## COSTAS: The Weighted Olympic Medal Count

by Andrew Mooney

A couple of days ago, I wrote about a different way to think about the traditional Olympic medal standings, which reflected the unevenness of the playing field from which athletes from all over the world come to the Games. But there’s another distortion to the medal count that is never accounted for in the usual tally and has a similarly large effect on the final standings: the differences in medals available in each sport.

In the spirit of PECOTA, KUBIAK, VUKOTA, and all other gratuitous acronyms by which sports analysts refer to their pet models, I now bring you COSTAS: the Congruent Olympic System for the Tabulation of Accolade Statistics.

First developed by Harvard student David Roher for the 2010 Winter Olympics, I adapted his model for the Summer Games to get a clearer view of the spectrum of international sporting supremacy. In the words of its founder:

“I wanted to develop a weighted medal count that not only adjusted for the importance of gold over silver over bronze, but also for the relative importance of one event over another. I also wanted its abbreviation to be COSTAS. I admit that the latter was the first requirement I thought of.”

As alluded to by Roher, the model is based on a couple of assumptions. The first is that, for the purposes of the medal standings, gold, silver, and bronze should not possess equal weights. Traditionally, every medal counts for one point for its winner’s home country, regardless of its hue, confusing the performances by which those medals were awarded in the first place.

For the debut of COSTAS at the Vancouver Olympics, Roher chose a 4-2-1 scoring system for gold, silver, and bronze, which I extended to the Summer Games. Admittedly, these weights are arbitrarily chosen—it could be argued that a 5-3-1 or a 3-2-1 system are just as valid—but they do successfully get across the main point, that medals should be treated as having different values in the medal standings, as they do on the playing fields.

The second assumption is that all sports should be treated as having equal importance. Swimming has a total of 34 events for its male and female participants, while basketball has only two. It doesn’t seem fair to conclude from this that swimming, as an Olympic sport, is 17 times more important than basketball, and yet, for the purposes of the medal count, that’s exactly how the two are treated. It’s simply the respective natures of the sports that cause the difference in each is organized; swimming wouldn’t make as much sense with the athletes of just two countries playing against each other, and basketball doesn’t have a series of disciplines in which its athletes can compete for multiple medals.

Under COSTAS, every sport is valued equally, so the total medals for swimming are worth the same amount as the total medals for basketball. By applying weights for the number of events in each individual sport, we get a clearer picture of the relative worth of each medal.

I recognize that the lines between different “sports” are sometimes hazy—for instance, trampolining doesn’t seem much different from gymnastics—so I used the official distinctions laid out by the IOC, which can be found here. I did make one exception to this: the IOC includes all track and field events under the umbrella of “Athletics,” so I separated the track events (those that consist in exclusively running) from the field events (all other events, including the decathlon and heptathlon) for the purposes of the weights. The final step in the process was to scale the COSTAS numbers into a format that looks more like the traditional medal count, so I made the total number of COSTAS points add up to the total number of medals available at the Summer Olympics (958).

So without further ado, here are the standings for the 2008 Summer Olympics in Beijing, as measured by traditional medal count:

Now here are the COSTAS standings for those same Olympics:

The country that receives the biggest boost from COSTAS is China, due to its impressive haul of gold medals and its dominance of whole events like table tennis, diving, and badminton. Under this system, the Chinese ascend firmly into first place, outpacing the second place Americans by about 28 “medals”—a humbling revelation for the red, white, and blue. Many of the Americans’ medals came from events with an enormous number of medals available, like swimming and track and field, providing them with a much smaller increase in points.

I’ll be updating the COSTAS standings for the London Olympics at various times during the Games, so stay tuned to see if the USA can wrest the mantle of supreme Olympic champions from the Chinese.

This post can also be seen on Boston.com here.

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### 6 Responses to COSTAS: The Weighted Olympic Medal Count

1. Anonymous User says:

Can this be done for an individual’s performance too? It would be interesting to see if a swimmer with, say, 19 medals is really the ultimate olympic champion next to someone who wins fewer medals but in a sport with fewer available.

2. Eric says:

Yes! Yes! A thousand times, yes!

A friend referred me to “COSTAS” only after I’d already posted about “EBOP;” otherwise, I’d’ve just argued for tweaks to your formula. For example, I’d favor heavier for golds, but pish-posh … hooray for COSTAS, and hooray for you!

3. scott says:

I agree with the premise of using the two dimensions to come up with a more balance scorecard of medal performance by country.

I completely agree with the first dimension being type of medal earned – goal, silver or bronze. It doesn’t really matter how you assigned the weightings as long as gold is worth more than silver etc

I’m not sure I agree with how you’ve defined the 2nd dimension. Certainly a problem with flat medal counts is that individual swimmer has more opportunities to earn a medal than an individual basket-ball player (who can only ever earn 1/12 of a medal). I agree in principle that a 2nd weighting factor is required to adjust for the differences between events and sports. However simply discounting a medal based on the number medal events per sport might be the wrong method. What about looking at the athletic effort/work units required to achieve the medal.

For example to win a gold medal in basketball requires 12 athletes to compete in 8 games (5 preminiary round games, quarterfinals, semi finals and finals) for a a total of 96 athletic effort units or 8*12). Where-as to win a typical individual swimming medal requires 1 athlete to swim 3 races (heats, semi’s and finals) or 3 athletic effort units. I think this method more fairly reflects the number of athletes and number of competitions required to earn a medal. The biggest difference between this method and your method would be greater rewards for team sports and events requiring multiple competitions like decathlon.

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