Sunday, August 12, 2012

Fair London 2012 Olympic medals ranking - Final results

Here are my 'fair' Olympic medals rankings, based on the final results of the London 2012 Olympics, after the final medals were awarded on August 12th. This updates my earlier posts on August 8th and August 9th, which proved quite popular.

What have I done to make the rankings fairer:
  1. I have weighted the rankings by population.
  2. I have further normalized by UN development index. Developed countries have an index closer to 1, but developing countries, which have much less capacity to train athletes, are ranked lower, typically in the 0.5 range.
  3. I have weighted silver medals as worth two bronze medals, and gold medals as worth two silver medals. This seems considerably fairer than the two schemes widely used by the International Olympic Committee and the press, either ranking strictly by gold medals (breaking ties with silver and bronze), or else weighting all medals evenly.
The first table below gives my final rankings, ordered by this scheme. The raw score is column WM10M, and the ranking is column WMR.

Population and development index, used for normalization, are shown on the right. 

In all the columns in the table below, I have highlighted the top 20 countries (and ties) in the different rankings, so you can see how the different schemes affect the sequence. My preferred WM10M ranking is in blue. I have also marked the top 20 countries by population, and by development index, using grey.

Small island countries of Grenada and The Bahamas come first and second in WM10M score by virtue of winning a medal despite their extremely small population. Jamaica and New Zealand come third and fourth. Congratulations to those countries.

Column definitions
  • Gold, Silv, Bro - medal counts
  • GR: Ranking, based on Gold medals, with ties resolved by silver and bronze (top 20 orange)
  • TotM: Total medals (top 20 yellow)
  • WTotM: Total medals weighted using the 4 2 1 scheme described above (top 20 green)
  • G10M: Gold medals per 10 million, weighted by development index (purple)
  • M10M: Total medals per 10 million, weighted by development index (pink)
  • WM10M: 4-2-1 weighted medals per 10 million, weighted by development index (blue)
The second table below shows the same data, organized by population. The third table shows the same data, organized by the 'Gold medal' rankings used by the IOC.

No ranking will ever be totally fair. Maybe team sports, or sports which only give one medal such as modern pentathlon, should be given higher rankings for the medals. But there is no clear way to do come up with an unbiased ranking scheme if those adjustments are made. I think what I present is a good compromise.

Table 1: Rankings ordered by WM10M: 4-2-1 weighted medals per 10 million, weighted by development index.

Table 2: The same data ordered by size of country (PopM)

Table 3: The same data, ordered using the IOC's gold medal based rankings

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