“We can’t eliminate all risk,” he added, “but the plan Darlington turned in, I think it will work. And the extent that it works, will have an impact on future events.”

The situation in South Carolina demonstrates another variable in determining the magic number: the facility itself.

Some stadiums have wider concourses than others. Some have more gates, meaning less congestion. Some have second and third decks, or premium seating and luxury boxes, that break up the vast ocean of regular seating. Some even have wider seats than others, creating a head-spinning number of considerations.

That’s a big reason why Arrowhead Stadium settled on 22% of capacity while Sporting Kansas City, the Major League Soccer team just across the state line in Kansas, determined that 14% of capacity (about 2,500 fans) is appropriate.

Are any of these magic numbers actually safe?

“These stadiums are massive, so 20-30% is often in the tens to 20,000 people,” said Lucia Mullen, an epidemiologist and analyst for the Johns Hopkins University Center for Health Security. “That’s larger than we’ve had really to date in most venues right now. And we know this virus, it’s very capable of spreading within people quite quickly. And so with just that small amount of people, if it’s allowed to spread, it could reach huge numbers in a community.”

Mullen suggested another factor in determining the magic number: the ability to do contact tracing. If several people test positive for COVID-19 after attending a game, there must be a manageable number of tickets sold — and a way to get in touch with those fans — so that they can pinpoint the potential spread.

“You’re bringing people from different communities to one area,” Mullen said, “and then they’re going to at the end of the game go back to their communities. And so there’s two big risks. The first is if they’re bringing the virus with them and then allowing it to circulate in the community where the game is. Or as an individual, if they happen to contract the virus at a game and then they bring it back to their community and allow it to spread there.”