World Football Elo Ratings

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]

Top 100

The following table shows the top 100 teams in the World Football Elo Ratings as they were on 5 February 2021, using data from the World Football Elo Ratings web site.[3]

Each national team's FIFA World Ranking is shown as per the latest release on 10 December 2020.[4]

AFC

CAF

CONCACAF

CONIFA

CONMEBOL

OFC

UEFA

Elo Rank 1 Year Change Team Elo Rating FIFA Rank 1 1  Brazil 2136 3 2 1  Belgium 2111 1 3  France 2092 2 4  Spain 2050 6 5 1  Portugal 2038 5 6 2  Italy 1998 10 7 2  Netherlands 1995 14 8 1  Argentina 1991 7 9 3  England 1962 4 10 1  Germany 1956 13 11 2  Uruguay 1954 8 12 2  Mexico 1931 9 13 3  Denmark 1927 12 14 7  Colombia 1896 15 15   Switzerland 1871 16 16 3  Croatia 1860 11 17 2  Ukraine 1834 24 18 7  Wales 1829 18 19 19  Ecuador 1826 56 20 2  Sweden 1821 20 21  Chile 1813 17 3  Poland 1813 19 23 3  Venezuela 1802 28 24 7  Peru 1793 25 25 6  Austria 1786 23 26 3  Serbia 1775 30 27  South Korea 1772 38 28 5  Paraguay 1769 34 29 3  Iran 1763 29 10  Norway 1763 44 31 3  Czech Republic 1761 42 32 4  Senegal 1758 20 33 7  Turkey 1753 32 34 5  Algeria 1751 31

Elo Rank 1 Year Change Team Elo Rating FIFA Rank 35 2  United States 1749 22 36 19  Hungary 1745 40 37 7  Japan 1744 27 38 16  Russia 1743 39 39 1  Australia 1712 41 40 9  Finland 1709 55 41 6  Morocco 1683 35 42 1  Nigeria 1670 35 43 1  Romania 1666 37 44 9  Slovakia 1664 33 45 5  Scotland 1660 48 46 10  Republic of Ireland 1658 42 47 1  Qatar 1640 58 48 4  Bosnia & Herzegovina 1634 55 49 6  Iceland 1633 46 50 10  Slovenia 1628 62 51 6  Greece 1627 53 52 1  Iraq 1626 69 53 5  Costa Rica 1623 51 54 2  Ivory Coast 1619 61 55 2  Tunisia 1618 26 56 4  Honduras 1610 64 57 6  Cameroon 1607 50 58 7  Ghana 1606 52 59 2  Egypt 1605 49 60 2  Canada 1600 72 61 10  Israel 1592 87 62 17  Northern Ireland 1586 45 63 1  Jamaica 1584 47 64 5  Bolivia 1583 79 65 7  Mali 1577 57 66 4  North Macedonia 1569 65 67 6  Bahrain 1562 97 68 1  Haiti 1558 84

Elo Rank 1 Year Change Team Elo Rating FIFA Rank 69 6  Albania 1556 66 70 2  Saudi Arabia 1555 67 71 5  Burkina Faso 1553 58 72 8  Uzbekistan 1550 85 73 6  Panama 1539 78 74 3  Montenegro 1531 63 75 18  Armenia 1523 99 76 3  South Africa 1518 71 77 8  Georgia 1507 89 78 13  Bulgaria 1505 68 79 1  DR Congo 1503 60 80 2  Oman 1501 82 81 6  Jordan 1497 95 82 1  Belarus 1496 88 83 17  Kosovo 1491 117 84 3  Guatemala[lower-alpha 1] 1488 131 85 1  New Zealand 1486 118 86  Syria 1485 76 8  Uganda 1485 79 88 1  Benin 1481 83 89 4  El Salvador 1479 70 90  China PR 1460 75 91 1  Northern Cyprus[lower-alpha 2] 1456 — 92 3  Martinique[lower-alpha 3] 1446 — 93 6  Zambia 1443 90 94 2  Guinea 1438 73 95 5  Gabon 1434 86 96 2  United Arab Emirates 1430 74 97 1  Madagascar 1425 94 98 2  Kurdistan Region[lower-alpha 4] 1424 — 99 4  Zimbabwe 1421 108 100 2  Curaçao 1414 76 101 6  Palestine 1412 102 102 2  Vietnam 1408 93

1. Guatemala is ranked significantly lower in the FIFA Ranking partly because they were inactive from September 2016 to August 2018 due to their suspension from FIFA. While this caused their FIFA Ranking to fall dramatically under the former system, their World Football Elo Rating remained the same.
2. Northern Cyprus is not a member of FIFA and is not included in the FIFA Rankings. Also, the team has played only 17 matches against other Elo-ranked teams, so its Elo rating is provisional.
3. Martinique is also not a member of FIFA, so is not included in the FIFA Rankings.
4. Iraqi Kurdistan is not a member of FIFA and is not included in the FIFA Rankings. Also, the team has played only 4 matches against other Elo-ranked teams, so its Elo rating is provisional.

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.[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/[1]

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.[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.[1]

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] 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.[8] 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:

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

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

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.[8]

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 (${\displaystyle \forall }$ N ≥ 3)

${\displaystyle G={\frac {11+N}{8}}}$

Table of examples:

Goal Difference	0	+1	+2	+3	+4	+5	+6	+7	+8	+9	+10
G	1	1	1.5	1.75	1.875	2	2.125	2.25	2.375	2.5	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

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 (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.[8]

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:

	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

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	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

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.

See also

• Statistical association football predictions

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. "World Football Elo Ratings". Elo ratings. Retrieved 5 February 2021.
4. "FIFA/Coca-Cola World Ranking" (Press release). FIFA. 10 December 2020. Retrieved 10 December 2020.
5. Lyons, Keith. "What are the World Football Elo Ratings?". The Conversation. Retrieved 16 July 2018.
6. "The World Football Elo Rating System". Eloratings.net. Retrieved 26 February 2012.
7. FIFA Council, 2026 FIFA World Cup™: FIFA Council designates bids for final voting by the FIFA Congress, 10 June 2018
8. FIFA council, Revision of the FIFA / Coca-Cola World Ranking

External links

• Website