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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.

Since being developed, the Elo rankings have been found to have the highest predictive capability for football matches.^[1] FIFA's official rankings, both the FIFA World Rankings for men and the FIFA Women's World Rankings are based on a modified version of the Elo formula, the men's rankings having switched away from FIFA's own system for matches played since June 2018.^[2]

Top 100

The following table shows the top 100 teams in the World Football Elo Ratings as they were on 7 February 2019, using data from the World Football Elo Ratings web site.^[3]

Each national team's FIFA World Ranking is shown as per the latest release on 20 December 2018.^[4]

AFC

CAF

CONCACAF

CONIFA

CONMEBOL

OFC

UEFA

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 the first international match in 1872:^[5]

Ranking by matches played as leader

Nation	Games[a]	Days as leader[b]	First date as leader	Last date as leader
Brazil	301	8,587	12 Jun 1958	current
England	154	10,605	30 Nov 1872	11 Jun 1988
Germany [c]	139	4,704	25 Jul 1966	9 Nov 2017
Argentina	123	9,165	20 Jul 1902	10 Nov 2016
Spain	78	2,869	28 Aug 1920	12 Oct 2013
France	73	2,022	12 Sep 1984	11 Oct 2018
Hungary	57	1,897	20 Sep 1952	13 Mar 1960
Scotland	42	5,966	4 Mar 1876	20 Oct 1926
Italy	41	2,694	7 Jun 1934	16 Aug 2006
Soviet Union [d]	41	1,367	21 Mar 1963	25 Jun 1988
Uruguay	37	1,794	29 Aug 1920	16 Jun 1929
Netherlands	32	1,039	1 Jun 1978	4 Jul 2014
Denmark	6	676	5 Jun 1914	8 Oct 1916
Austria	3	11	27 May 1934	7 Jun 1934
Czech Republic	2	8	27 Jun 2004	8 Jun 2005

All-time team highs and lows

The following is a list of national football teams ranked by the highest Elo rating they ever reached.^[7] The table also includes the highest ranking as well as the lowest rating and ranking reached by each nation. The team that has achieved the highest rank in each confederation is shown in color.

Average ratings

Time averaged Elo or Elo-like scores are routinely used to compare chess player strengths.^[8][9][10]

Highest average over entire team history

This table is directly extracted from the eloratings.net website. The averages are not directly comparable, as they represent strengths over different periods and in different pools. For example, they represent 146 years of matches for Scotland (34 years in a pool of 3 or 4 British nations only), 98 years for Spain, 26 years for Ukraine, and 11 years for Montenegro. For Croatia and Slovakia the average is dominated by the single rating during the 50 years between the few games played between 1940 and 1943 and the rebirth of the countries in the 1990s. Likewise, South Africa's average is mostly determined by the 44 matches (of a 417 total in 2018) played in the 86 years before it rejoined FIFA in 1992.

Highest average ratings since 1970

This table is a list of the national teams with the highest average Elo score over approximately the last half century, from 1 January 1970 to 1 January 2019. 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. Only teams playing over the entire period are included. Short-lived or recently originated strong football teams, like East-Germany and Croatia, appear in the decades table below.

Averages by decade

The table below shows the teams with the best average Elo score per decade (Jan 1 XXX0 - Dec 31 XXX9).

Highest rated matches

A list of the 25 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	4287	Germany	2203	Argentina	2084	1–0 aet	2014-07-13	World Cup Final	Rio de Janeiro
		Germany	2223	Argentina	2064	2–4	2014-09-03	Friendly	Düsseldorf
3	4278	Hungary	2230	West Germany	2048	2–3	1954-07-04	World Cup Final	Bern
4	4263	Spain	2136	Netherlands	2127	1–0 aet	2010-07-11	World Cup Final	Johannesburg
5	4245	Great Britain	2184	Denmark	2061	4–2	1912-07-04	Olympic Games Final	Stockholm
6	4242	Brazil	2120	Germany	2122	1–7	2014-07-08	World Cup SF	Belo Horizonte
7	4238	West Germany	2114	Brazil	2124	0–1	1973-06-16	Friendly	Berlin
8	4236	Brazil	2086	Spain	2150	3–0	2013-06-30	Confederations Cup Final	Rio de Janeiro
9	4224	Hungary	2208	Uruguay	2016	4–2	1954-06-30	World Cup SF	Lausanne
10	4223	Germany	2104	Brazil	2119	0–1	2018-03-27	Friendly	Berlin
11	4218	Hungary	2180	Brazil	2038	4–2	1954-06-27	World Cup QF	Bern
12	4207	Netherlands	2077	Brazil	2130	2–1	2010-07-02	World Cup QF	Port Elizabeth
13	4200	Brazil	2083	Netherlands	2117	0–0	2011-06-04	Friendly	Goiânia
14	4199	Brazil	2088	West Germany	2111	1–0	1982-03-21	Friendly	Rio de Janeiro
15	4198	Brazil	2060	West Germany	2138	1–1	1977-06-12	Friendly	Rio de Janeiro
16	4197	West Germany	2123	Netherlands	2074	2–1	1974-07-07	World Cup Final	Munich
17	4191	Brazil	2166	Czechoslovakia	2025	3–1	1962-06-17	World Cup Final	Santiago
		West Germany	2135	Brazil	2056	0–1	1978-04-05	Friendly	Hamburg
19	4187	Brazil	2132	Italy	2055	4–1	1970-06-21	World Cup Final	Mexico City
20	4179	Spain	2110	Germany	2069	1–0	2010-07-07	World Cup SF	Durban
		Netherlands	2096	Argentina	2083	0–0	2014-07-09	World Cup SF	São Paulo
22	4177	Germany	2076	Brazil	2101	1–2	1998-03-25	Friendly	Stuttgart
23	4173	West Germany	2097	Netherlands	2076	1–1	1975-05-17	Friendly	Frankfurt
24	4172	West Germany	2104	Poland	2068	1–0	1974-07-03	World Cup 2nd round	Frankfurt
25	4168	England	2141	Denmark	2017	3–0	1911-10-21	Friendly	London

Biggest upsets

This is a list of matches with the biggest point exchange.^[11] Since the importance of the match, the goal differential and the perceived home team advantage are factored in the exchange, these are not necessarily the most surprising wins as expressed by the difference in Elo rating.^[a]
The nations' points before the matches are given.

Rank	Point exchange	Nation 1	Elo 1	Nation 2	Elo 2	Score	Date	Occasion	Location
1	98	Sweden	1676	Belgium	1845	8–1	1924-05-29	Olympic Games	Paris
2	92	Italy	1824	Spain	1991	7–1	1928-06-04	Olympic Games	Amsterdam
		Turkey	1397	China *	1655	4–0	1948-08-02	Olympic Games	Walthamstow
4	87	Norway	1478	Great Britain	2041	3–1	1920-08-28	Olympic Games	Antwerp
5	84	Egypt *	1677	Hungary	1919	3–0	1924-05-29	Olympic Games	Paris
		Czechoslovakia	1855	Argentina	2003	6–1	1958-06-15	World Cup	Helsingborg
7	83	Fiji	1171	New Zealand	1523	4–0	1980-02-23	OFC Nations Cup	Nouméa
8	82	Ghana	1606	Czech Republic	2005	2–0	2006-06-17	World Cup	Cologne
9	81	Brazil	2120	Germany	2122	1–7	2014-07-08	World Cup	Belo Horizonte
10	80	Germany	1642	Russia *	1567	16–0	1912-07-01	Olympic Games	Solna
		Turkey	1604	South Korea *	1668	7–0	1954-06-20	World Cup	Geneva
		Trinidad & Tobago	1481	Mexico	1783	4–0	1973-12-14	CONCACAF Championship	Port-au-Prince
		South Korea	1677	Germany	2044	2–0	2018-06-28	World Cup	Kazan
14	78	Paraguay	1685	Uruguay	2054	3–0	1929-11-01	Copa América	Buenos Aires
		Chile	1587	Uruguay	1957	3–0	1937-01-10	Copa América	Buenos Aires
16	77	Uruguay	1813	Brazil	2162	3–0	1959-12-12	Copa América	Guayaquil
		Croatia	1912	Germany	2090	3–0	1998-07-04	World Cup	Lyon
18	76	Germany	1906	Norway	1714	0–2	1936-08-07	Olympic Games	Berlin
		Costa Rica	1717	Guatemala	1491	1–4	1946-03-10	CCCF Championship	San José
		United States	1888	Mexico	1788	0–5	2009-07-26	CONCACAF Gold Cup	East Rutherford
21	75	Denmark	1759	Italy	2044	5–3	1948-08-05	Olympic Games	London
		Venezuela	1336	Bolivia	1646	3–0	1967-01-28	Copa América	Montevideo
		Netherlands	1986	Spain	2109	5–1	2014-06-13	World Cup	Salvador
24	74	Chile	1800	Brazil	2032	4–0	1987-07-03	Copa América	Córdoba
25	73	Montserrat	511	British Virgin Islands	758	7–0	2012-09-09	Caribbean Cup qualifier	Fort-de-France

*The initial ratings may be partially responsible for the high point exchange. The national teams of China, Egypt, Russia, and South Korea had played only 18, 3, 2, and 18 international matches before their respective upsets. China had only yet played against East Asian teams.

Elo Ratings before each World Championship

History and overview

The Elo system, developed by Hungarian-American mathematician 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.^[33] He was also the first maintainer of the World Football Elo Ratings web site, currently maintained by Kirill Bulygin. Other implementations of the Elo rating system are possible ^[34] but the Runyan system is the best known.

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 ratings consider all official international matches for which results are available. Ratings tend to converge on a team's true strength relative to its competitors after about 30 matches.^[35] 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 are considered provisional.

Comparison with other systems

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 (2006–2018 system) performed poorly. ^[34]

The FIFA World Rankings is the official national teams rating system used by the international governing body of football. The FIFA Women's World Rankings system has used a modified version of the Elo formula since 2003. In June 2018, the FIFA ranking switched to an Elo-based ranking as well, starting from the current FIFA rating points.^[36] The major difference between the World Football Elo Rating and the new men's FIFA rating system is that the latter does not consider goal differential and counts a penalty shoot-out as a win/loss rather than a draw; thus, a 7:0 blowout is considered equal to a 7:6 penalty shoot-out win (neither method distinguishes a win in extra time from a win in regular time). The FIFA method is also less sensitive to the difference in ratings and more sensitive to match status.^[37] Finally, World Football Elo Ratings considers all official international matches for which results are available, including those involving "unaffiliated" teams that are not a member of FIFA.

Calculation principles

The ratings are based on the following formulae:

Rn=Ro+P{displaystyle R_{n}=R_{o}+P}

where

P=KG(W−We){displaystyle P=KG(W-W_{e})}

Where;

Rn{displaystyle R_{n}}	= The new team rating
Ro{displaystyle R_{o}}	= The old team rating
K{displaystyle K}	= Weight index regarding the tournament of the match
G{displaystyle G}	= A number from the index of goal differences
W{displaystyle W}	= The result of the match
We{displaystyle W_{e}}	= The expected result
P{displaystyle P}	= Points Change

"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 constant reflects the importance of a match, which, in turn, is determined entirely by which tournament the match is in; the weight constant for each major tournament is:

Tournament or Match type	K
World Cup, Olympic Games (1908–1980)	60
Continental championship and intercontinental tournaments	50
World Cup and Continental qualifiers and major tournaments	40
All other tournaments	30
Friendly matches	20

The FIFA adaptation of the Elo rating will feature 8 weights, with the knockout stages in the World Cup weighing 12x more than some friendly matches.^[37]

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

G=1{displaystyle G=1}

If the game is won by two goals

G=32{displaystyle G={frac {3}{2}}}

If the game is won by three or more goals

• Where N is the goal difference

G=11+N8{displaystyle G={frac {11+N}{8}}}

Table of examples:

Goal Difference	G
0	1
+1	1
+2	1.5
+3	1.75
+4	1.875
+5	2
+6	2.125

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:

We=110−dr/400+1{displaystyle 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.

The FIFA adaptation of the Elo rating does not incorporate a home team advantage and has a larger divisor in the formula (600 vs 400), making the points exchange less sensitive to the rating difference of two teams.^[37]

Examples for clarification

The same example of a three-team friendly tournament on neutral territory is used as on the FIFA World Rankings page. Beforehand team A had a rating of 630 points, team B 500 points, and teams C 480 points.
The first table shows the points allocations based on three possible outcomes of the match between the strongest team A, and the somewhat weaker team B:

	Team A	Team B	Team A	Team B	Team A	Team B
Score	3 : 1		1 : 3		2 : 2
K{displaystyle K}	20	20	20	20	20	20
G{displaystyle G}	1.5	1.5	1.5	1.5	1	1
W{displaystyle W}	1	0	0	1	0.5	0.5
We{displaystyle 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

When the difference in strength between the two teams is less, so also will be the difference in points allocation. The next 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{displaystyle K}	20	20	20	20	20	20
G{displaystyle G}	1.5	1.5	1.5	1.5	1	1
W{displaystyle W}	1	0	0	1	0.5	0.5
We{displaystyle 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

Team B drops more points by losing to Team C, which has shown about the same strength, than by losing to Team A, which has been considerably better than Team B.

See also

• Statistical association football predictions

Notes

References

External links

• Website