World Ice Hockey Elo Ratings
The World Ice Hockey Elo Ratings is a ranking system for men's national ice hockey teams that is published by the website eloratings.net. It is based on the Elo rating system but includes modifications to take various ice hockey-specific variables into account, like the margin of victory, importance of a match, and home rink advantage. Other implementations of the Elo rating system are possible and there is no single nor any official Elo ranking for ice hockey teams. The IIHF World Ranking, not based on the Elo method, is the official national teams rating system used by the international governing body of ice hockey 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.[1] Ratings for teams with fewer than 30 matches are considered provisional.
Ratings[edit]
The following table shows teams in the World Ice Hockey Elo Ratings as they were on 24 May 2018, using data from the World Ice Hockey Elo Ratings web site.[2]
Each national team's IIHF World Ranking is shown as per the latest release on 24 May 2018.[3]
| Championship | Division I A | Division I B | Division II A | Division II B | Division III | Division III Qualification |
|
|
|
|
^ Note 1: IIHF Associate members.
^ Note 2: IIHF Affiliate members.
^ Note 3: Not IIHF members.
^ Note 4: Former team.
^ Note 5: Haven't played 30 matches against other Elo-ranked teams, so Elo Rating is provisional.
History[edit]
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. In 2018, the web site included to have the international ice hockey.
Overview[edit]
The Elo system was adapted for ice hockey 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:
- Olympic Finals
- World and Continental Championship finals and major Intercontinental tournaments
- Olympic, World Championship and Continental qualifiers and major tournaments
- 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[edit]
The basic principle behind the Elo ratings is only in its simplest form similar to that of a league; 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.
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 |
The number of Points Change is rounded to the nearest integer before updating the team rating.
Status of match[edit]
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:
| Tournament or Match type | Index (K) |
|---|---|
| Olympic finals | 60 |
| World and Continental Championship finals and major Intercontinental tournaments | 50 |
| Olympic, World Championship, and Continental qualifiers and major tournaments | 40 |
| All other tournaments | 30 |
| Friendly matches | 20 |
Number of goals[edit]
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 | 1.3 |
| +3 | 1.5 |
| +4 | 1.6 |
| +5 | 1.7 |
| +6 | 1.8 |
| +7 | 1.9 |
| +8 | 2.0 |
| +9 | 2.1 |
| +10 | 2.2 |
Result of match[edit]
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 in overtime or shootout.
Expected result of match[edit]
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.
Examples[edit]
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.
| Team | Points |
|---|---|
| A | 630 |
| B | 500 |
| C | 480 |
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[edit]
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 | |||
|---|---|---|---|---|---|---|
| 20 | 20 | 20 | 20 | 20 | 20 | |
| 1.3 | 1.3 | 1.3 | 1.3 | 1 | 1 | |
| 1 | 0 | 0 | 1 | 0.5 | 0.5 | |
| 0.679 | 0.321 | 0.679 | 0.321 | 0.679 | 0.321 | |
| Total (P) | +8.35 | −8.35 | −17.65 | +17.65 | −3.58 | +3.58 |
Example 2[edit]
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 | |||
|---|---|---|---|---|---|---|
| 20 | 20 | 20 | 20 | 20 | 20 | |
| 1.3 | 1.3 | 1.3 | 1.3 | 1 | 1 | |
| 1 | 0 | 0 | 1 | 0.5 | 0.5 | |
| 0.529 | 0.471 | 0.529 | 0.471 | 0.529 | 0.471 | |
| Total (P) | +12.25 | −12.25 | −13.75 | +13.75 | −0.58 | +0.58 |
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.
See also[edit]
Notes[edit]
References[edit]
- ↑ "The World Ice Hockey Elo Rating System". Eloratings.net. Retrieved 18 June 2018.
- ↑ "World Ice Hockey Elo Ratings". Elo ratings. Retrieved 18 June 2018.
- ↑ "IIHF/ World Ranking" (Press release). IIHF. 24 May 2018. Retrieved 24 May 2018.
External links[edit]
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