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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. 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.

Other implementations of the Elo rating system are possible. 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 in place until July 2018 performed poorly.

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. Following the 2018 World Cup, the FIFA ranking will switch to an Elo-based ranking as well, starting from the current FIFA rating points.

The major difference between the World Football Elo Rating and the future men's FIFA rating system is that the latter will not consider goal differential and will count a penalty shoot-out as a win/loss rather than a draw; thus, a 7:0 blowout will be 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 will further be less sensitive to the difference in ratings and more sensitive to match status. 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.

Top 80 ratings as of 3 July 2018
Elo Rank	1 Year Change	Team	Elo Rating	FIFA Rank*
1		Brazil	2156	2
2	4	France	2029	7
3	8	Belgium	2010	3
	1	Spain	2010	10
5	13	Uruguay	1986	14
6	4	Germany	1964	1
7	9	Croatia	1950	20
8	2	England	1944	12
9	4	Portugal	1940	4
10	3	Colombia	1939	16
11	6	Netherlands	1908	17
12	7	Sweden	1906	24
10	10	Argentina	1896	5
	20	Denmark	1896	12
15	7	Italy	1891	19
16	1	Peru	1890	11
17	3	Switzerland	1879	6
18	9	Chile	1869	9
19	7	Mexico	1829	15
20	3	Iran	1816	37
21	8	Poland	1783	8
22	3	Wales	1777	18
23	9	Serbia	1772	34
24	2	United States	1764	25
25	11	Senegal	1763	27
26	8	South Korea	1757	57
27		Slovakia	1752	28
28	2	Ukraine	1750	35
29	9	Ecuador	1747	60
30		Bosnia & Herzegovina	1745	40
31	8	Austria	1742	26
32	8	Venezuela	1739	33
33	9	Republic of Ireland	1729	31
34	3	Paraguay	1728	32
	12	Turkey	1728	38
36	8	Romania	1727	30
37	8	Costa Rica	1726	23
38	22	Morocco	1720	41
39	4	Australia	1713	36
	1	Czech Republic	1713	46
41	2	Russia	1710	70
42	1	Scotland	1709	42
43	23	Iceland	1708	22
44	9	Nigeria	1702	48
45	17	Japan	1699	61
46	1	Northern Ireland	1676	29
47	19	Tunisia	1662	21
48	7	Bolivia	1661	59
49	3	Greece	1646	44
50	3	Cameroon	1645	49
	17	Ghana	1645	47
52	17	Norway	1640	53
53	2	Slovenia	1626	56
54	1	Bulgaria	1615	49
55	13	Syria	1606	73
56	20	Finland	1605	63
57	8	Ivory Coast	1602	68
58	6	Uzbekistan	1599	95
59	1	Burkina Faso	1597	52
	3	Montenegro	1597	43
61	11	Panama	1596	55
62	1	Honduras	1590	62
63	2	DR Congo	1589	38
64	7	Saudi Arabia	1588	67
65	11	Hungary	1576	51
66	18	Egypt	1575	45
67	18	Jamaica	1574	54
68	4	South Africa	1565	74
69	10	Albania	1560	58
70	8	Iraq	1550	89
71	24	Oman	1539	84
72	9	Canada	1534	79
	1	China	1534	75
74	2	United Arab Emirates	1532	77
75	5	Israel	1527	93
76	11	Belarus	1522	78
77	2	Mali	1519	64
78	15	North Macedonia	1518	71
79	1	Guatemala	1511	146
80	25	Algeria	1508	66
*FIFA rankings per 7 June 2018
Complete rankings at eloratings.net

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. He was also the first maintainer of the World Football Elo Ratings web site, currently maintained by Kirill Bulygin.

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

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.

Calculation principles

The ratings are based on the following formulae:

${\displaystyle R_{n}=R_{o}+KG(W-W_{e})}$

or

${\displaystyle P=KG(W-W_{e})}$

Where;

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

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.

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

${\displaystyle G=1}$

If the game is won by two goals

${\displaystyle G={\frac {3}{2}}}$

If the game is won by three or more goals

• Where N is the goal difference

${\displaystyle G={\frac {11+N}{8}}}$

Table of examples:

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:

${\displaystyle W_{e}={\frac {1}{10^{-dr/400}+1}}}$

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 will not incorporate a home team advantage and will have a larger divisor in the formula (600 vs 400), making the points exchange less sensitive to the rating difference of two teams.

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 600 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
${\displaystyle K}$	20	20	20	20	20	20
${\displaystyle G}$	1.5	1.5	1.5	1.5	1	1
${\displaystyle W}$	1	0	0	1	0.5	0.5
${\displaystyle W_{e}}$	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
${\displaystyle K}$	20	20	20	20	20	20
${\displaystyle G}$	1.5	1.5	1.5	1.5	1	1
${\displaystyle W}$	1	0	0	1	0.5	0.5
${\displaystyle W_{e}}$	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.

List of number one teams

The following is the list of nations who reached a first rank in ratings since 1872.

Start Date Nation # of days 30 Nov 1872  England 1,190 4 Mar 1876  Scotland 5,873 2 Apr 1892  England 3,760 20 Jul 1902  Argentina 2,148 6 Jun 1908  England 2,190 5 Jun 1914  Denmark 5 10 Jun 1914  Denmark  England 361 6 Jun 1915  Denmark 490 8 Oct 1916  England 1,420 28 Aug 1920  Spain 1 29 Aug 1920  Uruguay 7 5 Sep 1920  Spain 13 18 Sep 1920  Uruguay 386 9 Oct 1921  Spain 959 25 May 1924  Uruguay 419 18 Jul 1925  Spain 273 17 Apr 1926  Scotland 186 20 Oct 1926  Argentina 4 24 Oct 1926  Uruguay 583 29 May 1928  Argentina 1 30 May 1928  Uruguay 3 2 Jun 1928  Argentina 1 3 Jun 1928  Uruguay 3 6 Jun 1928  Argentina 1 7 Jun 1928  Uruguay 374 16 Jun 1929  Argentina 1,806 27 May 1934  Austria 11 7 Jun 1934  Italy 1,277 5 Dec 1937  Argentina 182 5 Jun 1938  Italy 630 25 Feb 1940  Argentina 144 18 Jul 1940  Italy 136 1 Dec 1940  Argentina 56 26 Jan 1941  Italy 3 29 Jan 1941  Argentina 445 19 Apr 1942  Italy 36 25 May 1942  Argentina 307 28 Mar 1943  Argentina  Italy 7 4 Apr 1943  Argentina 98 11 Jul 1943  Argentina  Italy 545 6 Jan 1945  Argentina 36 11 Feb 1945  Italy 4 15 Feb 1945  Argentina 142 7 Jul 1945  Italy 127 11 Nov 1945  Argentina  Italy 35 16 Dec 1945  Argentina 4 20 Dec 1945  Italy 52

Start Date Nation # of days 10 Feb 1946  Argentina 455 11 May 1947  Argentina  Italy 182 9 Nov 1947  Argentina 335 9 Oct 1948  England 182 9 Apr 1949  Argentina 442 25 Jun 1950  England 4 29 Jun 1950  Argentina 814 20 Sep 1952  Hungary 218 26 Apr 1953  Argentina 21 17 May 1953  Hungary 1,417 3 Apr 1957  Argentina 3 6 Apr 1957  Hungary 67 12 Jun 1957  Argentina 95 15 Sep 1957  Hungary 8 23 Sep 1957  Argentina 13 6 Oct 1957  Hungary 249 12 Jun 1958  Hungary  Brazil 3 15 Jun 1958  Brazil 634 10 Mar 1960  Hungary 3 13 Mar 1960  Argentina 47 29 Apr 1960  Brazil 27 26 May 1960  Argentina 3 29 May 1960  Brazil 1,026 21 Mar 1963  Soviet Union 836 4 Jul 1965  Brazil 322 22 May 1966  Soviet Union 13 4 Jun 1966  Brazil 41 15 Jul 1966  Soviet Union 10 25 Jul 1966  West Germany 5 30 Jul 1966  England 1,408 7 Jun 1970  Brazil 742 18 Jun 1972  Brazil  West Germany 10 28 Jun 1972  West Germany 11 9 Jul 1972  Brazil 129 15 Nov 1972  West Germany 91 14 Feb 1973  Brazil 484 13 Jun 1974  West Germany 9 22 Jun 1974  Brazil 11 3 Jul 1974  West Germany 1,429 1 Jun 1978  Netherlands 6 7 Jun 1978  West Germany 3 10 Jun 1978  Netherlands 1 11 Jun 1978  West Germany 3 14 Jun 1978  Brazil 504 31 Oct 1979  West Germany 434 7 Jan 1981  Brazil 3 10 Jan 1981  West Germany 71 22 Mar 1981  Brazil 10

Start Date Nation # of days 1 Apr 1981  West Germany 44 15 May 1981  Brazil 152 14 Oct 1981  West Germany 243 14 Jun 1982  Brazil 486 13 Oct 1983  Soviet Union 335 12 Sep 1984  France 232 2 May 1985  West Germany 41 12 Jun 1985  France 91 11 Sep 1985  Soviet Union 133 22 Jan 1986  France 154 25 Jun 1986  Brazil 3 28 Jun 1986  France 1 29 Jun 1986  Argentina 346 10 Jun 1987  Brazil 23 3 Jul 1987  England 57 29 Aug 1987  Soviet Union 74 11 Nov 1987  England 141 31 Mar 1988  England  Soviet Union 2 2 Apr 1988  England 71 12 Jun 1988  Soviet Union 5 17 Jun 1988  West Germany 1 18 Jun 1988  Soviet Union 7 25 Jun 1988  Netherlands 715 10 Jun 1990  Netherlands  West Germany 2 12 Jun 1990  West Germany 7 19 Jun 1990  Brazil 5 24 Jun 1990  West Germany 725 18 Jun 1992  Netherlands 3 21 Jun 1992  Germany 5 26 Jun 1992  Netherlands 75 9 Sep 1992  Germany 35 14 Oct 1992  Brazil 2 16 Oct 1992  Argentina 246 19 Jun 1993  Germany 370 24 Jun 1994  Brazil 3 27 Jun 1994  Germany 12 9 Jul 1994  Brazil 708 16 Jun 1996  Germany 3 19 Jun 1996  Germany  Brazil 4 23 Jun 1996  Germany 352 10 Jun 1997  Brazil 380 25 Jun 1998  Germany 2 27 Jun 1998  Brazil 2 29 Jun 1998  Germany 4 3 Jul 1998  Brazil 9 12 Jul 1998  France 331 8 Jun 1999  Brazil 374 16 Jun 2000  France 5

Start Date Nation # of days 21 Jun 2000  Brazil 4 25 Jun 2000  France 711 6 Jun 2002  Argentina 1 7 Jun 2002  Italy 1 8 Jun 2002  France 3 11 Jun 2002  Netherlands 10 21 Jun 2002  Brazil 236 12 Feb 2003  Netherlands 210 10 Sep 2003  France 291 27 Jun 2004  Czech Republic 4 1 Jul 2004  France 65 4 Sep 2004  Argentina 273 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 7 Feb 2007  Brazil 119 6 Jun 2007  Brazil  France 21 27 Jun 2007  France 14 11 Jul 2007  Argentina 4 15 Jul 2007  Brazil 334 13 Jun 2008  Netherlands 8 21 Jun 2008  Spain 368 24 Jun 2009  Brazil 339 29 May 2010  Brazil  Spain 4 2 Jun 2010  Brazil 1 3 Jun 2010  Spain 4 7 Jun 2010  Spain  Brazil 1 8 Jun 2010  Spain 7 15 Jun 2010  Spain  Brazil 1 16 Jun 2010  Brazil 16 2 Jul 2010  Netherlands 5 7 Jul 2010  Spain 1,089 30 Jun 2013  Brazil 45 14 Aug 2013  Spain 59 12 Oct 2013  Brazil 260 29 Jun 2014  Netherlands 5 4 Jul 2014  Germany 695 29 May 2016  Argentina 165 10 Nov 2016  Brazil 329 5 Oct 2017  Germany 36 10 Nov 2017  Brazil 2,619