You also need to subtract the risk of dying or serious injury CAUSED by the vaccine when looking at its benefirts.
Using the most simplistic approach, that the 90% effective vaccine will save you 90% of the 0.2% of the time you'd have died from COVID, you'd have a 0.18 percentage point benefit from the vaccine. That is, if you would have died 20 out of 1,000 times before, now you'll die only 2 out of 1,000. We don't know the risks of death or serious complications, but its likely around or above 0.18%. That would mean getting the vaccine puts you at higher risk of serious complications or death from COVID or the vaccine than just not taking it.
And these numbers are for the population overall. Death rates are even lower than 0.2% for younger and healthier subpopulations.
You're off by a factor of 10 on your percentage calculations. With a 99.8% recovery rate, your risk of dying is 0.2%, or 0.002. Without the vaccine, you would die 2 times out of 1000. If the vaccine is 90% effective, then by your calculation you would die 0.2 times out of 1000.
Another way to say it is, the vaccine supposedly increases your recovery rate from 99.80% to 99.98%
Its 99.8% recovery. Not 98.
You also need to subtract the risk of dying or serious injury CAUSED by the vaccine when looking at its benefirts.
Using the most simplistic approach, that the 90% effective vaccine will save you 90% of the 0.2% of the time you'd have died from COVID, you'd have a 0.18 percentage point benefit from the vaccine. That is, if you would have died 20 out of 1,000 times before, now you'll die only 2 out of 1,000. We don't know the risks of death or serious complications, but its likely around or above 0.18%. That would mean getting the vaccine puts you at higher risk of serious complications or death from COVID or the vaccine than just not taking it.
And these numbers are for the population overall. Death rates are even lower than 0.2% for younger and healthier subpopulations.
You're off by a factor of 10 on your percentage calculations. With a 99.8% recovery rate, your risk of dying is 0.2%, or 0.002. Without the vaccine, you would die 2 times out of 1000. If the vaccine is 90% effective, then by your calculation you would die 0.2 times out of 1000.
Another way to say it is, the vaccine supposedly increases your recovery rate from 99.80% to 99.98%