# IIHF Elo Ratings

If someone's asked about the best countries in world hockey, a few answers quickly come to mind. Canada, Sweden, Russia are usually among the frontrunners, Finland, the US and the Czech Republic are a step below that and then it gets really tough with Slovakia and Switzerland a step below them, etc.

This order is rarely depicted in the official IIHF World Rankings.

Looking over the 2013 Rankings, there are definitely some question marks. For instance, is Norway really to the US (210 Point difference) what the US is to Sweden (210 points)? Is Switzerland really a closer comparable to Canada (95 point difference) than Sweden (165) or Finland (125)?

Rang | Nation | Punkte |
---|---|---|

1 | Sweden | 3105 |

2 | Finland | 3065 |

3 | Russia | 3040 |

4 | Czech Republic | 2975 |

5 | Canada | 2940 |

6 | USA | 2895 |

7 | Switzerland | 2845 |

8 | Slovakia | 2840 |

9 | Norway | 2685 |

10 | Germany | 2650 |

The IIHF Rankings only take into account the Rankings at the end of each World Championship or Olympic Tournament. This has a few disadvantages:

- A team can beat everyone in the round robin (7 games), get a tough draw in the quarterfinals, lose a game and at best place fifth despite going 7-1.
- The quality of opponents are not taken into account. A win against Kazachstan counts the same as a win against Canada.
- The quality of the victory is not taken into account. A 2-1 win over Kazachstan is equal to a 6-0 against Canada

One possible way to account for these variables is to use the Elo Rating System, originally designed to rank chess players.

## The Elo Rating System

The Elo Rating System, named after its inventor, Arpad Elo, is a Rating System that relies on using the results of single games instead of using the final rankings or standings of competition.

Every player gets assigned a starting value. Before the match, the ratings of both players make it possible to calculate an expected outcome. After the match, this expected outcome is compared to the actual outcome and the ratings of both players are adjusted accordingly. If a player outperformed the expectations, his rating improves, if he underperforms the expectation, his rating is lowered. The amount that each score is adjusted after the match is also dependent on the relative talent differences beforehand. So the tougher the opponent, the more the victory improves the score. This way, match by match, the Elo Rating of a player gets closer to his "true" rating.

An example: Player A has an Elo Rating of 2000. Player B has an Elo Rating of 2100. Based on these ratings, the expected outcome is for Player A to win 36% of the matches between A and B.

Contrary to expectations, A wins the match. Therefore, A's rating improves to 2013, B's new rating is 2087.

Player | Elo before | Exp. Outcome | Outcome | Elo after |
---|---|---|---|---|

A | 2000 | 0.36 | 1 | 2013 |

B | 2100 | 0.64 | 0 | 2087 |

If A and B now play each other a lot, their ratings will eventually reflect the true talent levels of both players.

### Calculation

For those interested, here is the actual calculation behind the later rankings:

The Expected Outcome for Team A (**E(A)**) can be calculated with this formula with the knowledge of the Elo Ratings of Team A (**A**) and Team B (**B**):

**E(A)** = 1 / (1+10^((**B**-**A**)/400))

**S(A)** / **S(B)** are the results of the game from the perspective of Team A / Team B expressed as percentage of points. The point system used here is the (superior) european system:

Regulation Win = 3 points, OT or shootout win = 2 points, OT/SO loss = 1 point, regulation loss = 0 points.

In case of a Tie (in use before the 2007 WC), both teams were awarded 1.5 points.

So, if Team A wins in regulation, A gets 3 points, and therefore **S(A)** = 3 / 3 = **1**, **S(B)** = 0 / 3 = **0**.

With the knowledge of the result **S** the new Elo Ratings **Anew** und **Bnew **can be calculated:

**Anew** = **A** + **G** * **K** * (**S(A)** - **E(A)**) bzw. **Bnew** = **B** + **G** * **K** * (**S(B)** - **E(B)**)

### Correction factors

**G** and **K** are factors that correct for goal difference and Tournament.

**G** corrects for the goal difference. The values are the same as the ones used by the FIFA Elo Ratings. If the game is decided by one goal, **G = 1**. If the game is decided by two goals, **G = 1.5**, if the goal differential is 3 or larger, **G = (11 + Goal Difference) / 8**.

If the game is a World Championship game, **K = 20**, if it's a game at an Olympic tournament, **K = 30 **(Because of the inclusion of NHL players, Olympic Tournaments were given more weight).

These calculations were done for every World Championship and Olympic Tournament starting with the 2004 World Championship. Since the Division I Tournaments are not incorporated yet, the teams not qualified for the Championship are deducted 25 points (The average Team relegated from a World Championship worsened their ranking by 23 points). Teams not qualified for the Olympics were deducted 35 points.

### Starting Values

With the calculations now accounting for opponents, final score and tournament, the final question is which starting values to use. To check whether the starting values matter, calculations were done for two cases:

1. All teams are given starting rankings based on the 2003 World Rankings

2. All teams start with an equal rating

To make the comparison easier, the teams are colour coded the following way:

- Top teams Canada, Russia, Sweden, USA, Czech Republic and Finland are depicted in red
- In-between teams Slovakia and Switzerland are coloured blue
- Typical Non-Relegation Teams Germany, Latvia, Belarus, France, Denmark and Norway are coloured green
- Teams that are often relegated to Division I, Austria, Slovenia, Kazachstan, Italy, Hungary, Japan, Ukraine are coloured yellow:

Compared to the ratings that come with equal starting ratings:

The strength of the Elo System shines through here. Eventually the "true" talent levels establish themselves in the ratings.

While it makes historical comparisons very difficult, I decided to use the ratings that use equal starting values for the final rankings, since these show no bias to previous results or the IIHF World Rankings at the time and truly reflect what's happened in the last 10 years.

## Ratings

This leads to the following current Elo Ratings:

Nation | Last 2 years | Current | Expected Win% v CAN |
---|---|---|---|

Russia | 2014 | 2036 | 52,62% |

Canada | 1997 | 2018 | 50,00% |

Sweden | 1976 | 1990 | 45,96% |

Finland | 1913 | 1929 | 37,49% |

USA | 1892 | 1891 | 32,49% |

Czech Republic | 1868 | 1839 | 26,27% |

Switzerland | 1761 | 1760 | 18,44% |

Slovakia | 1731 | 1692 | 13,29% |

Latvia | 1581 | 1591 | 7,91% |

Germany | 1617 | 1579 | 7,39% |

Belarus | 1559 | 1571 | 7,11% |

Norway | 1594 | 1556 | 6,55% |

France | 1511 | 1527 | 5,59% |

Denmark | 1534 | 1504 | 4,94% |

Slovenia | 1414 | 1432 | 3,31% |

Austria | 1406 | 1386 | 2,57% |

Kazachstan | 1361 | 1330 | 1,87% |

Italy | 1323 | 1315 | 1,72% |

**Last 2 years**: Average Elo Rating over the last two years

**Current**: Current Elo Rating (after the conclusion of the 2014 WC)

**Expected W% v CAN**: The Expected Win% of a team against Canada based on the current Elo Ratings

Obviously, this still does not represent the true talent level of the teams at the top end, especially Team Canada. But with the NHL only participating in the Olympic tournament, a proper representation that's also more current and accurate than one that's based on a single elimination tournament and a 3-game round robin every 4 years is not possible.

The Elo Rating System does however, do a better job to...

- Relate team strengths to each other. Norway is no longer to the US (Exp W% = 12.7%) as the US is to Sweden (Exp W% = 36.7%). Canada's closest comparables are now Sweden and Russia, not Switzerland.
- Reduce noise of single tournament outbursts (Germany 2010, Switzerland 2013) while still allowing mobility and showing long-term trends (Slovakia's drop from the top group of nations, France's establishment away from being a steady candidate for relegation, Switzerland & Slovakia's position in the very large gap between the top group and the rest)

For better viewing, the following charts show the Top group, the Non-Relegation Teams and the relegation teams in single charts: