"Breakthrough infections" is a bad name
The vaccines work and infections among the vaccinated were expected all along
If you search Google News for “breakthrough infections” you’ll get a ton of results. Everyone seems to be wondering — do the vaccines work against these new variants? What would happen if everyone got vaccinated? And so on.
Unfortunately, “breakthrough” infections — that is, Covid cases among people that have been fully vaccinated — implies that there was some impenetrable wall that has been surmounted by a new and more formidable enemy. This isn’t true and it isn’t helpful.
As I dug into way back in March, the way that vaccines are shown to be effective is by preventing some portion of cases that would have otherwise happened. If a vaccine is stated to be 95% effective, that means that out of 100 cases that would have happened without a vaccine, only 5 cases did actually happen with the vaccine, meaning that 95 cases didn’t happen relative to this without-vaccine counterfactual.
But 5 is not zero! And those 5 cases are not “breakthrough” cases, they are normal, expected cases that will sometimes happen even with a vaccine that is 95% effective.
And the 5 cases that you expect is also a relative number. If there were 500 cases among people that were unvaccinated, you’d expect 5 * 5 = 25 cases among vaccinated folks.
So how do these numbers compare with the Delta variant?
Unvaccinated people still make up the vast majority of cases, hospitalizations, and deaths. They’ve made up more than 94 percent of reported Covid-19 cases in states with available data, a report last week from the Kaiser Family Foundation found. They’ve also made up similar, or higher, shares of hospitalizations and deaths.
The key number I’m looking at is the 94% figure. That means that for every 94 cases that happened without a vaccine, only about 6 have happened with a vaccine. (This is of course putting aside confounding factors, so this will be rough justice, no more). That means that approximately 6/94 = 6.4% of Covid cases are not prevented by the vaccine, or that it has an efficacy of 1 - (6 / 94) = 93.6%. (!!!!!)
So, yes, the vaccines work. They work well! Very well!