It is often argued that because the number of infections is greater in the vaccinated fraction of a population, compared to the unvaccinated fraction, the corresponding vaccine is not effective. But this is a simple logical error. The point being that while the number of infections in the vaccinated can be greater, because of a high vaccinate rate, the percentage will be lower unless the vaccine really is ineffective.

Another way to think about it, is to consider that a small percentage of a large fraction of a population can easily be greater than a large percentage of a small fraction of a population.

In the default scenario, the number of infections in the vaccinated is twice that of the unvaccinated, but the vaccine is still 90% effective; i.e. it reduces infections by 90%.

Use the sliders to set up your own scenario. Use the "Get Link" button to get a URL to your scenario.

The NUMBER of infections is greater in the vaccinated
but the PERCENTAGE of infections is lower
and the vaccine is effective.

The vaccine is effective.