In the spirit of the Olympic games, I used some statistical models last month to produce medal count forecasts for Rio 2016. An emerging scandal involving Russian state-sponsored doping and the resultant uncertainty about which Russian athletes would be allowed to compete forced some last minute tweaks. Now the results are in and the models look pretty good, if imperfect.
Careful readers may recall that I produced two models, both of which involved predicting medal counts for men and women separately. The first was a kind of standard model that gave weight to past performance, level of per capita income, status as a host nation, and other variables. But this model seemed to not fully capture the superior performance of some countries such as Jamaica and Kenya so a second model was specified, based on each country's performance at the previous Games with only the marginal changes in the explanatory taken into account. The correlation between the “standard” model forecast and actual performance at Rio was 0.97; the “marginal changes” model did slightly better at 0.98.
But there were some large errors, and these may be instructive. The United States and the United Kingdom performed much better than expected. The United States, predicted to win between 104 and 108 medals came home with 121. The bulk of the unforeseen success came from the American women. Several researchers have tried to tie American women’s achievements in Olympic competitions to Title IX, a federal law that forbids gender-based discrimination in federally funded activities, thus far without success. The stellar performance of American female athletes in Rio will surely encourage a re-examination of that relationship.
Likewise, it was expected that the United Kingdom would experience a letdown after hosting the 2012 London Games. There is some statistical evidence that the “post-host” country continues to get a boost in the Games immediately following the one that they hosted. Perhaps the British success in Rio (and the Chinese collapse after their success in Beijing 2008 and London 2012) will encourage re-consideration of that relationship as well. Or maybe British performance can be ascribed to targeting niche competitions for state support. But be forewarned: Picking winners among Olympic disciplines may be easier than picking winners in the economy.
Which brings us to the Rio host, Brazil. The models said that it would get 31 to 32 medals, but the Brazilians only netted 19. But this shortfall was not unexpected: As I noted at the time, the home field advantage appears to be particularly acute in judged sports such as gymnastics in the Summer Games or figure skating in the Winter Games. Historically Brazil has not been particularly competitive in judged events and as a consequence was not in a position to take full advantage of “home cooking.” This judgment appears to be borne out in the numbers. Having a country in turmoil might have something to do with Brazilian underperformance as well. The same could be said for Ukraine, which was forecast to win 19 to 20 medals but only came home with 11.
The North Koreans promised to compete with “guerilla tactics” and “heated zeal.” I put them down for five to six medals. They captured seven, so maybe the “guerilla tactics” are working, though I suspect that the Russian absence in weightlifting where the North Koreans got four of their medals might have something to do with it. South of the 38th parallel, the models forecasted South Korea to remain in the top 10, winning 26 to 30 medals, but they fell short, grabbing 21. Maybe they should borrow some of that “heated zeal.”
And the Russians? The models predicted 55 to 56 medals. They garnered 56. Well, at least I got some things right on target!
Sadly, all of this analysis has to be regarded as provisional. Athletes are now subject to post-competition doping analyses, and it is almost certain medals will be stripped from some athletes and given to other competitors. The authorities are still trying to sort out the true winners from the London Games. But in the meantime, to all the Olympians who competed cleanly, whether or not you medaled: We salute you! See you again in four years.