Elo Rating System for football

Add links
From Wikipedia, the free encyclopedia

This is an old revision of this page, as edited by 198.84.253.202 (talk) at 16:30, 4 July 2018 (→‎Biggest upsets: this might be listed directly on the site, but again little significance and the WP:OR comment about "most surprising" doesn't qualify as proper commentary to keep this in the article). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

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. Ratings tend to converge on a team's true strength relative to its competitors after about 30 matches.[1] Ratings for teams with fewer than 30 matches are considered provisional.

Other implementations of the Elo rating system are possible. 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 in place until July 2018 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. Following the 2018 World Cup, the FIFA ranking will switch to an Elo-based ranking as well, starting from the current FIFA rating points.[3]

The major difference between the World Football Elo Rating and the future men's FIFA rating system is that the latter will not consider goal differential and will count a penalty shoot-out as a win/loss rather than a draw; thus, a 7:0 blowout will be 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 will further be less sensitive to the difference in ratings and more sensitive to match status.[4] 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.

Top 80 ratings as of 3 July 2018[5]
Elo
Rank		 1 Year
Change		 Team Elo
Rating		 FIFA
Rank*
1 Steady  Brazil 2156 2
2 Increase 4  France 2029 7
3 Increase 8  Belgium 2010 3
Increase 1  Spain 2010 10
5 Increase 13  Uruguay 1986 14
6 Decrease 4  Germany 1964 1
7 Increase 9  Croatia 1950 20
8 Increase 2  England 1944 12
9 Decrease 4  Portugal 1940 4
10 Decrease 3  Colombia 1939 16
11 Increase 6  Netherlands 1908 17
12 Increase 7  Sweden 1906 24
13 Decrease 10  Argentina 1896 5
Increase 20  Denmark 1896 12
15 Decrease 7  Italy 1891 19
16 Decrease 1  Peru 1890 11
17 Decrease 3   Switzerland 1879 6
18 Decrease 9  Chile 1869 9
19 Decrease 7  Mexico 1829 15
20 Increase 3  Iran 1816 37
21 Decrease 8  Poland 1783 8
22 Increase 3  Wales 1777 18
23 Increase 9  Serbia 1772 34
24 Increase 2  United States 1764 25
25 Increase 11  Senegal 1763 27
26 Increase 8  South Korea 1757 57
27 Steady  Slovakia 1752 28
28 Increase 2  Ukraine 1750 35
29 Decrease 9  Ecuador 1747 60
30 Steady  Bosnia & Herzegovina 1745 40
31 Increase 8  Austria 1742 26
32 Increase 8  Venezuela 1739 33
33 Decrease 9  Republic of Ireland 1729 31
34 Increase 3  Paraguay 1728 32
Decrease 12  Turkey 1728 38
36 Increase 8  Romania 1727 30
37 Decrease 8  Costa Rica 1726 23
38 Increase 22  Morocco 1720 41
39 Decrease 4  Australia 1713 36
Decrease 1  Czech Republic 1713 46
41 Increase 2  Russia 1710 70
42 Decrease 1  Scotland 1709 42
43 Decrease 23  Iceland 1708 22
44 Increase 9  Nigeria 1702 48
45 Decrease 17  Japan 1699 61
46 Decrease 1  Northern Ireland 1676 29
47 Increase 19  Tunisia 1662 21
48 Decrease 7  Bolivia 1661 59
49 Decrease 3  Greece 1646 44
50 Decrease 3  Cameroon 1645 49
Increase 17  Ghana 1645 47
52 Increase 17  Norway 1640 53
53 Decrease 2  Slovenia 1626 56
54 Increase 1  Bulgaria 1615 49
55 Increase 13  Syria 1606 73
56 Increase 20  Finland 1605 63
57 Decrease 8  Ivory Coast 1602 68
58 Decrease 6  Uzbekistan 1599 95
59 Decrease 1  Burkina Faso 1597 52
Increase 3  Montenegro 1597 43
61 Decrease 11  Panama 1596 55
62 Increase 1  Honduras 1590 62
63 Decrease 2  DR Congo 1589 38
64 Decrease 7  Saudi Arabia 1588 67
65 Decrease 11  Hungary 1576 51
66 Decrease 18  Egypt 1575 45
67 Increase 18  Jamaica 1574 54
68 Decrease 4  South Africa 1565 74
69 Decrease 10  Albania 1560 58
70 Increase 8  Iraq 1550 89
71 Increase 24  Oman 1539 84
72 Increase 9  Canada 1534 79
Decrease 1  China 1534 75
74 Decrease 2  United Arab Emirates 1532 77
75 Decrease 5  Israel 1527 93
76 Decrease 11  Belarus 1522 78
77 Decrease 2  Mali 1519 64
78 Increase 15  North Macedonia 1518 71
79 Increase 1  Guatemala 1511 146
80 Decrease 25  Algeria 1508 66
*FIFA rankings per 7 June 2018 [6]
Complete rankings at eloratings.net
AFC CAF CONCACAF CONIFA
CONMEBOL OFC UEFA


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.

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

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.

Calculation principles

The ratings are based on the following formulae:

or

Where;

= The new team rating
= The old team rating
= Weight index regarding the tournament of the match
= A number from the index of goal differences
= The result of the match
= The expected result
= 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 Index (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.[4]

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

If the game is won by two goals

If the game is won by three or more goals

  • Where N is the goal difference

Table of examples:

Goal Difference Coefficient of K (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:

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 will not incorporate a home team advantage and will have a larger divisor in the formula (600 vs 400), making the points exchange less sensitive to the rating difference of two teams.[4]

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 600 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
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
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
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
Total (P) +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.

List of number one teams

The following is the list of nations who reached a first rank in ratings since 1872.[7]

  1. ^ a b c Number one position reached at / after first match

All-time highest ratings

The following is a list of national football teams ranked by their highest Elo score ever reached.[8] The team in each confederation that has achieved the highest rank is shown in color.

  1. ^ at present as Russia
  2. ^ at present as Serbia
  3. ^ Switzerland reached a low of 1485 after its second match in March 1908.
  4. ^ a b The combined Ireland national football team was in 4th place from its first match in 1882 to 1902, in a period that only 4 teams were in the rankings. It reached a low ratings of 1237 on 29 March 1890.
  5. ^ Wales was in 3 place from its first match in 1876 to 1902, in a period that only 3 to 4 teams were in the rankings
  6. ^ On 1 January 2006, Football Federation Australia moved from the OFC to the AFC
  7. ^ Algeria had only played 4 matches to reach their highest ranking and 8 matches to reach their highest ratings.
  8. ^ South Africa had only played 1 match when they reached their highest ratings and ranking between 1906 and 1908
  9. ^ Slovakia's highest rank of 17 was after their first match in August 1939
  10. ^ Finland reached their highest ranking after their 4th match, after beating Italy and Russia in the 1912 Olympic Games

See also

External links

References

  1. ^ "The World Football Elo Rating System". Eloratings.net. Retrieved 26 February 2012.
  2. ^ J. Lasek, Z. Szlávik and S. Bhulai (2013), The predictive power of ranking systems in association football, Int. J. Applied Pattern Recognition1: 27-46.
  3. ^ FIFA Council, 2026 FIFA World Cup™: FIFA Council designates bids for final voting by the FIFA Congress, 10 Jun 2018
  4. ^ a b c FIFA council, Revision of the FIFA / Coca-Cola World Ranking
  5. ^ "World Football Elo Ratings". Elo ratings. Retrieved 30 June 2018.
  6. ^ "FIFA/Coca-Cola World Ranking" (Press release). FIFA. 7 June 2018. Retrieved 17 May 2018.
  7. ^ Graph of rankings at eloratings.net. Yearly graphs, like this one for 2018, give enough resolution. For individual dates, the Elo ratings table is also a good source.
  8. ^ World Football Elo Ratings; under the columns tab choose "Highest Rank / Rating" as well as "Lowest Rank / Rating"
Retrieved from "https://en.wikipedia.org/w/index.php?title=Elo_Rating_System_for_football&oldid=848828432"