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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. The FIFA World Rankings, not based on the Elo method, but changing soon, is the official national teams rating system used by the international governing body of football and is therefore more prevalent.

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. Ratings for teams with fewer than 30 matches are considered provisional.

The FIFA Women's World Rankings system uses a modified version of the Elo formula whereas the FIFA men's ranking system uses a non-Elo formula. 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 performed poorly.

Top 100
The following table shows the top 100 teams in the World Football Elo Ratings as they were on 7 July 2018 (23:40 FET), using data from the World Football Elo Ratings web site.

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

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:

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

All-time highest ranking
The following is a list of national football teams ranked by their highest Elo ranking ever reached.

The biggest point gap between 1st and 2nd national team was between 14 march and 21 March 1885, when Scotland (at 2094) led by 205 points over 2nd ranked England (at 1889).
 * The biggest point gap:

Average ratings
Time averaged Elo or Elo-like scores are routinely used to compare chess player strengths. The following is a list of the national teams with the highest average Elo score from 1 January 1970 to 1 January 2018. Before this time intercontinental play was fairly limited and many nations in Africa, North America, and Asia had played too few games yet to create a representative Elo score.

Averages by decade
The table below shows the teams with the best average Elo score per decade (Jan 1 XXX0 - Dec 31 XXX9).

Highest rated matches
A list of the 25 matches between teams with the highest combined Elo ratings (the nations' points before the matches are given).

Biggest upsets
This is a list of matches with the biggest point exchange. 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. The nations' points before the matches are given. * 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.

History
The Elo system, developed by Hungarian-American mathematician Dr. 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. He was also the first maintainer of the World Football Elo Ratings web site, now maintained by Kirill Bulygin.

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 and Intercontinental tournaments
 * World Cup and Continental championship qualifiers
 * All other tournaments
 * Friendly matches

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.

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:


 * $$R_n = R_o + K G (W - W_e)$$

or


 * $$P = K G (W - W_e)$$

Where;

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:

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
 * $$G = 1$$

If the game is won by two goals
 * $$G = \frac{3}{2}$$

If the game is won by three or more goals
 * Where N is the goal difference
 * $$G = \frac{11+N}{8}$$

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). 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:


 * $$W_e = \frac{1}{10^{-dr/400} + 1}$$

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. 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)

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:

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.