In 2016, I wrote about how scoring the Olympics by total medal counts, or by just the number of golds, was an inaccurate way to say which nation did best, because different nations have different abilities. Either Kenya or Tajikistan "won", by my chosen measurements.
This year, I took the same "weighted medal score" (henceforth called WMS) that I used before, and compared it to a bunch of national statistics, looking for correllations. Athelete counts of course had the strongest, because the more athletes a nation has competing, the better chance they have of winning something. I don't think this was good enough on its own, because a richer country will have more athletes.
The next-best correlation was looking at the number of athletes divided by the purchasing-power parity GDP (basically, how much does the average person make each year, normalized by the cost of resources) of each nation.
For another scale of measurement, I decided to also use the nominal GDP of each nation, as that had the best correlation with the WMS without involving athlete counts.
Finally, I divided the number of golds won by each nation by the two statistical numbers, and multiplied by a bunch to get a more-readable number. I used just golds instead of taking in to account silvers and bronzes, because the winner's the only one that really matters.
So, by these calculations, Belarus "wins", based on the fact that got two gold medals but their GDP is in the tens of billions of dollars. For comparison, the USA, with it's GDP in the tens of trillions, only got 9 golds. Nearly 400 times more GDP, but only 4.5 times more gold medals.
I'm not sure what to make of the Athletes/PPP results. I think the fact that the number of athletes is still included is messing with stuff too much. I'm making a note to only include athlete counts, if I do this again, if I'm normalizing things to work with athletes performing in multiple events.
Again, neither of my methods really answered the question for me, but I feel like it does give an idea of which nations did some outstanding work.
Now that everyone has paid their biennial homage to deus ex circenses, get back to work.