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{{Use dmy dates|date=February 2012}}
The '''Elo Rating 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. 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 |date= |accessdate=26 February 2012}}</ref> 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.<ref>J. Lasek, Z. Szlávik and S. Bhulai (2013), , Int. J. Applied Pattern Recognition1: 27-46.</ref>

The ] is the official national teams rating system used by the ]. The ] has used a modified version of the Elo formula since 2003. Following the ], the FIFA ranking will switch 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 ] and the future men's FIFA rating system is that the latter will not consider goal differential and will count a ] as a win/loss rather than a draw; thus, a 7:0 ] will be 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 will further be 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.

{| class="wikitable" style="font-size: 90%; float: right; margin-left: 1em"
|-
|colspan="5" style="text-align:center; font-size: 100%"|''']'''<!--(23:40 ])--><ref>{{cite web|title=World Football Elo Ratings|url=http://www.eloratings.net|website=Elo ratings|accessdate=10 July 2018}}</ref>
|-
!Elo<br>Rank!!1 Year<br>Change!!scope="col" style="width: 160px;"|Team!!Elo<br>Rating!!FIFA<br>Rank*
|- style="background:#ccebc5;"
|1||{{steady}} ||align=left|{{fb|BRA}}||2114||2
|- style="background:#d9edf4;"
|2||{{increase}} 4||align=left|{{fb|FRA}}||2097||7
|- style="background:#d9edf4;
|3||{{increase}} 9||align=left|{{fb|BEL}}||2023||3
|- style="background:#d9edf4;"
|4||{{steady}} ||align=left|{{fb|ESP}}||2010||10
|- style="background:#d9edf4;"
|5||{{increase}} 5||align=left|{{fb|ENG}}||1984||12
|- style="background:#d9edf4;"
|6||{{decrease}} 4||align=left|{{fb|GER}}||1964||1
|- style="background:#ccebc5;"
|7||{{increase}} 11||align=left|{{fb|URU}}||1946||14
|- style="background:#d9edf4;"
|8||{{decrease}} 3||align=left|{{fb|POR}}||1940||4
|- style="background:#ccebc5;"
|rowspan=2 bgcolor=#cccccc|9 ||{{decrease}} 2||align=left|{{fb|COL}}||1939||16
|- style ="background:#d9edf4;"
|{{increase}} 7||align=left|{{fb|CRO}}||1939||20
|- style="background:#d9edf4;"
|11||{{increase}} 6||align=left|{{fb|NED}}||1908||17
|- style="background:#d9edf4;"
|12||{{increase}} 21||align=left|{{fb|DEN}}||1896||12
|- style="background:#ccebc5;"
|13||{{decrease}} 10||align=left|{{fb|ARG}}||1895||5
|- style="background:#d9edf4;"
|14||{{decrease}} 6||align=left|{{fb|ITA}}||1891||19
|- style="background:#ccebc5;"
|15||{{steady}} ||align=left|{{fb|PER}}||1890||11
|- style="background:#d9edf4;"
|16||{{decrease}} 2||align=left|{{fb|SUI}}||1879||6
|- style="background:#ccebc5;"
|17||{{decrease}} 8||align=left|{{fb|CHI}}||1869||9
|- style="background:#d9edf4;"
|18||{{increase}} 1||align=left|{{fb|SWE}}||1866||24
|- style="background:#decbe4;"
|19||{{decrease}} 8||align=left|{{fb|MEX}}||1829||15
|- style="background:#fbb3ad;"
|20||{{increase}} 3||align=left|{{fb|IRN}}||1816||37
<!--On the cusp
|- style="background:#d9edf4;"
|21||{{decrease}} 8||align=left|{{fb|POL}}||1783||8
|- style="background:#d9edf4;"
|22||{{increase}} 4||align=left|{{fb|WAL}}||1777||18
|- style="background:#d9edf4;"
|23||{{increase}} 9||align=left|{{fb|SRB}}||1772||34
|- style="background:#decbe4;"
|24||{{increase}} 5||align=left|{{fb|USA}}||1764||25
|- style="background:#fed9a5;"
|24||{{increase}} 12||align=left|{{fb|SEN}}||1764||27
-->
|-
! colspan="5" | <small>*FIFA rankings per 7 June 2018 <ref>{{cite press release |title= FIFA/Coca-Cola World Ranking |publisher= ] |date=7 June 2018|url= https://www.fifa.com/fifa-world-ranking/ranking-table/men/index.html |accessdate=17 May 2018}}</ref></small>
|-
| colspan="5" style="text-align:center;"|<small></small>
|}
{| class="wikitable floatright" style="font-size: 70%; margin-left: 1em"
|-
| style="background:#fbb3ad; width:7em; text-align: center"|]
| style="background:#fed9a5; width:7em; text-align: center"|]
| style="background:#decbe4; width:7em; text-align: center"|]
|-
| style="background:#ccebc5; width:7em; text-align: center"|]
| style="background:#faecc8; width:7em; text-align: center"|]
| style="background:#d9edf4; width:7em; text-align: center"|]
|}
{{TOC hidden}}

==History and overview==
The Elo system, developed by ]-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. 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
<!--This duplicates what is spelled out in a little table a few paragraphs down
The different weights of competitions in descending order are:
*] Finals
*] finals and Intercontinental tournaments
*World Cup and Continental championship qualifiers
*All other tournaments
*]es
-->
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==
<!--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 + K G (W - W_e)</math>'''
or
:'''<math>P = K G (W - W_e)</math>'''

Where;
{| style="width:50%;"
|-
|width=4%|
|-
|'''<math>R_n</math>'''||= The new team rating<br>
|-
|'''<math>R_o</math>'''||= The old team rating<br>
|-
|'''<math>K</math>'''||= Weight index regarding the tournament of the match<br>
|-
|'''<math>G</math>'''||= A number from the index of goal differences<br>
|-
|'''<math>W</math>'''||= The result of the match<br>
|-
|'''<math>W_e</math>'''||= The expected result<br>
|-
|'''<math>P</math>'''||= Points Change<br>
|}

"Points Change" is rounded to the nearest integer before updating the team rating. <br>

===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!!Index (K)
|-
|], ] (1908-1980) ||60
|-
|] and intercontinental tournaments||50
|-
|World Cup and Continental qualifiers and major tournaments||40
|-
|All other tournaments||30
|-
|]es||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.<ref name=fifarev/>

===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!!Coefficient of K (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.<br>
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.<ref name=fifarev/>

===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==
{{Main|World Football Elo Ratings}}
*]

==References==
{{reflist|30em}}

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

]
]

Latest revision as of 14:32, 9 July 2019

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