Digging more, say that it turns out that 90% of the doctors were vaccinated. To make it easy, assume that there are 1,000 total doctors. 90% vaccinated means there were 900 vaccinated and 100 unvaccinated. If 10 died from each group, that means:
- 10 / 100, or 10% of unvaccinated doctors died
- 10 / 900, or 1.1% of vaccinated doctors died
Unvaccinated doctors were 9 times as likely to die as vaccinated ones. Another way of phrasing that is that the vaccine's efficacy was:
vaccine efficacy = 1 - (vaccinated risk/unvaccinated risk) = 1 - (0.011/0.1) = 89%
This is how you have to think about things like this. Vaccines, masks, seat belts, helmets, etc. aren't 100% effective. Use the calculation above whenever you see headlines like this and want to know the actual story.
You can even have more vaccinated deaths than unvaccinated. Imagine for the 89% efficacy vaccine above, you have 99% of the population vaccinated. For 10,000 doctors in that example, you'd expect to have 10% of the 100 unvaccinated die and 1.1% of the vaccinated 9900 die, so that's 10 unvaccinated deaths and 120 vaccinated deaths. A highly effective vaccine can still have more vaccinated people die than unvaccinated ones.
In case a visual helps, here is the initial example's distribution as a colored grid (red = dead and green = alive):
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