Generally, countries that host the Olympics put together some of the best athletic performances in their histories and finish with significantly more medals than they normally do at the Games. However, Great Britain proved to be a significant exception to that in 2016 when British athletes took home more medals from Rio de Janeiro, Brazil, than they did during the 2012 Olympics, which they hosted in London.
However, the first part of that trend remained true. In 2012, those representing Great Britain won 65 medals, easily the largest medal haul that the Brits have had since 1908 and a significant improvement over the 49 that they had taken home from Beijing four years earlier. But then they improved even more when they won 67 medals at the Games in Rio despite only bringing 366 athletes to Brazil, two-thirds of the 541 British athletes who had competed in London four years earlier.
But it should be noted that China nearly became the first to accomplish this interesting feat as Chinese athletes claimed 100 medals at the Beijing Games in 2008 before winning 91 in London in 2012. However, four years earlier, Greece took a significant step down from the 16 medals that Greek athletes had won at the Games in Athens in 2004 as the country was only able to get on the podium three times in Beijing.
One country that seemed to experience little positive impact on its medal haul when it most recently hosted was the United States. At the 1996 Olympics in Atlanta, American athletes were able to garner medals on 101 occasions. At the seven Summer Olympics from 1988-2012, the U.S. took home between 93 and 112 medals, so claiming 101 the year that it hosted during that stretch was par for the course for the Americans.