I saw the viral tik-tok video of the woman who was "good with numbers" and rattled off statistics about how bad the odds are if you are unvaccinated. Something struck me as "statistically disingenuous" about her analysis so I set about to verify (or debunk) what she was saying, f-word every three seconds notwithstanding. This chart represents the best data set I could find for the U.S. up to the first week in September.
The first thing I thought was that she was using the entire U.S. population numbers, not just those vaccine-eligible. This included children under 18 (factoring out the 25% of 12-18 year-olds who have been vaccinated) totaling around 65 million or about 20% of the U.S. population. While her overall odds were correct, at least in the math, it was not a perfect indicator of vaccine efficacy. In fact, when you take out those ineligible numbers, the general odds of getting sick once vaccinated are less by close to 40%.
Now, the pre-vaccine numbers do represent a relatively real risk assessment IF (big if) we jumped in a time machine to one year ago. This was because all we had were distancing and masks and the Delta variant hadn't arrived in the U.S. The post vaccine numbers are a better assessment of the odds today, but that could easily change given the rapidly changing factors of this pandemic.
What I did find startling was that throughout the entire pandemic, whether vaccinated or not, once and individual gets COVID, the odds for being hospitalized or dying are relatively similar.
DISCLAIMER: I draw no conclusions and make no recommendations. This is just a slightly more granular examination of the odds statistics -- it's math. The numbers were from both the CDC and the COVID data project.