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The World Football Elo Ratings (Elo is pronounced E.L.O. despite the fact it is not an initialism) is a ranking system for men's national teams in football. The method used to rank teams is based upon the Elo rating system method but modified to take various football-specific variables into account. It is arguably superior to the FIFA World Rankings, the rating system used by FIFA, the international governing body of football, for men's national teams.

The 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.

The FIFA Women's World Rankings uses a simplified version of the Elo formula. The FIFA men's ranking, however, uses a non-Elo formula.

Top 20 ranking as of July 31 2006

Current table of Football Elo rankings, compiled by the World Football Elo Ratings web site based on data provided by Advanced Satellite Consulting.

List of number one teams

The following is the list of nations who have achieved the number one position on the World Football Elo Ratings since 2000:

Complete list since 1872: see World Football Elo Ratings leaders.

History

This system, developed by Hungarian mathematician Dr. Árpád Élő, is used by FIDE, the international chess federation, to rate chess 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.

Overview

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;

• World Cup Finals
• Continental championships finals
• World Cup and Continental championship qualifiers
• All other tournaments
• Friendly matches

A large difference here is that FIFA ranks the Confederations Cup third highest while the Elo system ranks it fifth (treating Continental and World Cup qualifiers separately for the purposes of comparison, because FIFA does)

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. Match data are primarily from International Football 1872 - Present web site.

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 tables 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 formulas:

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

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

Status of match

The status of the match is incorporated by the use of a weight constant. The weight is a constant regarding the "weight" or importance of a match, defined by which tournament the match is in, they are as follows;

Number of goals

The number of goals is taken into account by use of a goal difference index. G is increased by half if a game is won by two goals, and if the game is won by three or more goals by a number decided through the appropriate calculation shown below;

If the game is won by one goal

${\displaystyle G={\frac {1}{1}}}$

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).

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 plus 100 points for a team playing at home. 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.

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)

	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

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:

	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

See also

• FIFA World Rankings
• FIFA Women's World Rankings
• AQB Sports Ratings
• Elo rating system

References

1. http://www.englandstats.com/elo.php Why do we use ELO ratings over FIFA's official rankings?

External links

• World Football Elo ratings
• How the rankings are calculated

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Europe (UEFA)	UEFA European Championship U-21 U-19 U-17 UEFA Nations League Regional Central European Cup Balkan Cup Baltic Cup British Home Championship Nordic Championship
Inter-Continental	CONMEBOL–UEFA Cup of Champions CPF Panamerican Championship CAF-AFC Afro-Asian Cup of Nations AFC–OFC Challenge Cup FIFA Arab Cup Palestine Cup Kuneitra Cup Overseas Cup Afro-Asian Games Arab Games Francophone Games GANEFO Goodwill Games Islamic Games Islamic Solidarity Games Lusofonia Games Mediterranean Cup Mediterranean Games Pan American Games
Non-FIFA	CONIFA World Football Cup CONIFA European Football Cup CONIFA South America Football Cup CONIFA Africa Football Cup FIFI Wild Cup UIAFA Great European Tournament Island Games Micronesian Games Universiade World Unity Football Alliance
See also Geography Codes Player/Club of the Century Women's football

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