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{{Use dmy dates|date=February 2012}}
The '''Elo Ratings System for football''' is a ranking system for men's national ] teams that is published by the website eloratings.net. It is based on the ] 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.<ref name="Laesk et. al."/> FIFA's official rankings, both the ] for men and the ] 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.<ref>{{cite web |url=https://www.fifa.com/about-fifa/news/y=2018/m=6/news=2026-fifa-world-cuptm-fifa-council-designates-bids-for-final-voting-by-the-fifa-.html|title=2026 FIFA World Cup™: FIFA Council designates bids for final voting by the FIFA Congress|work=fifa.com|publisher=FIFA|date=10 June 2018|accessdate=2 July 2018}}</ref>

==Top 25==
The following table shows the top 25 teams in the World Football Elo Ratings as they were on 8 July 2019.<ref>{{cite web|title=World Football Elo Ratings|url=http://www.eloratings.net|website=Elo ratings|accessdate=3 June 2019}}</ref> Each team's ] is shown for comparison, as per the latest release on 14 June 2019.<ref>{{cite press release |title=FIFA/Coca-Cola World Ranking |publisher=] |date=15 June 2019 |url=https://www.fifa.com/fifa-world-ranking/ranking-table/men/index.html |accessdate=14 June 2019 }}</ref>

{| class="wikitable sortable" style="text-align:center"
|-
!Elo<br>Rank!!1 Year<br>Change!!scope="col" |Team!!Elo<br>Rating!!FIFA<br>Rank!!Confederation
|-
|1||{{steady}} ||align=left|{{fb|BRA}}||2126||3||CONMEBOL
|-
|2||{{steady}} ||align=left|{{fb|FRA}}||2050||2||UEFA
|-
|3||{{steady}} ||align=left|{{fb|BEL}}||2049||1||UEFA
|-
|4||{{steady}} ||align=left|{{fb|ESP}}||2029||7||UEFA
|-
|5||{{increase}} 4||align=left|{{fb|COL}}||2012||13||CONMEBOL
|-
|6||{{increase}} 2||align=left|{{fb|POR}}||1981||5||UEFA
|-
|7||{{increase}} 4||align=left|{{fb|NED}}||1979||14||UEFA
|-
|8||{{decrease}} 2||align=left|{{fb|GER}}||1971||11||UEFA
|-
|9||{{decrease}} 2||align=left|{{fb|URU}}||1956||8||CONMEBOL
|-
|10||{{decrease}} 5||align=left|{{fb|ENG}}||1940||4||UEFA
|-
|11||{{increase}} 1||align=left|{{fb|ARG}}||1926||11||CONMEBOL
|-
|12||{{increase}} 2||align=left|{{fb|ITA}}||1922||14||UEFA
|-
|13||{{increase}} 3||align=left|{{fb|SUI}}||1901||9||UEFA
|-
|14||{{decrease}} 2||align=left|{{fb|DEN}}||1890||10||UEFA
|-
|15||{{increase}} 4||align=left|{{fb|MEX}}||1886||18||CONCACAF
|-
|16||{{decrease}} 6||align=left|{{fb|CRO}}||1885||6||UEFA
|-
|17||{{decrease}} 2||align=left|{{fb|PER}}||1876||21||CONMEBOL
|-
|18||{{steady}} ||align=left|{{fb|SWE}}||1827||17||UEFA
|-
|19||{{increase}} 9||align=left|{{fb|UKR}}||1824||24||UEFA
|-
|20||{{decrease}} 3||align=left|{{fb|CHI}}||1809||16||CONMEBOL
|-
|21||{{steady}} ||align=left|{{fb|POL}}||1804||19||UEFA
|-
|22||{{increase}} 10||align=left|{{fb|VEN}}||1797||33||CONMEBOL
|-
|rowspan=2|23||{{decrease}} 3||align=left|{{fb|IRN}}||1796||20||AFC
|-
|{{steady}} ||align=left|{{fb|SRB}}||1796||34||UEFA
|-
|25||{{increase}} 1||align=left|{{fb|KOR}}||1786||37||AFC
|}

==Ranking by matches played as leader==
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, ranked by number of days at the top position.<ref> at eloratings.net. Yearly graphs, like , give enough resolution. For individual dates, the is also a good source.</ref>
<!--Data from eloratings.org as of January 1 2019; let's check for historical changes at the website just once a year -->
{| class="wikitable sortable" style="font-size: 100%;"
|-
!Nation!!Games{{efn|Number of games played (started) with the highest Elo rating amongst nations}}!!Days as<br/>leader{{efn|Days spent as co-leaders are counted as a ½ day}}!!First date<br/>as leader!!Last date<br/>as leader
|-
|{{fb|BRA}} ||align=center|301 ||align=center|{{age in days|11 Oct 2018|{{extract|currentdate|add=8461d}}}} || align=right|12 Jun 1958 ||align=center|''current''
|-
|{{fb|ENG}} ||align=center|154 ||align=center|10,605 ||align=right|30 Nov 1872 ||align=right|11 Jun 1988
|-
|{{fb|GER}} {{efn|Combined record of the ] (1908–1950 & 1990–present) and ] (1950–1990) national football teams.}} ||align=center|139 ||align=center|4,704 ||align=right|25 Jul 1966 ||align=right|9 Nov 2017
|-
|{{fb|ARG}} ||align=center|123 ||align=center|9,165 ||align=right|20 Jul 1902 ||align=right|10 Nov 2016
|-
|{{fb|ESP}} ||align=center|78 ||align=center|2,869 ||align=right|28 Aug 1920 ||align=right|12 Oct 2013
|-
|{{fb|FRA}} ||align=center|73 ||align=center|2,022 ||align=right|12 Sep 1984 ||align=right|11 Oct 2018
|-
|{{fb|HUN}} ||align=center|57 ||align=center|1,897 ||align=right|20 Sep 1952 ||align=right|13 Mar 1960
|-
|{{fb|SCO}} ||align=center|42 ||align=center|5,966 ||align=right|4 Mar 1876 ||align=right|20 Oct 1926
|-
|{{fb|ITA}} ||align=center|41 ||align=center|2,694 ||align=right|7 Jun 1934 ||align=right|16 Aug 2006
|-
|{{fb|URS}} {{efn|So far, only the ] (1924–1992) has reached the #1 position, but any future efforts by the ] (1992–present) will be included.}} ||align=center|41 ||align=center| 1,367 ||align=right|21 Mar 1963 ||align=right|25 Jun 1988
|-
|{{fb|URU}} ||align=center|37 ||align=center|1,794 ||align=right|29 Aug 1920 ||align=right|16 Jun 1929
|-
|{{fb|NED}} ||align=center|32 ||align=center|1,039 ||align=right|1 Jun 1978 ||align=right|4 Jul 2014
|-
|{{fb|DEN}} ||align=center|6 ||align=center|676 ||align=right|5 Jun 1914 ||align=right|8 Oct 1916
|-
|{{fb|AUT}} ||align=center|3 ||align=center|11 ||align=right|27 May 1934 ||align=right|7 Jun 1934
|-
|{{fb|CZE}} ||align=center|2 ||align=center|8 ||align=right|27 Jun 2004 ||align=right|8 Jun 2005
|}
{{notelist}}
{{clear}}

==History and overview==
The Elo system, developed by Hungarian-American mathematician ], is used by ], the international chess federation, to rate ] players, and by the ], to rate ] players. In 1997, Bob Runyan adapted the Elo rating system to international ] and posted the results on the Internet.<ref>{{cite web |last1=Lyons |first1=Kieth |title=What are the World Football Elo Ratings? |url=https://theconversation.com/what-are-the-world-football-elo-ratings-27851 |publisher=The Conversation |accessdate=16 July 2018}}</ref> 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 <ref name="Laesk et. al.">J. Lasek, Z. Szlávik and S. Bhulai (2013), , Int. J. Applied Pattern Recognition1: 27-46.</ref> 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:
*] Finals
*] finals and Intercontinental tournaments
*World Cup and Continental championship qualifiers
*All other tournaments
*]es

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.<ref>{{cite web|url=http://www.eloratings.net/about |title=The World Football Elo Rating System |publisher=Eloratings.net |accessdate=26 February 2012}}</ref> 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.<ref name="Laesk et. al." />

The ] is the official national teams rating system used by the ]. The ] 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.<ref>FIFA Council, , 10 Jun 2018</ref> 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 ] as a win/loss rather than a draw; thus, a 7:0 ] is considered equal to a 7:6 penalty shoot-out win (neither method distinguishes a win in ] from a win in regular time). The FIFA method is also less sensitive to the difference in ratings and more sensitive to match status.<ref name=fifarev>FIFA council, </ref> 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==
<!--This text is a tad unclear and as it is doesn't add to the understanding
The basic principle behind the Elo ratings is only in its simplest form similar to that of a league; unlike the FIFA rankings, 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:

:'''<math>R_n = R_o + P</math>'''
where
:'''<math>P = K G (W - W_e)</math>'''

Where;
{| style="width:50%;"
|-
|width=4%|
|-
|'''<math>R_n</math>'''||= The new team rating
|-
|'''<math>R_o</math>'''||= The old team rating
|-
|'''<math>K</math>'''||= Weight index regarding the tournament of the match
|-
|'''<math>G</math>'''||= A number from the index of goal differences
|-
|'''<math>W</math>'''||= The result of the match
|-
|'''<math>W_e</math>'''||= The expected result
|-
|'''<math>P</math>'''||= 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:
{| class="wikitable" style="font-size: 90%;"
|-
!Tournament or Match type!!K
|-
|], ] (1908–1980) ||60
|-
|] and intercontinental tournaments||50
|-
|World Cup and Continental qualifiers and major tournaments||40
|-
|All other tournaments||30
|-
|]es||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
:<math>G = 1</math>

If the game is won by two goals
:<math>G = \frac{3}{2}</math>

If the game is won by three or more goals
*Where '''N''' is the goal difference
:<math>G = \frac{11+N}{8}</math>

Table of examples:

{| class="wikitable" style="font-size:90%"
|-
!Goal Difference!!G
|-
|0||1
|-
|<nowiki>+1</nowiki>||1
|-
|<nowiki>+2</nowiki>||1.5
|-
|<nowiki>+3</nowiki>||1.75
|-
|<nowiki>+4</nowiki>||1.875
|-
|<nowiki>+5</nowiki>||2
|-
|<nowiki>+6</nowiki>||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<sub>e</sub> is the expected result (win expectancy with a draw counting as 0.5) from the following formula:

:<math>W_e = \frac{1}{10^{-dr/400} + 1}</math>

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 for clarification===
The same example of a three-team friendly tournament on neutral territory is used as on the ] page. Beforehand team A had a rating of 630 points, team B 500 points, and teams C 480 points.<br>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:

{| class="wikitable" style="font-size: 90%;"
|-
| ||'''Team A'''||'''Team B'''||'''Team A'''||'''Team B'''||'''Team A'''||'''Team B'''
|-
!Score
|colspan="2" style="text-align: center;"|3 : 1||colspan="2" style="text-align: center;"|1 : 3||colspan="2" style="text-align: center;"|2 : 2
|-
!'''<math>K</math>'''
|20||20||20||20||20||20
|-
!'''<math>G</math>'''
|1.5||1.5||1.5||1.5||1||1
|-
!'''<math>W</math>'''
|1||0||0||1||0.5||0.5
|-
!'''<math>W_e</math>'''
|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:

{| class="wikitable" style="font-size: 90%;"
|-
| ||'''Team B'''||'''Team C'''||'''Team B'''||'''Team C'''||'''Team B'''||'''Team C'''
|-
!Score
|colspan="2" style="text-align: center;"|3–1||colspan="2" style="text-align: center;"|1–3||colspan="2" style="text-align: center;"|2–2
|-
!'''<math>K</math>'''
|20||20||20||20||20||20
|-
!'''<math>G</math>'''
|1.5||1.5||1.5||1.5||1||1
|-
!'''<math>W</math>'''
|1||0||0||1||0.5||0.5
|-
!'''<math>W_e</math>'''
|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==
*]
*]

==References==
{{reflist}}

==External links==
*

{{International Football}}
{{Sport world rankings}}

]
]

Latest revision as of 14:32, 9 July 2019

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