No nation officially wins the Olympics, but that doesn’t stop journalists and others from trying to keep score by counting gold, silver and bronze medals. Unfortunately, the two main approaches are equally flawed. The raw medal count overly favors populous nations, while ranking nations by medals per capita overly favors small nations that win one, two or a few medals, possibly by fluke.
There is a better way to rank nations by their Olympic prowess. I was put in touch with the researchers who developed the concept by Pete Pfitzinger, a college classmate of mine who was the top American marathoner in the Olympics of 1984 and 1988.
First, though, let me go into what’s wrong with the medals-per-capita approach, which certainly seems fair. The problem, as I said, is that it’s not reliable when it comes to the performance of very small nations. In the Tokyo Games held in 2021, for example, the medals-per-capita winner by far was San Marino, which somehow won three medals (two in trap shooting, one in wrestling) despite a population of only around 34,000. Behind it were Bermuda and Grenada, with one medal apiece.
As statisticians know, the smaller a sample is, the bigger its variance. People who ignore or don’t know about this statistical property can be badly misled. For example, rural counties dominate the list of counties with the highest kidney cancer rates, which seems like a good reason to rush funding to rural health authorities. But guess what — rural counties also dominate the list of counties with the lowest kidney cancer rates.
Same goes in education. After researchers noticed that small schools dominated the list of best performers based on average student test scores, there was a flurry of interest in promoting small schools, and even breaking up big ones. But then statisticians pointed out that the very worst performing schools by average student scores were also mostly small ones. There’s simply a wider spread when samples are small. For more on this, I recommend this excellent article in American Scientist by Howard Wainer, a past principal research scientist at the Educational Testing Service.
The better Olympic rating system I mentioned is more balanced, advantaging neither the biggest nor the smallest nations. It was created by Robert Duncan, an astrophysicist now retired from the University of Texas, and Andrew Parece, a vice president at Charles River Associates, a consulting firm in Boston. After I started corresponding with them, their paper on the matter, “Population-Adjusted National Rankings in the Olympics,” was published in The Journal of Sports Analytics.
The Duncan-Parece model ranks countries according to how improbable their medal counts are if one assumes that all medal-winning nations have an equal propensity per capita for winning medals. Its measure of improbability is based on the so-called binomial distribution formula, which is the one you would use to calculate the likelihood of flipping heads, say, 10 times in a row.
Applying their method to the Tokyo Olympics, the top 10 countries in order were Australia, Britain, the Netherlands, New Zealand, Hungary, the United States, Italy, Japan, Cuba and Jamaica. In the 2016 Olympic Games in Rio de Janeiro, their top 10 were Britain, the United States, New Zealand, Australia, France, Denmark, Azerbaijan, Jamaica, Germany and the Netherlands.
The authors thank Pfitzinger, the Olympic marathoner, for identifying the problem with the conventional ranking methods and urging them to solve it. They acknowledge that “there exists no perfect and absolutely ‘correct’ way to do Olympic national ranking.”
I asked Andrew Gelman, a statistics professor at Columbia and blogger, what he thinks of the Duncan-Parece model. “Good for them,” he said. He said theirs was a reasonable way, though not the only one, to strike a balance between big and small countries.
Small sample sizes are tricky to interpret no matter what ranking method one uses, Gelman added. For example, if a small country wins a surprisingly high number of Olympic medals, it might not match that performance in four or eight years. Or it might!
The Duncan-Parece model is good for ranking, as in the Olympic comparisons, but possibly not so much for diagnostics, as in kidney cancer and school test scores. “I think that for those problems there are clearer targets and it makes sense to attack the problems directly. The Olympics thing is different because there the goal is to rank, not to measure,” Gelman wrote.
If you want to see how nations fare in the Summer Games in Paris according to Duncan and Parece’s model, check out this website.
Elsewhere: Minimum Wages in California
California was tied with Nevada as of June for the highest unemployment rate in the 50 states. California also has high minimum wages. Is there a connection? Two recent studies reached opposite conclusions. Beacon Economics, a Los Angeles-based forecaster that has received research support in the past from the California Restaurant Association, found that the increase in California’s unemployment was led by people under 25 and wrote, “Look no further than the state’s aggressive minimum wage mandates.” In contrast, a report by four economists for the Washington Center for Equitable Growth, which receives support from nonprofit foundations, found that minimum wage increases in California and New York “did not cause disemployment effects” for fast-food workers in 36 big counties in California and New York.
The Equitable Growth researchers theorize that before the increase in minimum wages, fast-food restaurants were using their market power to suppress wages and that they absorbed the higher minimums partly by accepting slimmer profit margins. In an email, they wrote that the Beacon Economics study found correlation between higher wage floors and unemployment in California, but not causation. Christopher Thornberg, the founding partner of Beacon Economics, claimed that the authors of the Equitable Growth paper “started with the answer and tortured the data to get it to confess.” He added: “Mind you, I appreciate they will say the same about me!”
Quote of the Day
“The most fateful change that unfolded during the past three decades was not an increase in greed. It was the expansion of markets, and of market values, into spheres of life where they don’t belong.”
— Michael Sandel, “What Money Can’t Buy: The Moral Limits of Markets” (2012)
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