Olympic Medal Predictions:"No Bangladeshi competitor has ever qualified for the Olympics"
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Economist Tyler Cowen has an article in Grantland predicting long-run trends in Summer Olympic medals totals based on population growth rates, age, and income. Cowen explains:
Economists have taken time out of their busy schedules of destroying the world to provide insights into which factors help make countries successful in their bids for Olympic glory. 
The first factor is population. If athletic ability is roughly equally distributed around the globe, the more citizens you have, the more great athletes you are likely to have. It stands to reason, for example, that Australia will likely win more medals than New Zealand, simply because it has five times the population.
And that's why India wins 50 times as many medals as Australia. And then, as jody reminds us, there's always Bangladesh, population 150,000,000. From Wikipedia's striking article "Bangladesh at the Olympics:"
Bangladesh has competed in seven Summer Olympic Games. They have never competed in the Winter Games. 
No Bangladeshi competitor has ever qualified for the Olympics; the country sends representatives to the Games thanks to the wildcard process.[1] Bangladesh is the most populous country in the world never to have won an Olympic medal. 
Not only no medals, but "No Bangladeshi competitor has ever qualified for the Olympics ..."
It looks to me more like the countries that win a lot of medals are the countries that A) want to win a lot of medals and B) are pretty competent at what they do. The East Germans used to win a lot of medals, for example, but then, they'd almost conquered the world. 
Moreover, it helps to have a lot of power and tradition to get your favorite sports treated well by the Olympics. You'll notice, for instance, that the Olympics hand out a ton of swimming medals, which benefit the U.S. and Australia in the medal counts. In track, there are medals for running and a couple for walking, but in swimming there are medals for four separate strokes, even though one, the butterfly is obviously inferior to the crawl (freestyle) on all dimensions. It's like if they gave out gold medals in track for a couple of silly walks choreographed by John Cleese.
From Cowen's summary on his blog:
1. Medal totals will become more diversified over time. The market share of the “top 10? countries will continue to fall (it was 81 percent in 1988) as economic and population growth slows in the rich world. The developing world has greater room for rapid economic growth, and most parts of the developing world also have higher population growth. The Olympic playing field will get more and more level. 

That's an easy prediction to make. My guess is that it will be less true than Cowen thinks. My prediction is that there will be a countervailing trend. In some ways, the Summer Olympics will become even more like the Winter Olympics: a refuge for the global upper middle class, who have the resources to pick obscure sports for their scions and then pay for intensive tutoring as a path to get them into American colleges.

In contrast, the burgeoning ranks of the global poor, will obsess over a handful of big money sports, especially soccer in Africa, but also cricket in South Asia, neither one of which is a good way to pile up a lot of Olympic medals. The word "diversity" tends to freeze the brains of people these days, but an obvious global cultural trend is away from diversity in sports toward soccer uber alles.

Most of the major sports in the world today were institutionalized by English-speakers. The Victorian Anglosphere had the right combination of eccentricity, cooperativeness, fair-play, and cultural prestige to impose their favorite games upon the world. There was a second efflorescence centered in post-War California that's now institutionalized in the X Games. Today's global poor are unlikely to have a similar creative impact. They are more likely to follow fewer and fewer channels among the existing sports.

Many of today's Olympic sports will increasingly become museum pieces that will remain alive because wealthy people like the idea of their kind of people having an opportunity to win an Olympic gold medal.

2. Japan will continue to fade, mostly because of aging and population shrinkage. 

Actually, rather than continuing to fade like it did in 1988 through 2000, Japan made a big comeback in the 2004 and 2008 Olympics. After finishing no higher than 14th in total medals from 1988 through 2000, Japan finished 5th and 8th in the last two Olympics. The Japanese will always have the problem that they are rather small in stature, but I have this vague hunch that the particular Japanese problems in the late 20th Century were psychological, caused by the growth of the media in Japan. An American friend who teaches college in Japan wrote me in 2000:

When Japanese athletes compete in the Olympics they feel they are representing, not only their country, but also their race and all its members. When a Japanese is leading in a race the announcer's voice becomes flushed with emotion. When interviewed after competition, swimmers and judo-ists say they can't remember what happened, so great was their emotion. In fact in the moments leading up to a competition, Japanese seem almost paralyzed by nervousness. They are not competing for themselves, but for their coach, their team, their family, and everyone. If they win, it was not because of their own effort, but because of everyone's support. Their greatest emotion then is relief from the relentless pressure. If they lose, they have let everyone down. They cannot be good sportsmen and congratulate their opponents with a smile because their minds are elsewhere thinking about how they will apologize to their supporters.

Perhaps the Japanese are learning to deal with this kind of pressure better.

3. Italy will follow Japan for similar demographic reasons, as well as because the Eurozone crisis will continue to cut into budgets, training and otherwise.

Perhaps, but Italy has had low birth rates for awhile, and yet their Olympic medal performance has been better in the last four Summer Olympics than in 1988-1992. I'm not saying that the general mechanism Cowen identifies isn't a factor, just that if you are going to cite two examples — Japan and Italy — you ought to bother to go to Wikipedia and find examples that have actually been in decline already.

4. Since Rio is host to the next Olympics, Brazil should do better than expected due to the “pre-host” bump.

Maybe, but Brazil is close to the ultimate in soccer obsession. We'll see.

5. Many African nations will rise. Currently about half of the approximately 1 billion people in Africa have a cell phone, and the middle class is growing. The chance that an African star will be spotted and trained at the appropriate age is much higher than before. Africa also continues to grow in population, and that means lots of young people. Most of us still think of African nations as very poor, but infant mortality has been falling and per-capita income rising across Africa for the better part of a decade now.

Is there much evidence that African countries are getting better at winning men’s Olympic medals? Sure, it sounds plausible in theory, but where’s the evidence? Ethiopia has been winning distance running medals since 1960 and Kenya since 1964, so this isn’t exactly a hot, late-breaking trend. In the sprints, the African Diaspora continues to do better than African themselves.

Nigeria, for example, started getting better at wining Olympic medals in 1992, but it still only averages three medals per Summer Olympics in this century, which isn't much for a country with 162 million West Africans. In contrast, Cuba has averaged 27 medals per Olympics in this century.

My guess is that as more Africans get television in their homes, they’ll become even more obsessed with soccer and the World Cup rather than with the Olympics. Soccer experts have been predicting a major African breakthrough in the World Cup for a long time now, but it hasn’t happened yet.

6. China will level off and then decline as a medal powerhouse. In less than 15 years, the typical person living in China is likely to be older on average than the typical person living in the United States, in part due to the country’s one-child policy.

I think it will depend upon whether the Chinese state keeps pushing Olympic medals for nationalistic reasons. Even if they don't, the Chinese upper middle class might intelligently exploit obscure Olympic events as a way into American colleges.

I'll make a lame prediction: the easy way to win medals is in women's events. Various countries and cultures will exploit this, although in an unpredictable fashion.

One interesting question is what impact demographic trends will have on the U.S. Down through history, U.S. medal totals have been heavily carried by Californians, either natives or students / alumni of UCLA, USC, Stanford, etc. In 2008, Sports Illustrated counted 175 Californians on the U.S. Olympic team, versus 176 from the next seven states combined.

There are lots of reasons for this: California and Australia are similarly outdoorsy. California's culture has always been open to eccentric sports. California was a center of innovation in performance enhancing drugs going back to the 1950s. L.A. hosted summer Olympics in 1932 and 1984.

The new populations in California, however, aren't terribly athletic.

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