Usain Bolt is the fastest man in recorded human history. Chris Johnson is the fastest man in the National Football League. Yesterday, Johnson claimed that, with a bit of training, he could beat Bolt in a 100m race. Ridiculous? Credible? I have no idea. But it raises a question I've been debating with some friends and colleagues for a while: How much do you think about the fact that professional sports dilute Olympic competition that is supposed to determine, to a certain extent, the fastest, high-jumping, most athletic people in the world?

Put differently: If professional sports didn't exist, would NBA and NFL players overrun the track-and-field events?

This is purely speculative exercise! But some caveats to begin: For super-athletic people, choosing how to put to use your super-athleticism is not a choice driven exclusively by market economics. Country-by-country culture matters, public park and school resources matter, the kind of sports that schools choose to offer the most scholarships for matters, and there are lots of social norms that come into play when you're trying to answer the question, Why do our best athletes play the sports that they do? But as with all professions, there are economic incentives, too.

Here's a graph of the cash prize of a gold medal for the top five countries, followed by China (#35) and the US (#55) and the UK (which offers no cash reward). At the end, somewhat mischievously, I've included the minimum wages for professional baseball, basketball, and football in America.

Click to enlarge. The upshot here is that the cash reward for winning a gold medal in the U.S., $25k, is 1/20th of the minimum wage in American professional sports. In every country except Singapore and Azerbaijan, the cash reward for gold medal is less than minimum wage in American professional sports. Assuming that supremely athletic people are choosing their sports even partially based on perceived financial rewards (which are hardly the only rewards in sports), we should expect that the best athletes, with access to the best training facilities and coaching in the world, aren't necessarily competing in track-in-field Olympic sports, where we honor the world's "best" throwers, runners, jumpers, and all-around athletic specimens. Moreover, as monetizable audiences for global professional sports grow, we should expect the rewards of playing professional sports to grow even further away from the financial rewards of competing in the Olympics.

This sort of kill-joy analysis is somewhat obvious ("Your point is professional sports pay more than amateur sports? Uh, got it.") and somewhat unprovable. There is no way to know whether LeBron James would have won the decathlon if he'd set his mind to it, nor that Chris Johnson could have been the fastest man, not just in his league of professionally fast men, but in the world. The question is, when watching the Olympics, how important is it to you, as an Olympics fan, that the financial rewards for playing professional sports are so much higher, and growing so much faster, than the cash and endorsement incentives for competing in the Olympics, that it's reasonable to think the pool of Olympic competition is hopelessly diluted, and might get more diluted over time?