Which Country Will Win the Paris Olympics? Don’t Just Count Medals.

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.