User:Onak Proudmoore/sandbox

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. 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.

Top 100
The following table shows the top 100 teams in the World Football Elo Ratings as they were on 27 March 2021, 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 18 February 2021.

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 the first international match in 1872:

All-time team highs and lows
The following is a list of national football teams ranked by the highest Elo rating they ever reached. The table also includes the highest ranking as well as the lowest rating and ranking reached by each nation. The team that has achieved the highest rank in each confederation is shown in color.

Average ratings
Time averaged Elo or Elo-like scores are routinely used to compare chess player strengths.

Highest average ratings since 1970
This table is a list of the national teams with the highest average Elo score since 1 January 1970, i.e. over approximately the last half century. 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. Only those teams are displayed that started playing before 1970 and played the entire period without a 5-year or longer interruption. Some excluded strong national football teams, like East-Germany and Croatia, appear in the decades tables below.

Averages by decade
The tables below shows the teams with the best average Elo score per decade (1 Jan XXX0 - 31 Dec XXX9). Only those teams are displayed that had played before the start of the decade and played at least ten games in the decade, and only teams which had already played at least one game before or on the start date are displayed.

Highest average over entire team history
The eloratings.net website presents the average ratings since the first international match of each team. Such averages can not really be compared to each other, as they represent strengths over different periods and in different pools. For example, they represent 151 years of matches for Scotland (34 years of which in a pool of 3 or 4 British nations only), 103 years for Spain, 32 years for Ukraine, and 17 years years for Montenegro. For Croatia and Slovakia the average is dominated by the single rating during the 50 years between the few games played between 1940 and 1943 and the rebirth of the countries in the 1990s. Likewise, South Africa's average is mostly determined by the 44 matches (of a 417 total in 2018) played in the 86 years before it rejoined FIFA in 1992.

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 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. 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/

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 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.

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.

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. The major difference between the World Football Elo Rating and the new men's FIFA rating system is that the latter does not consider goal differential and counts a penalty shoot-out as a win/loss rather than a draw; thus, a 7:0 blowout is 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 is also less sensitive to the difference in ratings and more sensitive to match status. 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.

Calculation principles
The ratings are based on the following formulae:


 * $$R_n = R_o + P$$

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

Where;

"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: 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.

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 ($$ \forall $$ N ≥ 3)
 * $$G = \frac{11+N}{8}$$

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.

The FIFA adaptation of the Elo rating does not incorporate a home team advantage and has a larger divisor in the formula (600 vs 400), making the points exchange less sensitive to the rating difference of two teams.

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:

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:

Team B drops fewer 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.