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Qatar and Bahrain aren't the only countries boosted by foreign-born Olympians

An athlete doesn't need to be born in the same country to be part of its Olympic team.

Some countries have been criticized for stacking their teams with Kenyan runners or Chinese table tennis players, while Bahrain and Qatar are often singled out for their mercenary recruiting techniques. But naturalized citizens have long been a crucial addition to national teams, and the percentage of Olympians born outside of the country they represent has been growing slowly in recent years for most major teams.

CNBC looked at the thousands of Olympic athletes listed on sports-reference.com, which includes the birthplace of each athlete. Almost 8 percent of the athletes competing in the 10 largest Olympic teams were born in another country in the last Summer Games, according to the data. That's the highest that figure has been since the 1930s.

The percentage of foreign-born athletes was even higher between the first modern Olympic games in 1896 and 1920, when as many as 20 percent were not native born. That's not surprising considering that the data include both athletes who were recruited for their talents and immigrants who moved to the U.S. at some point and then became athletes.

In those earlier decades, many of those Olympians in the U.S. were part of the mass immigration from places including Ireland, Germany, Italy and Hungary. Since 1980, more of those athletes were born in countries such as China, Cuba, Russia, Japan or Jamaica.

The most medals that have ever been won by a foreign-born American athlete so far is nine, a record set by the Irish-American Martin Sheridan in the 1904, 1906 and 1908 Olympics. Sheridan emigrated to the U.S. when he was 16 and won five gold medals, three silver and one bronze in discus, shot put, stone throw, long jump and high jump. (The 1906 games were considered official games at the time, but are not currently recognized by the IOC as being an official Olympiad.)

American gymnast Anton Heida also won five gold medals — all at the 1904 Olympics. Heida competed earlier that year as an Austrian national and became a U.S. citizen only weeks before competing on its behalf in his events.

While 2016 data were not available in this dataset, this year's Team USA delegation included 46 athletes who were born in foreign countries, according to the New York Times. That's a little over 8 percent, compared to about 5 percent in 2004. That includes Kenyan-American runner Bernard Lagat, Cuban-American gymnast Danell Leyva, and Australian-born equestrian Phillip Dutton.

Overall, foreign-born Americans have earned at least 130 out of the more than 2,600 medals earned by the U.S. in the Olympics since 1896. That includes the country's only medal in ski jumping (Anders Haugen, born in Norway), and a substantial share of the tug-of-war (21 percent), gymnastics (19 percent), weightlifting (15 percent), freestyle skiing (14 percent), tennis (13 percent) and luge (11 percent) medals.

Disclosure: CNBC parent NBCUniversal owns NBC Sports and NBCOlympics. NBC Olympics is the U.S. broadcast rights holder to all Summer and Winter Games through the year 2032.