Breakthrough infections — in which vaccinated people nonetheless get the Covid-19 virus — are one of those vexing topics that can be difficult to put in perspective.

On the one hand, breakthrough infections are obviously occurring. They’ve happened to the New York Yankees and to White House officials, as well at summer gatherings in Massachusetts, Oklahoma and elsewhere. My colleague Liam Stack recently got sick with a breakthrough infection (and I’ll tell you his story below).

On the other hand, the scale of breakthrough infections remains unclear. Are they a significant reason that cases are now surging in the U.S. — and a reason for vaccinated people to be concerned? Or are breakthrough infections rare exceptions that receive outsize attention?

Those are two very different scenarios. If breakthrough infections are an important source of Covid spread, it would suggest that vaccinated people should resume some of their previous precautions, like avoiding crowded places. If Covid is instead spreading overwhelmingly among the unvaccinated, it would suggest that the behavior of the vaccinated doesn’t matter very much; the only reliable way to reduce caseloads would involve more vaccinations.

I’m going to warn you up front that I don’t have a definitive answer for you. “There’s a lot of uncertainty right now,” as Natalie Dean, a biostatistician at Emory University, told me. But there is some evidence that can help you think through the situation while scientists collect more data.

Let’s start with a few facts that are clear: