Some people asked me for the official definition of vaccine efficacy (or VE as it is usually abbreviated). As I suspect you might be thinking, it’s a fraction expressed as a percent. For example, suppose you had 300 cases in the unvaccinated group and 100 cases in the vaccinated group. The VE is then gotten by putting the number of cases in the unvaccinated group in the bottom of the fraction (the denominator) and the difference between the unvaccinated cases and the vaccinated cases in the top of the fraction (numerator). So in our example, this is:
VE = (300-100)/300 = 2/3 = 66.67%
Some people define it as the percentage reduction of cases you got in the vaccinated group compared to the unvaccinated group but personally I think this is one of those examples where looking at the fraction is easier to understand than parsing the words in the definition!
(unvaccinated-vaccinated)/unvaccinated
Elementary algebra then allows us to compute how many cases in the vaccinated group we can have per hundred cases in the unvaccinated group to achieve the 50% vaccine efficiency that the FDA says they will need before a vaccine meets the efficiency threshold. If X is the number of cases in the vaccinated group, we only need to solve the equation:
(100-X)/100 = .5
which gives X = 50 as you might expect. So no more than 50 cases in the vaccinated group for each 100 cases in the unvaccinated group gives us our efficacy signal.