au-Prince
10	79	Turkey	1453	China *	1604	4 : 0	1948-08-02	Olympic Games	Walthamstow
11	78	Croatia	1877	Germany	2062	3 : 0	1998-07-04	World Cup	Lyon
		Khmer Republic	1228	Kuwait	1508	4 : 0	1972-05-14	Asian Cup	Bangkok
		Paraguay	1600	Uruguay	1974	3 : 0	1929-11-01	Copa América	Buenos Aires
14	77	Uruguay	1786	Brazil	2127	3 : 0	1959-12-12	Copa América	Guayaquil
15	76	Netherlands	1967	Spain	2091	5 : 1	2014-06-13	World Cup	Salvador
		United States	1866	Mexico	1769	0 : 5	2009-07-26	CONCACAF Gold Cup	East Rutherford
		Chile	1553	Uruguay	1885	3 : 0	1937-01-10	Copa América	Buenos Aires
18	75	Venezuela	1318	Bolivia	1625	3 : 0	1967-01-28	Copa América	Montevideo
		Costa Rica	1684	Guatemala *	1469	1 : 4	1946-03-10	CCCF Championship	San José
20	74	Chile	1771	Brazil	2002	4 : 0	1987-07-03	Copa América	Córdoba
		Denmark	1720	Italy	1985	5 : 3	1948-08-05	Olympic Games	London
		Germany	1849	Norway	1682	0 : 2	1936-08-07	Olympic Games	Berlin

*The national teams of Egypt, China and Guatemala had only played 3, 18, and 24 international matches before their respective upsets (China only yet against East Asian teams), and their Elo rating may still be partially determined by the starting rating they have been assigned (the points exchanges could be lower when these are adjusted).

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 change are based on the following formulae:

or

Where;

	= The new team rating
	= The old team rating
	= Weight index regarding the tournament of the match
	= A number from the index of goal differences
	= The result of the match
	= The expected result
	= 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.

If the game is a draw or is won by one goal

If the game is won by two goals

If the game is won by three or more goals

• Where N is the goal difference

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:

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
	20	20	20	20	20	20
	1.5	1.5	1.5	1.5	1	1
	1	0	0	1	0.5	0.5
	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
	20	20	20	20	20	20
	1.5	1.5	1.5	1.5	1	1
	1	0	0	1	0.5	0.5
	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

Notes

References

External links

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