# World Football Elo Ratings

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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]

## 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.[3] 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 [4] 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:

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.[5] 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. [4]

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.[6] 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.[7] 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 100

The following table shows the top 100 teams in the World Football Elo Ratings as they were on 15 July 2018, using data from the World Football Elo Ratings web site.[8]

Each national team's FIFA World Ranking is shown as per the latest release on 7 June 2018.[9]

 AFC CAF CONCACAF CONIFA CONMEBOL OFC UEFA

1. ^ Northern Cyprus are not a member of FIFA and are not included in the FIFA Rankings. Also, they have played only 17 matches against other Elo-ranked teams, so their Elo rating is provisional.
2. ^ Martinique are also not members of FIFA, so are not included in the FIFA Rankings.
3. ^ Kuwait is ranked much lower in the FIFA Ranking because they were inactive from October 2015 to December 2017 due to their suspension from FIFA. While this caused their FIFA Ranking to fall dramatically, their Elo rating remained the same. The same applies to Guatemala but to a lesser extent.

## 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 1872:[10]

## Ranking by days as leader

Nation Days[b] First Date as Leader Last Date as Leader
10,605 30 November 1872 11 June 1988
9,044 29 July 1908 9 November 2016
8,521 12 June 1958 14 July 2018
6,059 4 March 1876 19 Oct 1926
[c] 4,631 25 July 1966 9 November 2017
2,771 28 August 1920 11 October 2013
2,694 7 June 1934 15 August 2006
1,964 20 September 1952 12 March 1960
1,955 12 September 1984 Current
1,775 29 August 1920 15 June 1929
[d] 1,414 21 March 1963 24 June 1988
1,042 1 June 1978 3 July 2014
676 5 June 1914 7 Oct 1916
11 27 May 1934 6 June 1934
8 27 June 2004 7 June 2005
1. ^ a b c Number one position reached at / after first match
2. ^ Days spent as co-leaders are counted as a ½ day
3. ^ Combined record of the Germany (1908-1950 & 1990-present) and West Germany (1950-1990) national football teams.
4. ^ So far, only the Soviet Union national football team (1924-1992) has reached the #1 position, but any future efforts by the Russia national football team (1992-present) will be included.[11]

## Elo all-time records

### All-time highest ratings

The following is a list of national football teams ranked by their highest Elo score ever reached.[12] The team in each confederation that has achieved the highest rank is shown in color.

## Biggest upsets

This is a list of matches with the biggest point exchange.[13] 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.[f]
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 1676 1845 8–1 1924-05-29 Olympic Games Paris
2 92 1824 1991 7–1 1928-06-04 Olympic Games Amsterdam
1397 * 1655 4–0 1948-08-02 Olympic Games Walthamstow
4 87 1478 2041 3–1 1920-08-28 Olympic Games Antwerp
5 84 * 1677 1919 3–0 1924-05-29 Olympic Games Paris
1855 2003 6–1 1958-06-15 World Cup Helsingborg
7 83 1171 1523 4–0 1980-02-23 OFC Nations Cup Nouméa
8 82 1606 2005 2–0 2006-06-17 World Cup Cologne
9 81 2120 2122 1–7 2014-07-08 World Cup Belo Horizonte
10 80 1642 * 1567 16–0 1912-07-01 Olympic Games Solna
1604 * 1668 7–0 1954-06-20 World Cup Geneva
1481 1783 4–0 1973-12-14 CONCACAF Championship Port-au-Prince
1677 2044 2–0 2018-06-27 World Cup Kazan
14 78 1685 2054 3–0 1929-11-01 Copa América Buenos Aires
1587 1957 3–0 1937-01-10 Copa América Buenos Aires
16 77 1813 2162 3–0 1959-12-12 Copa América Guayaquil
1912 2090 3–0 1998-07-04 World Cup Lyon
18 76 1906 1714 0–2 1936-08-07 Olympic Games Berlin
1717 1491 1–4 1946-03-10 CCCF Championship San José
1888 1788 0–5 2009-07-26 CONCACAF Gold Cup East Rutherford
21 75 1759 2044 5–3 1948-08-05 Olympic Games London
1336 1646 3–0 1967-01-28 Copa América Montevideo
1986 2109 5–1 2014-06-13 World Cup Salvador
24 74 1800 2032 4–0 1987-07-03 Copa América Córdoba
25 73 511 758 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.

## Basic calculation principles

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:

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

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

The number of 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 given in the table below:

Tournament or Match type Index (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

### 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:

Goal Difference Coefficient of K (G)
0 1
+1 1
+2 1.5
+3 1.75
+4 1.875
+5 2
+6 2.125
+7 2.25
+8 2.375
+9 2.5
+10 2.625

### 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

We 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.

### Examples

The same examples have been used on the FIFA World Rankings for a fair comparison. Some actual examples should help to make the methods of calculation clear. In this instance it is assumed that three teams of different strengths are involved in a small friendly tournament on neutral territory.

Before the tournament the three teams have the following point totals.

Team Points
A 630
B 500
C 480

Thus, team A is by some distance the highest ranked of the three: The following table shows the points allocations based on three possible outcomes of the match between the strongest team A, and the somewhat weaker team B:

#### Example 1

Team A versus Team B (Team A stronger than Team B)

 Score Total (P) ${\displaystyle K}$ ${\displaystyle G}$ ${\displaystyle W}$ ${\displaystyle W_{e}}$ Team A Team B Team A Team B Team A Team B 3 : 1 1 : 3 2 : 2 20 20 20 20 20 20 1.5 1.5 1.5 1.5 1 1 1 0 0 1 0.5 0.5 0.679 0.321 0.679 0.321 0.679 0.321 +9.63 -9.63 -20.37 +20.37 -3.58 +3.58

#### Example 2

Team B versus Team C (both teams approximately the same strength)

When the difference in strength between the two teams is less, so also will be the difference in points allocation. The following 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:

 Score Total (P) ${\displaystyle K}$ ${\displaystyle G}$ ${\displaystyle W}$ ${\displaystyle W_{e}}$ Team B Team C Team B Team C Team B Team C 3–1 1–3 2–2 20 20 20 20 20 20 1.5 1.5 1.5 1.5 1 1 1 0 0 1 0.5 0.5 0.529 0.471 0.529 0.471 0.529 0.471 +14.13 -14.13 -15.87 +15.87 -0.58 +0.58

Note that Team B drops more ranking points by losing to Team C, which is approximately the same strength, than by losing to Team A, which is considerably better than Team B.

## Notes

1. ^ at present as Russia
2. ^ at present as Serbia
3. ^ On 1 January 2006, Football Federation Australia moved from the OFC to the AFC
4. ^ Algeria had only played 8 matches to this point.
5. ^ South Africa had only played 1 match to this point.
6. ^ In those terms, most surprising may have been the 2:1 win of Luxembourg (Elo rating 1036) over Switzerland (ER 1794) in a World Cup qualification match in September 2008 (a 758 point difference). In another World Cup qualifier in October 2004 Liechtenstein (ER 1049) held the 853 points higher rated Portuguese team (ER 1902) to a 2:2 draw.

## References

1. ^ J. Lasek, Z. Szlávik and S. Bhulai (2013), The predictive power of ranking systems in association football, Int. J. Applied Pattern Recognition1: 27-46.
2. ^ "2026 FIFA World Cup™: FIFA Council designates bids for final voting by the FIFA Congress". fifa.com. FIFA. 10 June 2018. Retrieved 2 July 2018.
3. ^ Lyons, Kieth. "What are the World Football Elo Ratings?". The Conversation. Retrieved 16 July 2018.
4. ^ a b J. Lasek, Z. Szlávik and S. Bhulai (2013), The predictive power of ranking systems in association football, Int. J. Applied Pattern Recognition1: 27-46.
5. ^ "The World Football Elo Rating System". Eloratings.net. Retrieved 26 February 2012.
6. ^ FIFA Council, 2026 FIFA World Cup™: FIFA Council designates bids for final voting by the FIFA Congress, 10 Jun 2018
7. ^ FIFA council, Revision of the FIFA / Coca-Cola World Ranking
8. ^ "World Football Elo Ratings". Elo ratings. Retrieved 15 July 2018.
9. ^ "FIFA/Coca-Cola World Ranking" (Press release). FIFA. 7 June 2018. Retrieved 17 May 2018.
10. ^ Graph of rankings at eloratings.net. Yearly graphs, like this one for 2018, give enough resolution. For individual dates, the Elo ratings table is also a good source.
11. ^ "History of the Football Union of Russia". Rfs.ru. Retrieved 2016-06-04.
12. ^ World Football Elo Ratings; under the columns tab choose "Highest Rank / Rating"
13. ^ Upsets at eloratings.net (per June 2018 this page is under reconstruction)
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