2021 Summer Olympics is now over, and we can now play around with the results without having to speculate about future performance of countries. I wanted to quickly test different ranking methods and see how they compare.

Why?

Because ranking the olympic performance of countries is not very straightforward, and people aren’t aware of the tradeoffs between different ranking methods.

Ranking methods

In this section I will go through some sensible ways to rank countries. Before we do that, let’s have a quick look at the data as it is presented on the olympics website.

Out [4]:
          country  gold  silver  bronze
0             USA    39      41      33
1           China    38      32      18
2           Japan    27      14      17
3   Great Britain    22      21      22
4          Russia    20      28      23
..            ...   ...     ...     ...
88          Ghana     0       0       1
89        Grenada     0       0       1
90         Kuwait     0       0       1
91        Moldova     0       0       1
92          Syria     0       0       1

[93 rows x 4 columns]

Number of gold medals

This is the most common ranking method I’ve seen. It ranks countries by the number of gold medals earned, using the number of silver and bronze medals as tie-breakers.

Out [5]:
          country  gold  silver  bronze
0             USA    39      41      33
1           China    38      32      18
2           Japan    27      14      17
3   Great Britain    22      21      22
4          Russia    20      28      23
5       Australia    17       7      22
6     Netherlands    10      12      14
7          France    10      12      11
8         Germany    10      11      16
9           Italy    10      10      20
10         Canada     7       6      11
11         Brazil     7       6       8
12    New Zealand     7       6       7
13           Cuba     7       3       5
14        Hungary     6       7       7

Total number of medals

This is another common method that attempts to fix the downsides of “ranking by gold”. Instead, it ranks the countries by the total number of medals earned.

Out [6]:
          country  gold  silver  bronze  total
0             USA    39      41      33    113
1           China    38      32      18     88
4          Russia    20      28      23     71
3   Great Britain    22      21      22     65
2           Japan    27      14      17     58
5       Australia    17       7      22     46
9           Italy    10      10      20     40
8         Germany    10      11      16     37
6     Netherlands    10      12      14     36
7          France    10      12      11     33
10         Canada     7       6      11     24
11         Brazil     7       6       8     21
12    New Zealand     7       6       7     20
14        Hungary     6       7       7     20
15    South Korea     6       4      10     20
43        Ukraine     1       6      12     19
21          Spain     3       8       6     17
13           Cuba     7       3       5     15
16         Poland     4       5       5     14
23    Switzerland     3       4       6     13
34         Turkey     2       2       9     13
33         Taiwan     2       4       6     12

Weighted ranking

This is a mixture of the previous two methods. It ranks countries based on the total number of medals, but each gold medal is worth 3 points, each silver medal is worth 2 points, and each bronze medal is worth 1 point.

Out [7]:
           country  gold  silver  bronze  weighted
0              USA    39      41      33       232
1            China    38      32      18       196
4           Russia    20      28      23       139
3    Great Britain    22      21      22       130
2            Japan    27      14      17       126
5        Australia    17       7      22        87
9            Italy    10      10      20        70
6      Netherlands    10      12      14        68
8          Germany    10      11      16        68
7           France    10      12      11        65
10          Canada     7       6      11        44
11          Brazil     7       6       8        41
12     New Zealand     7       6       7        40
14         Hungary     6       7       7        39
15     South Korea     6       4      10        36
13            Cuba     7       3       5        32
21           Spain     3       8       6        31
16          Poland     4       5       5        27
43         Ukraine     1       6      12        27
17  Czech Republic     4       4       3        23
23     Switzerland     3       4       6        23
18           Kenya     4       4       2        22
22          Sweden     3       6       0        21
24         Denmark     3       4       4        21
33          Taiwan     2       4       6        20
34          Turkey     2       2       9        19

There are other weighted ranking methods such as 5:3:2.

Out [8]:
           country  gold  silver  bronze  weighted
0              USA    39      41      33       384
1            China    38      32      18       322
4           Russia    20      28      23       230
3    Great Britain    22      21      22       217
2            Japan    27      14      17       211
5        Australia    17       7      22       150
9            Italy    10      10      20       120
8          Germany    10      11      16       115
6      Netherlands    10      12      14       114
7           France    10      12      11       108
10          Canada     7       6      11        75
11          Brazil     7       6       8        69
12     New Zealand     7       6       7        67
14         Hungary     6       7       7        65
15     South Korea     6       4      10        62
13            Cuba     7       3       5        54
21           Spain     3       8       6        51
43         Ukraine     1       6      12        47
16          Poland     4       5       5        45
23     Switzerland     3       4       6        39
17  Czech Republic     4       4       3        38
18           Kenya     4       4       2        36
24         Denmark     3       4       4        35
33          Taiwan     2       4       6        34
34          Turkey     2       2       9        34

Interpreting the results

There are a few interesting observations to make.

  1. United States is always ranked number 1.
  2. China is always ranked number 2.
  3. Great Britain is always ranked number 4.
  4. Australia is always ranked number 6.