Olympic medals and their rankings

As the winter olympics in Vancouver drew to a close last Sunday, the media went through the usual exercise of tabulating national medal tallies. Although the International Olympic committee doesn’t recognise any of these arrangements, they make for interesting analysis. While some of the medal tallies are arranged in descending order of total medals won, some others are  ordered based on the number of gold medals won, with silver and bronze medals used only to break ties. The latter scheme apparently enjoys wider appeal and is used in the wikipedia entries of the medal tables too but the total medal count is favoured by most American newspapers. Each scheme has advantages and disadvantages.

Ranking performances based on total medal count obviously treats all medals the same and hence fails to appropriately credit a Gold medal over silver or bronze. Also, this scheme falls prey to one handicap of the system where the third best performance in a discipline is awarded a medal alsongside the first and second while the fourth is not. So, a country which had one 3rd place performance is ranked above another with many 4th place performances.

Rankings based primarily  on the number of Gold medals won and using silver and bronze medals progressively to split ties, while failing to allay the injustice to the 4th place completely is at least not as glaring. Any number of third places now don’t make up for a second or first place. But, it instinctively seems unfair to rank 1 gold medal over 10 silver medals either.

A fair system of assigning weights ot Gold, Silver and Bronze medals is required to compare them against each other in compiling the final medals table. Wikipedia lists such  schemes that have been previously used by newspapers like 5:2:1, 3:2:1 and 4:2:1 as the ratio for Gold, Silver and Bronze medal weights respectively. Perhaps a poll among past olympians in a field can be used to set the right ratio for olympic medals in that field. It seems to be a matter of opinion but that shouldn’t stop us from exploring the possibilities!

Applying these schemes to some of the top nations in the 2008 olympics, we have the following rank list-

Gold First	Total	05:02:01	03:02:01	04:02:01
China	United states	China	China	China
United States	China	United States	United States	United States
Russia	Russia	Russia	Russia	Russia
Great Britain	Great Britain	Great Britain	Great Britain	Great Britain
Germany	Australia	Australia	Australia	Australia
Australia	Germany	Germany	Germany	Germany
South Korea	France	South Korea	France	South Korea
France	South Korea	France	South Korea	France

The three weighted schemes used are obviously attempts at compromising the colour-blind medals list and gold first list. Considering this list, it isn’t surprising why the American media insisted on using the total medals are their ranking criterion!