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The Elo Rating System for football 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 used in chess 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.

In football, the Elo system has no official status. It was adapted for football in 1997, through frustration at the absence of better ranking systems in the sport. In June 2018, FIFA adapted their official world rankings to become much closer to the ELO system.

Top 20 ratings as of 11 July 2018
Elo Rank	1 Year Change	Team	Elo Rating	FIFA Rank*
1		Brazil	2114	2
2	4	France	2097	7
3	9	Belgium	2023	3
4		Spain	2010	10
5	11	Croatia	1973	20
6	4	Germany	1964	1
7	3	England	1950	12
8	11	Uruguay	1946	14
9	3	Portugal	1940	4
10	2	Colombia	1939	16
11	6	Netherlands	1908	17
12	21	Denmark	1896	12
13	10	Argentina	1895	5
14	6	Italy	1891	19
15		Peru	1890	11
16	2	Switzerland	1879	6
17	8	Chile	1869	9
18	1	Sweden	1866	24
19	8	Mexico	1829	15
20	3	Iran	1816	37
*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. Other implementations of the Elo rating system are possible 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

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.

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.

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. 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.

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 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
${\displaystyle K}$	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.

See also

• Statistical association football predictions

References

1. "The World Football Elo Rating System". Eloratings.net. Retrieved 26 February 2012.
2. ^ Lyons, Kieth. "What are the World Football Elo Ratings?". The Conversation. Retrieved 12 July 2018.
3. Arora, Abhishek. "FIFA revises World Ranking system, to follow a modified version of the Elo system now". Sports Keeds. Retrieved 12 July 2018.
4. "World Football Elo Ratings". Elo ratings. Retrieved 10 July 2018.
5. "FIFA/Coca-Cola World Ranking" (Press release). FIFA. 7 June 2018. Retrieved 17 May 2018.
6. ^ J. Lasek, Z. Szlávik and S. Bhulai (2013), The predictive power of ranking systems in association football, Int. J. Applied Pattern Recognition1: 27-46.
7. FIFA Council, 2026 FIFA World Cup™: FIFA Council designates bids for final voting by the FIFA Congress, 10 Jun 2018
8. ^ FIFA council, Revision of the FIFA / Coca-Cola World Ranking

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• Use dmy dates from February 2012
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