Monday, October 28, 2013

World ice hockey champions — a network

The more sports-minded of you will know that Canada and Russia have at least one thing in common — ice hockey. Indeed, Canada dominated the sport at the international level from 1930–1953, and the Soviet Union from 1963–1976, with these two teams being equal rivals during the intervening decade.

The McGill University ice-hockey team in 1881
at the Crystal Palace Rink in Montreal.

Ice hockey is considered to have originated in the eastern parts of Canada, with the first informal rules appearing in 1873. The first organized game of hockey was apparently played on March 3 1875, at the Victoria Skating Rink in Montreal. The first Stanley Cup games were played in 1893; and the National Hockey League (NHL) was formed in 1917.

The first ice hockey games in Europe were played in 1902 at the Prince's Skating Club in Knightsbridge, London. On March 4 1905, Belgium and France played two international games in Brussels. Three years later, the Ligue International de Hockey sur Glace (LIHG) was founded in Paris, with representatives from Belgium, France, Great Britain and Switzerland, and later the same year also from Bohemia (now the Czech Republic). The first LIHG-organized games were played in Berlin, on November 3-5 1908, at which stage Germany also joined.

The 1920 Olympic Summer Games in Antwerp, Belgium, hosted the first international ice hockey tournament with North American participation, and it is from this date that World Championship ice hockey is considered to originate. The first World Championship outside the Olympics took place in 1930, although the Winter Olympics continued to host the Championships until 1972.

The LIHG became the International Ice Hockey Federation (IIHF) in 1954; and it currently has 52 full members, 18 associate members and 2 affiliate members. Only 48 of these members currently compete in the World Championships. It seems worthwhile to explore some of the Championship data, to look at the relative success of the different teams.

World Championships

There have been 77 World Championships between 1930 and 2013, inclusive. The number of teams participating has varied dramatically, with as few as four, due to financial crises, political boycotts, and disputes over professional versus amateur status of the players. For this reason, I have restricted myself solely to the data concerning medal winners (ie. the top three teams).

The data are from Wikipedia. I scored Gold, Silver and Bronze medals as 3, 2 and 1 points, respectively, with 0 points for all other participants. So, the network applies only to those 14 teams that have won at least one medal over the years. I have kept the various teams separate, which means that Czechoslovakia appears along with both Slovakia and the Czech Republic, the Soviet Union appears along with Russia, and both Germany and West Germany are listed.

The network analysis method follows what I have previously used for the FIFA World Cup (soccer). The similarity among the 77 scores for each pair of teams was calculated using the Manhattan distance. A Neighbor-net analysis was then used to display the between-team similarities as a phylogenetic network. Thus, teams that are closely connected in the network are similar to each other based on their overall World Championship results, and those that are further apart are progressively more different from each other.

The network shows the four most successful teams on the left and the less successful teams on the right.

Canada have won 46 medals over the 77 Championships, the Czech Republic (plus Czechoslovakia) has been involved in 12+34=46 medals, Sweden has won 44 medals, and Russia (plus the Soviet Union) has been involved in 8+34=42 medals. So, these four teams have won 178 of the 231 medals (77%). The next best teams are the United States (17 medals), Finland (11) and Switzerland (10). (Note: Slovakia technically has 4+34=38 medals, but the IIHF officially attributes all Czechoslovakian medals to the Czech Republic alone.)

Great Britain won 5 medals in the first 12 Championships, but has won nothing since 1938. The remaining foundation members, Belgium and France, have never won a medal. However, France is still ranked among the 16 teams in the Championship Division, although Great Britain is currently (2013) among the 12 teams in Division I (it was relegated in 1995), and Belgium is among the 12 teams in Division II (relegated in 2005). The other teams currently in the Championship Division that have never won medals are: Denmark, Italy and Norway, plus Belarus, Kazakhstan and Latvia from the former Soviet Union. Austria is the only other medal-winning team not currently in the Championship Division (it was relegated to Division I earlier this year).

World Rankings

The IIHF has provided a World Ranking for 50 of the teams every year since 2003. This provides a more detailed look at the recent history of the various teams (ie. over the past 11 years). The annual ranking is based on the success of the teams in the previous three World Championships plus the most recent Winter Olympics, with each competition being assigned a set number of points and the teams sharing these points based on their finishing position.

I have analyzed these data in the same way as above, except that the data are the actual ranking points awarded to each team each year. I excluded Armenia, Bosnia & Herzegovina, Georgia, Greece, Mongolia and the United Arab Emirates because they were not ranked in all 11 of the years.

The network shows a simple gradient from the most successful teams at the top-left to the least successful teams at the bottom-right. This network arrangement implies that the relative rankings of the teams are very consistent from year to year.

As before, the same four teams have dominated across the past 11 years as they did for all 77 of the Championships (Canada, Sweden, Russia and the Czech Republic) but now also including Finland. These teams are followed by Slovakia, the United States and Switzerland. Only three of these teams have been raked first: Canada and Russia in four years each, and Sweden for three years. However, Sweden is the only team to have been ranked in the top four every year. These same eight teams dominate the current IIHF rankings (2013), with a clear points gap between the eighth and ninth ranked teams.

Note that Switzerland should currently be included in the upper echelon, even though the other teams have been referred to as the "Big Seven". Sadly, in the 2013 World Championships Switzerland won every one of their games except the final, even beating the host nation (Sweden) in their first game; but it is a bit hard to beat the Swedes on their home ice twice in one tournament.

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