# World Football Elo Ratings

Rank Change Team Top 20 rankings 1 1 2126 2 1 2050 3 2049 4 2029 5 4 2012 6 2 1981 7 4 1979 8 3 1971 9 3 1956 10 1940 11 2 1926 12 2 1922 13 3 1901 14 2 1890 15 8 1886 16 3 1885 17 3 1876 18 1827 19 9 1825 20 3 1810 *Change from one year ago Complete rankings at eloratings.net

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.[2] 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.[3]

## 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.[4]

Nation Games[a] Days as
First date
Last date
301 8,772 12 Jun 1958 current
154 10,605 30 Nov 1872 11 Jun 1988
[c] 139 4,704 25 Jul 1966 9 Nov 2017
123 9,165 20 Jul 1902 10 Nov 2016
78 2,869 28 Aug 1920 12 Oct 2013
73 2,022 12 Sep 1984 11 Oct 2018
57 1,897 20 Sep 1952 13 Mar 1960
42 5,966 4 Mar 1876 20 Oct 1926
41 2,694 7 Jun 1934 16 Aug 2006
[d] 41 1,367 21 Mar 1963 25 Jun 1988
37 1,794 29 Aug 1920 16 Jun 1929
32 1,039 1 Jun 1978 4 Jul 2014
6 676 5 Jun 1914 8 Oct 1916
3 11 27 May 1934 7 Jun 1934
2 8 27 Jun 2004 8 Jun 2005
1. ^ Number of games played (started) with the highest Elo rating amongst nations
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.

## History and overview

The Elo system, developed by Hungarian-American mathematician Arpad Elo, 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.[5] 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 [2] 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.[6] 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.[2]

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.[7]

## Calculation principles

The ratings are based on the following formulae:

${\displaystyle R_{n}=R_{o}+P}$

where

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

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:

Tournament or Match type 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 G
0 1
+1 1
+2 1.5
+3 1.75
+4 1.875
+5 2
+6 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

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 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:

 Score ${\displaystyle K}$  ${\displaystyle G}$  ${\displaystyle W}$  ${\displaystyle W_{e}}$  Total (P) 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

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:

 Score ${\displaystyle K}$  ${\displaystyle G}$  ${\displaystyle W}$  ${\displaystyle W_{e}}$  Total (P) 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

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.