Several news items during the Olympics have commented on the twin phenomena of less violence than anticipated and the absence of American spectators. Apparently – and it's hard to evaluate this claim without data, as most of it seems to be anecdotal from journalists – fans have attended the games in ordinary or expected numbers from around the world with the conspicuous exception of the United States. The most obvious explanation, discussed in the linked EspnW story above, is the extensive amount of coverage in the American media of Rio violence and the Zika virus.
That makes sense on its face. But it doesn't hold up to much scrutiny.
Stories about the ineptitude of Rio's preparation for the games (shoddy housing, dirty water, etc) were not by any means unique to American media. Since the journalists' housing was among the shoddiest and the earliest occupied, journalists from around the world were all subject to the same conditions with ample time to write listicle-style "Look at this shit!" stories. Second, Rio's reputation for having a poverty-crime problem is hardly a secret. Not only was it written about prior to the games (again, not exclusively by American journalists) but it hardly even needs to be written about. Even in Brazil, where I traveled a bit in 2014 prior to the World Cup, Brazilians I encountered described their country's crime rate as totally overblown – except for Rio. The consensus was that Rio was in fact very dangerous, and not just for tourists. So, its reputation appears pretty well established and merited. Finally, stories about Zika were similarly popular in media outlets American and non-American alike. Tabloid media love a good "outbreak" story irrespective of nationality (Ebola, Avian flu, SARS, etc).
The more likely explanation is that Americans are really bad at traveling abroad in general. No doubt the sensational stories about Rio dissuaded some people who might have considered going, and things like warnings from the CDC and State Department reinforced that. But 64% of Americans do not even have a passport. Few of us have traveled abroad, and a good portion of those who have been to another country have been to places like Canada, Mexican resort towns, and Caribbean cruise-stop islands. Most of us have no paid vacation days. Most of us lack the disposable income for expensive vacations to overpriced Big Events like the Olympics. Most of us do not speak Portuguese and may know that unlike in Europe or even most of Asia, facility with English will be very rare among the population. The percentage of the American population able to go to these Olympics even if they wanted to is small. And if the media dissuaded some of them who were on the fence, it stands to reason that a drop in an already small cohort would be noticeable in the stands.
The scary media narrative isn't outright wrong, but it's deceptive. It suggests a set of conditions that are not in fact unique to the United States but ignores others that are.