Now these athletes are showing that while vaccines are exceptionally effective in preventing death and severe illness from the coronavirus and its known variants, some are far from foolproof in preventing infection altogether. Most of the athletes with so-called “breakthrough” infections are asymptomatic. The infections wouldn’t have been noticed except for the fact that people who work in sports are among the last being tested intensely for the virus. These surprising positive tests are a problem for the hosts of large events. In the case of the Olympics, they could trigger an outbreak in the surrounding Japanese population or beyond, to any of the 200 participating nations—in addition to creating chaos in competitions.