CNN  — 

In the United States, approximately 658 million Covid-19 vaccine doses have been administered since they were first distributed exactly two years ago Wednesday.

Framing the significance of preventive measures like vaccines can be challenging, which is why a new report from the Commonwealth Fund and Yale School of Public Health made headlines: According to their modeling of disease transmission across all age demographics and taking into account the existing health conditions in so many Americans, Covid vaccines prevented an estimated 3.2 million deaths and 18.5 million hospitalizations from their introduction in December 2020 to November 30, 2022.

That is why it is surprising to hear, according to a Kaiser Family Foundation analysis of data from the US Centers for Disease Control and Prevention, that from April through August – the last month included in the analysis – there were more vaccinated than unvaccinated people dying of Covid. The vaccinated categories include people who were vaccinated with the primary series and people who had been vaccinated and received at least one non-bivalent booster.

According to a CNN analysis of additional CDC data for September, 12,593 people died of Covid. A CDC sample of the deaths found 39% were unvaccinated, and 61% were vaccinated.

This phenomenon has many people – especially vaccine skeptics, but even stalwart vaccine supporters – confused and wondering if Covid vaccines and boosters are still effective and warranted.

The short answer is yes – but understanding why requires a crash course in statistics. We enlisted the help of Jeffrey Morris, a professor and the director of the Division of Biostatistics at the Perelman School of Medicine at the University of Pennsylvania, who helped us define three key reasons more vaccinated than unvaccinated people are dying of Covid.

Statistics, part 1: base rate fallacy

One of the main reasons we see more vaccinated than unvaccinated people dying of Covid is a basic one. At this point in time, there are simply many more people who are vaccinated.

Think of it like this: If we round the September deaths to 13,000 and use the CDC sampling percentages, approximately 7,800 were vaccinated and approximately 5,200 were unvaccinated. The conclusion might be that you are far more likely to die if you are vaccinated. And, mathematically that would be true based on the raw numbers alone. If you stopped your analysis at this point, you will have committed a statistical error known as a base rate fallacy.