LogFAQs > #961765807

SKARDAVNELNATE posted...

That's so strange. Isn't keeping people from needing to go to the hospital what the vaccine is for?

Let's use some hypothetical numbers for illustrative purposes:

-Unvaccinated people have a 15% chance of being hospitalized
-Vaccinated people have a 5% chance of being hospitalized

Now, let's do the math for 10%, 25%, 50%, and 75% vaccination rates to see what sort of distribution would be expected in hospitals, based on 10,000 randomly selected cases:

10% vaccination rate:
9000 unvaccinated cases * 15% = 1350 unvaccinated hospitalizations
1000 vaccinated cases * 5% = 50 vaccinated hospitalizations
3.5% of total hospitalizations are vaccinated

25% vaccination rate:
7500 unvaccinated cases * 15% = 1125 unvaccinated hospitalizations
2500 vaccinated cases * 5% = 125 vaccinated hospitalizations
8.3% of hospitalizations are vaccinated

50% vaccination rate:
5000 unvaccinated cases * 15% = 750 unvaccinated hospitalizations
5000 vaccinated cases * 5% = 250 vaccinated hospitalizations
25% of hospitalizations are vaccinated

75% vaccination rate:
2500 unvaccinated cases * 15% = 375 unvaccinated hospitalizations
7500 vaccinated cases * 5% = 375 vaccinated hospitalizations
50% of hospitalizations are vaccinated

As you can see, even with the vaccine reducing the risk of hospitalization by a factor of 3, the proportion of vaccinated people in hospitals increases as the vaccination rate of the general population increases. This doesn't mean the vaccine doesn't reduce the risk of hospitalization, it means that increasing your sample size while keeping the odds the same increases the number of success rolls ("success" in this case meaning hospitalization).

There's nothing strange about it. This is just basic math.