Thursday, February 13, 2014

Country Standings

Four years is a long time. Every four years, about this time in an Olympics, I get confused when I see the country rankings.  In today’s presentation, for example, the Netherlands and the United States both have 12 total medals, but Norway ranks higher than the US. In the same list Russia with 10 total medals is ranked below Switzerland with a mere 4. So then the next question is, how much weight does each medal have to produce this result.

It turns out that the various ranking schemes one can find on the Internet merely confuse the issue, as illustrated in the following spreadsheet layout:

Sochi Standings as of February 13, 2014
Rank as
Points for each kind of medal
Reported
Medal count
Gold
Silver
Bronze
Total
Total
Gold
Silver
Bronze
4
2
1
Medals
Points
1
Germany
6
2
1
24
4
1
9
29
2
Canada
4
4
2
16
8
2
10
26
3
Norway
4
3
6
16
6
6
13
28
4
Netherlands
4
3
5
16
6
5
12
27
5
USA
4
2
6
16
4
6
12
26
6
Switzerland
3
0
1
12
0
1
4
13
7
Russia
2
4
4
8
8
4
10
20

I’m showing the countries in rank order as reported by Sochi Olympics itself. To these rankings I’ve applied one of the ranking schemes (4/2/1) in which gold is multiplied by 4, silver by 2, and bronze by 1. There are also other schemes, e.g., 3/2/1 and 5/3/1. Notice that, in the last column, Canada should be fourth, with the US, and Russia sixth. Indeed no matter what the ranking scheme, each produces the same results. 

Well, it turns out that no “weighting” is used at all. What actually happens, I discovered, is that the results are subjected to a sorting algorithm with five parameters. The data are sorted by (1) gold count, then (2) silver, then (3) bronze, then (4) total metals—and if two countries are identical at that point, the last ranking is (5) alphabetical. No “points” or weights need to be applied—and Excel does a right fine job.

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