Adjusting Medal Totals for Number of Events

The Olympics are an event that stimulates a competitive spirit in everyone involved, even simple spectators.  Despite the Games not being designed to crown an overall winner, this often spawns debates over who is the overall winner of the games.  There are several different methods I have seen from determining such a victor, but a common critique I hear of many of these methods is they are unfavorably weighted in favor of nations that are particularly successful in sports with a large number of events.

In particular, this accusation is often levied at the United States’ success with swimming.  I have seen some people using this to argue that there should be fewer swimming events in the Olympics and I’ve seen some people rendering medal tables that completely remove swimming.

As a former swimmer myself, I find myself incapable of being able to favor completely removing swimming or reducing the number of events.  In fact, in the Tokyo 2020 Olympics I was celebrating the fact that they finally added the event which was my main event when I swam in the NCAA (Men’s 800m Freestyle).  

However, as a scientist and data analysis junky I found myself compelled by the argument that the number of swimming events is unfair when it comes to medal totals.  There is some truth to the argument that the United States gets a bump from swimming.  There are 35 swimming events which is only exceeded by Athletics (known better as Track and Field in the US).  The US won a total of 11 Gold Medals in swimming this year which is the most that any country won in any single sport.  In fact, Australia’s 9 Gold Medals in swimming is tied for the second most Gold Medals than any country won in a single sport (matched by China’s 9 Gold Medals in diving).  So, I began exploring methods of controlling for the different number of events in different sports.

Methods

Before getting into the details of how I approached this, I want to make clear what these calculations were not trying to achieve.  I made no attempt to control for the size of different nation’s populations or economies.  Other people have done this analysis and there are some nations that are very impressive in this approach that are not properly represented in other scales.  My approach was to preserve the way that typical medal totals look are the raw total athletic performance rather than a proportional analysis.

I also did not attempt to control for expectations.  There are some nations that had several upsets in their favor resulting in them massively overperforming expectations despite not ranking highly on medal totals.  There are other nations where the complete opposite is true.  A more detailed look at changing trends over time and predictions before the competition might reveal the success of some nations in this manner that my analysis ignores.

I made no attempt to speculate on which sports or Olympic Committees might be combined or further divided.  I used the official breakdown of sports available on the Olympics website.  Similarly, I used the medal totals for the officially recognized teams under the IOC.  So, despite some speculation that certain sports could be combined or further divided, they remain as listed.  Similarly, despite some Olympic Committees representing regions that are De Jure under the rule of another nation their medals are counted separately.

I also did not award any special bonuses for impressive achievements such as nations sweeping a podium or athletes breaking Olympic Records or World Records.  Both such accomplishments happened multiple times in the Tokyo Olympics and are impressive feats, but under my analysis are regarded as no different from winning the same number of medals across different events in the same sport and by a thin margin.

Finally, I made no attempt to separate men’s events and women’s events.  Some sports have more of one than the other, but I kept the sports as is.  I did notice that some nations appeared significantly more successful with one sex than the other one, but I have not attempted to compile those numbers.  I would be interested to see someone else do that because I feel like it says something about the sports culture of the different countries, but I feel as though I have bitten off enough number crunching myself.

Anther key detail is that I ran my calculations based on medal numbers pulled immediately after the conclusion of the games. In between me pulling the numbers and posting, I have seen some news about medals possibly being stripped due to doping. I have not accounted for those changes. I have not seen anything that appears as though it would have a major change. Even if it did occur, I think the more important thing here is how the math works out when comparing the impact of different sports on how we rank different countries.

I used 4 different methods of controlling for the number of events per sport.  3 of them were based on common medal table ranking systems I have seen, and the fourth was an unrelated approach.

Method 1

The first method I used was to count the number of Gold Medals for each sport and determine a first, second, and third place in each sport.  When the number of Gold Medals was equal, I used Silver Medals and then Bronze Medals as a tiebreaker.  I then created an overall medal table after assigning a Gold, Silver, and Bronze Medal for each sport.  That overall table was ranked in the same manner as the individual sports.  

So, the US receiving 11 Gold Medals in Swimming is of equal weight to Norway receiving a single Gold Medal in Beach Volleyball.  My expectation for this method was for it to best represent which countries were the dominant nation in the most sports.

Method 2

The second method I used was similar to the first method except instead of counting Gold Medals it counted total medals awarded.  It similarly assigned a first, second, and third place then assigned a Gold, Silver, and Bronze Medal to an overall medal table.  This medal table was then sorted by total medals.

So, the US receiving 11 Gold Medals, 10 Silver Medals, and 9 Bronze Medals in Swimming is of equal weight to India receiving a single Bronze Medal in Field Hockey.  My expectation for this method is that it would not represent dominance in any one sport, but rather having a widespread competitive presence even if isn’t a dominant presence.  In theory, a nation could win this ranking system without winning a single Gold Medal if they were a competitive presence in enough sports.

Method 3

The third method is a compromise between the first two.  It uses a weighting system where a Gold Medal is worth 4 points, a Silver Medal is worth 2 points, and a Bronze Medal is worth 1 point.  This method allows for nations that win a lot of Bronze Medals to be represented, but it gives greater weight to nations who won Gold Medals.  A Silver Medal and 2 Bronze Medals is equal in measure to a single Gold Medal.  Like the first two methods, I used this to determine a first, second, and third place in each sport and assign overall medals accordingly.  This overall table was then sorted using the weighted point system.

So, the US receiving 70 “points” from swimming is of equal weight to Brazil receiving 4 “points” from Soccer.  My expectation for this method was to represent a balance between the first two methods where nations who had both dominance in some sports and a broad spectrum competitive presence would do the best.

Method 4

The fourth method I used followed a different path.  Instead of assigning rankings in each individual sport, all nations would be represented in the overall table for all of the medals they had won.  However, all medals would have their value divided by the number of events in that sport.  This meant that all Gold Medals won would give points to an overall score, but winning a proportionally high number of medals in a given sport would have the greatest impact.  I then sorted the overall medal table based on the number of weighted Gold Medals.

So, the US winning 11 Gold Medals in swimming is worth less than Bermuda winning a single Gold Medal in the Triathlon.  I expected this to represent broad-spectrum athletic dominance without the represented nations necessarily needing that dominance focused on particular sports.  A significant number of Gold Medals in a wide variety of sports would shine through even if the nation was not the overall winner of many of those sports.

Results

Top 10 nations for each ranking method displayed.  Full tables can be viewed in Google Sheets.

Method 1

RankCountry NameGoldSilverBronze
1United States of America924
2People’s Republic of China711
3Great Britain642
4Japan523
5ROC437
6Brazil32
7France231
8Netherlands223
9New Zealand211
9Germany211
Table 1

Method 2

RankCountry NameGoldSilverBronzeTotals
1United States of America97420
2Great Britain94114
2ROC10414
4Australia34411
4Japan63211
4People’s Republic of China82111
7France2327
7Netherlands527
9Germany2316
9Italy1326
9New Zealand2316
9Spain1416
Table 2

Method 3

RankCountry NameGoldSilverBronzeTotalsWeighted Totals
1United States of America9241544
2ROC7521440
3Great Britain6521336
4People’s Republic of China711931
5Japan5231027
6Netherlands232716
7Brazil311515
7France231615
9Germany31413
10Australia44812
Table 3

Method 4

RankCountry NameGoldSilverBronzeTotalsWeighted Totals
1United States of America5.8446428574.1418803422.70807387112.6945970734.37040598
2Great Britain4.1812271062.6282509163.24610805910.0555860825.22751832
3People’s Republic of China4.1047619055.0078144081.67123015910.7838064728.10590659
4Japan3.2880341882.9430555562.8611874249.09227716721.89943529
5ROC2.3533119665.4656135531.6775335789.49645909622.02200855
6France2.0380952381.68751.6755.40059523813.20238095
7Brazil1.8316849821.3983516480.50906593413.73910256410.63250916
8Netherlands1.7130952381.5458333331.632280224.89120879111.57632784
9Germany1.6930555560.9559523811.9849206354.63392857110.66904762
10Australia1.6833333331.2732142863.0650183156.02156593412.34478022
Table 4

Conclusions

What is immediately evident is that none of these approaches hurt the ranking of the US the way that people would have initially suspected based on the US having a significant number of their total Gold Medals from swimming.  Looking through the various tables for different sports, the reason for this becomes obvious.  The US won a significant number of Gold Medals from sports with only two events.  Under every single one of these ranking systems, every single one of these Gold Medals carries significant weight.  The US also had two sports where they won both available Gold Medals.  There were several other nations who achieved this in other sports, but all of them only did it in a single sport.  No other nation had two sports as the US did.

Another surprising result is China dropping further than expected in several of these ranking systems.  Looking through the individual sports, it seems as though China tends to be either exceptionally dominant at a sport, or have little presence at all.  There were many sports where China had either no medal presence or so little of one that it had no effect on the ranking systems.

On the other hand, the ROC and Great Britain both benefited from these ranking systems.  Great Britain it seems has benefited significantly from my decision to not adjust the definition of different sports.  Of the 5 cycling events, Great Britain has either the most Gold Medals or tied for the most in 4 of them (5 out of 6 if you count Triathlon).  If I started combining these cycling sports together, Great Britain’s ranking would be significantly hurt.

The ROC seems to fit a model of a nation that is not overwhelmingly dominant at a large number of sports but is present as a significant competitor in a broad variety of sports.  So, when looking just at Gold Medals they aren’t that impressive, but as soon as other medals start having a significance the ROC is suddenly much more competitive overall.

While it is not displayed on the top 10 lists, both Bermuda and Figi benefited greatly from these lists.  Both nations only had a single Gold Medal, but they were Gold Medals in sports with a small number of events so both nations ended up ranking much higher than they do on lists that just have raw totals.

Similarly, Jamaica and Kenya suffer under this system.  Jamaica is very dominant with short-distance running and Kenya is very dominant at long-distance running.  Bother nations end up being well represented on overall medal charts despite having no presence in other sports due to how strong their dominance is in their chosen list of events.  Under these systems, they are both in the mix for athletics and aren’t nearly as well represented because medals in athletics have less weight than any other sport.  So, despite Jamaica achieving a podium sweep and Kenya being the nation to beat in the Marathon, they are barely on these charts at all.  Perhaps both would show up better if Athletics was divided between running, throwing, and jumping (or even further divisions).

I do think that this analysis has shown some interesting aspects of how different nations are dominant in different sports.  However, it definitely should not be looked at as the only ranking system.  The Olympics are a complicated series of events that are not designed for overall ranking.  Comparing several different ranking methods is the only way to fully understand how different nations compare with each other.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s