The Centers for Disease Control and Prevention reported a terrifying fact in July: Vaccinated people with the delta variant of the COVID virus carried roughly the same viral load in their noses and throats as unvaccinated people.

The news seemed to suggest that even the vaccinated were highly vulnerable to getting infected and passing the virus to others. Sure enough, stories about vaccinated people getting COVID — so-called breakthrough infections — were all around this summer: at a party in Provincetown, Massachusetts; among the Chicago Cubs; on Capitol Hill. Delta seemed as if it might be changing everything.

In recent weeks, however, more data has become available, and it suggests that the true picture is less alarming. Yes, delta has increased the chances of getting COVID for almost everyone. But if you're vaccinated, a COVID infection is still uncommon, and those high viral loads are not as worrisome as they initially sounded.

How small are the chances of the average vaccinated American contracting COVID? Probably about 1 in 5,000 per day, and even lower for people who take precautions or live in a highly vaccinated community.

Or maybe 1 in 10,000

The estimates here are based on statistics from three places that have reported detailed data on COVID infections by vaccination status: Utah; Virginia; and King County, which includes Seattle, in Washington state. All three are consistent with the idea that about 1 in 5,000 vaccinated Americans have tested positive for COVID each day in recent weeks.

The chances are surely higher in the places with the worst COVID outbreaks, such as the Southeast. And in places with many fewer cases — such as the Northeast, as well as the Chicago, Los Angeles and San Francisco areas — the chances are lower, probably less than 1 in 10,000. That's what the Seattle data show, for example. (These numbers don't include undiagnosed cases, which are often so mild that people do not notice them and do not pass the virus to anyone else.)

Here's one way to think about a 1-in-10,000 daily chance: It would take more than three months for the combined risk to reach just 1%.

"There's been a lot of miscommunication about what the risks really are to vaccinated people, and how vaccinated people should be thinking about their lives," as Dr. Ashish Jha of Brown University told my colleague Tara Parker-Pope.

For the unvaccinated, of course, the chances of infection are far higher, as Dr. Jeffrey Duchin, the top public-health official in Seattle, has noted. Those chances have also risen much more since delta began spreading.

Another way to understand the situation is to compare each state's vaccination rate with its recent daily COVID infection rate. The infection rates in the least vaccinated states are about four times as high as in the most vaccinated states.

If the entire country had received shots at the same rate as the Northeast or California, the current delta wave would be a small fraction of its current size. Delta is a problem. Vaccine hesitancy is a bigger problem.

The science, in brief

These numbers help show why the talking point about viral loads was problematic. It was one of those statements that managed to be both true and misleading. Even when the size of the viral loads are similar, the virus behaves differently in the noses and throats of the vaccinated and the unvaccinated.

In an unvaccinated person, a viral load is akin to an enemy army facing little resistance. In a vaccinated person, the human immune system launches a powerful response and tends to prevail quickly — often before the host body gets sick or infects others. That the viral loads were initially similar in size can end up being irrelevant.

I will confess to one bit of hesitation about walking you through the data on breakthrough infections: It's not clear how much we should be worrying about them. For the vaccinated, COVID resembles the flu and usually a mild one. Society does not grind to a halt over the flu.

In Britain, many people have become comfortable with the current COVID risks. The vaccines make serious illness rare in adults, and the risks to young children are so low that Britain may never recommend that most receive the vaccine. Letting the virus continue to dominate life, on the other hand, has large costs.

"There's a feeling that finally we can breathe; we can start trying to get back what we've lost," Devi Sridhar, the head of the global public health program at the University of Edinburgh, told The Times.

I know that many Americans feel differently. Our level of COVID anxiety is higher, especially in communities that lean to the left politically. And there is no "correct" response to COVID. Different people respond to risk differently.

But at least one part of the American anxiety does seem to have become disconnected from the facts in recent weeks: the effectiveness of the vaccines. In a new ABC News/Washington Post poll, nearly half of adults judged their "risk of getting sick from the coronavirus" as either moderate or high — even though 75% of adults have received at least one shot.

In reality, the risks of getting any version of the virus remain small for the vaccinated, and the risks of getting badly sick remain minuscule.

In Seattle on an average recent day, about 1 out of every 1 million vaccinated residents have been admitted to a hospital with COVID symptoms. That risk is so close to zero that the human mind can't easily process it. My best attempt is to say that the COVID risks for most vaccinated people are of the same order of magnitude as risks that people unthinkingly accept every day, like riding in a vehicle.

The bottom line

Delta really has changed the course of the pandemic. It is far more contagious than earlier versions of the virus and calls for precautions that were not necessary a couple of months ago, like wearing masks in some indoor situations.

But even with delta, the overall risks for the vaccinated remain extremely small. As Dr. Monica Gandhi, an infectious-disease specialist at the University of California, San Francisco, wrote on Friday, "The messaging over the last month in the U.S. has basically served to terrify the vaccinated and make unvaccinated eligible adults doubt the effectiveness of the vaccines." Neither of those views is warranted.

This article originally appeared in The New York Times.