Dan has kindly invited me to step back into the lounge for a bit.
What's on my mind is the Winter Olympics, and rankings.
As a part of Olympic coverage, we see the medal count rankings. NBC always uses total medal counts. Last night’s NBC ranking had the U.S. at No. 1 with 23 medals. But total medal count treats all medals as equal; if Ecuador had had 24 Bronze medals, it would have led the rankings.
But the mettle of a team is measured by metal, not just counts; Gold medals are better than Silver medals, which are better than Bronze medals. The rankings on the official Sochi website last night ranked Norway No. 1, even though it had only 20 medals.
Official Rankings |
|||||
Official Rank |
Country |
Gold |
Silver |
Bronze |
Total |
1 |
Norway |
9 |
4 |
7 |
20 |
2 |
Germany |
8 |
3 |
4 |
15 |
3 |
United States |
7 |
5 |
11 |
23 |
4 |
Russian Fed. |
6 |
9 |
7 |
22 |
5 |
Netherlands |
6 |
7 |
9 |
22 |
6 |
Switzerland |
6 |
3 |
1 |
10 |
7 |
Canada |
5 |
9 |
4 |
18 |
8 |
Belarus |
5 |
0 |
1 |
6 |
9 |
Poland |
4 |
0 |
0 |
4 |
10 |
France |
3 |
2 |
6 |
11 |
11 |
China |
3 |
2 |
1 |
6 |
12 |
Austria |
2 |
6 |
1 |
9 |
13 |
Sweden |
2 |
5 |
4 |
11 |
14 |
Czech Republic |
2 |
4 |
2 |
8 |
15 |
Slovenia |
2 |
1 |
4 |
7 |
16 |
Korea |
2 |
1 |
1 |
4 |
17 |
Japan |
1 |
4 |
2 |
7 |
18 |
Finland |
1 |
3 |
0 |
4 |
19 |
Great Britain |
1 |
0 |
1 |
2 |
20 |
Slovakia |
1 |
0 |
0 |
1 |
21 |
Italy |
0 |
2 |
5 |
7 |
22 |
Australia |
0 |
2 |
1 |
3 |
23 |
Latvia |
0 |
1 |
2 |
3 |
24 |
Croatia |
0 |
1 |
0 |
1 |
25 |
Kazakhstan |
0 |
0 |
1 |
1 |
25 |
Ukraine |
0 |
0 |
1 |
1 |
So far as I can tell, the Official counts ranks first by the number of Gold medals; Norway has 9, Germany 8, the U.S 7, etc. Where countries have the same number of Golds, they are ranked by Silver medals. Where they have the same number of Golds, and the same number of Silvers, they are ranked by Bronzes. By this approach, if Ecuador had had 10 Gold medals, but no other medals, it would have ranked highest.
How do you combine the number of medals and the quality of medals. I gave each team “quality” points— 3 points for a Gold Medal, 2 points for a Silver Medal, and 1 point for a Bronze medal, and added the total quality points. Norway then has 9x3 + 4x2 + 7x1 = 42 quality points. At this point, I let ties be ties.
Quality Points |
|||||
Official Rank |
Country |
Gold |
Silver |
Bronze |
Quality Points |
1 |
Norway |
9 |
4 |
7 |
42 |
2 |
Germany |
8 |
3 |
4 |
34 |
3 |
United States |
7 |
5 |
11 |
42 |
4 |
Russian Fed. |
6 |
9 |
7 |
43 |
5 |
Netherlands |
6 |
7 |
9 |
41 |
6 |
Switzerland |
6 |
3 |
1 |
25 |
7 |
Canada |
5 |
9 |
4 |
37 |
8 |
Belarus |
5 |
0 |
1 |
16 |
9 |
Poland |
4 |
0 |
0 |
12 |
10 |
France |
3 |
2 |
6 |
19 |
11 |
China |
3 |
2 |
1 |
14 |
12 |
Austria |
2 |
6 |
1 |
19 |
13 |
Sweden |
2 |
5 |
4 |
20 |
14 |
Czech Republic |
2 |
4 |
2 |
16 |
15 |
Slovenia |
2 |
1 |
4 |
12 |
16 |
Korea |
2 |
1 |
1 |
9 |
17 |
Japan |
1 |
4 |
2 |
13 |
18 |
Finland |
1 |
3 |
0 |
9 |
19 |
Great Britain |
1 |
0 |
1 |
4 |
20 |
Slovakia |
1 |
0 |
0 |
3 |
21 |
Italy |
0 |
2 |
5 |
9 |
22 |
Australia |
0 |
2 |
1 |
5 |
23 |
Latvia |
0 |
1 |
2 |
4 |
24 |
Croatia |
0 |
1 |
0 |
2 |
25 |
Kazakhstan |
0 |
0 |
1 |
1 |
25 |
Ukraine |
0 |
0 |
1 |
1 |
The table below compares the Official and Total Medals rankings to the Quality-Points rankings.
Compare Rankings |
|||
Country |
Official Rank |
Total Rank |
Quality Rank |
Russian Fed. |
4 |
2 |
1 |
Norway |
1 |
4 |
2 |
United States |
3 |
1 |
2 |
Netherlands |
5 |
2 |
4 |
Canada |
7 |
5 |
5 |
Germany |
2 |
6 |
6 |
Switzerland |
6 |
9 |
7 |
Sweden |
13 |
7 |
8 |
France |
10 |
7 |
9 |
Austria |
12 |
10 |
9 |
Belarus |
8 |
15 |
11 |
Czech Republic |
14 |
11 |
11 |
China |
11 |
15 |
13 |
Japan |
17 |
12 |
14 |
Poland |
9 |
17 |
15 |
Slovenia |
15 |
12 |
15 |
Korea |
16 |
17 |
17 |
Finland |
18 |
17 |
17 |
Italy |
21 |
12 |
17 |
Australia |
22 |
20 |
20 |
Great Britain |
19 |
22 |
21 |
Latvia |
23 |
20 |
21 |
Slovakia |
20 |
23 |
23 |
Croatia |
24 |
23 |
24 |
Kazakhstan |
25 |
23 |
25 |
Ukraine |
25 |
23 |
25 |
Obviously, there is some, often a lot, variation in the different rankings of the teams. The Correlation (R) Table below shows the correlations of the ranking methods. The statistically inclined know that correlation coefficients (R) do not show how much variation in one measure is associated with variation in another measure; R-squared (R x R) is the traditional statistic for that (sometimes called the coefficient of variation).
Correlation (R) Table |
|||
|
Official |
Total |
Quality |
Official |
--- |
0.86 |
0.94 |
Total |
0.86 |
--- |
0.97 |
Quality |
0.94 |
0.97 |
--- |
|
|
|
|
R-Squared Table |
|||
|
Official |
Total |
Quality |
Official |
--- |
0.74 |
0.88 |
Total |
0.74 |
--- |
0.94 |
Quality |
0.88 |
0.94 |
--- |
by Gary Rosin
Update: The obvious way to break ties in Quality-point rankings is to compare the QP average (QPA)--the average medal quality--of teams with the same number of QPs. Luckily, there's a way to do that without calculating QPAs. More later. GR
The whole idea of medal rankings is kind of silly. There is one gold medal in hockey that is probably worth more in my book than all the luge/skeleton/bobsled gold medals combined.
Posted by: Junior | February 20, 2014 at 12:05 PM
as humans, if we can't differentiate ourselves from others via rankings, then what good are we!
Posted by: E | February 20, 2014 at 01:15 PM