Them: The COVID-19 vaccines don’t work. The majority of hospitalizations/deaths/infections are fully vaccinated. Me: Base Rate Fallacy would like a word with you.

Let’s try something. Most people get this question wrong. Can you solve it? A town has only two colours of car: 85% are blue and 15% are green. A person witnesses a hit-and-run and says they saw a green car. If witnesses identify the colour of cars correctly 80% of the time, what

are the chances the car is actually green? You might have said 80%. A lot of people do. The correct answer is 41%. The reason so many struggle with this question is due to the Base Rate Fallacy. Our brains tend to ignore statistical information (aka base rates) and focus on

specific information related to people and events. We're distracted by the witness, and forget how rare green cars are in the town. This problem uses Bayes Theorem. If we randomly selected 100 cars, 85 would be blue and 15 would be green. If a witness correctly identifies green

cars 80% of the time they will identify 12 green cars correctly (80% × 15 green cars). The witness misidentifies 20% then they will misidentify 17 cars as green when they are actually blue (20% x 85 blue cars). In this case. 29 cars would be identified as green (12 + 17) but only

12 actually are green. Therefore there is only a 41% chance that the car the witness identified is actually green (12/29 = 0.41). THE BASE RATE FALLACY CAN SHOW UP IN LOTS OF PLACES, INCLUDING IN OUR UNDERSTANDING OF COVID-19 DEATHS OR HOSPITALIZATIONS. For example, last

summer, Iceland saw a rise in COVID-19 cases, and most cases were among those fully vaccinated. BUT vaccines STILL WORK. MORE CASES AMONG FULLY VACCINATED PEOPLE IN PLACES WITH HIGH VACCINATION RATES IS NORMAL: But the rate (infections per person) of COVID-19 in Iceland is HIGHER

in unvaccinated people than those vaccinated, meaning it's way better to be vaccinated. Almost everyone eligible for vaccines in Iceland is fully vaccinated. So when COVID cases do happen in Iceland, most of them happen in vaccinated people because they are the vast majority of

the population. Iceland and other countries with high vaccination rates are likely to see more cases among the vaccinated, even though the rate of infection is significantly HIGHER in unvaccinated people. Because there just aren't that many unvaccinated people for COVID-19 to

infect. You can find all of this here: scienceupfirst.com/project/the-ba… and credit for the extremely informative graphic above goes to @/MarcRummy.

So, when a headline or a random Twitter user says "vaccinated people now make up a majority of deaths" it is innumerate fear-mongering and misinformation when it comes down to it that will make some misinterpret that as "vaccines are only 50% effective” or worse misconceptions.

TLDR. The more people you vaccinate, the higher their share of hospitalizations, but the *TOTAL* number in the hospital is a FRACTION of what it would otherwise be. The FEWER people fully vaccinated, a smaller share of hospitalizations will be fully vaccinated as well, BUT this

isn’t good. Why? Overall there would be A LOT more people in the hospital or dead because far more of the population is unprotected. In other words, don't focus on whether fully vaccinated individuals make up a % of hospitalizations, focus on the RATES those individuals whether

vaccinated or unvaccinated are ending up in the hospital. SPOILER ALERT: Rates are A LOT higher for unvaccinated. An increasing ratio of hospitalized vaccinated individuals however is an inevitable result of increasing vaccination rates. It is a marker of success, NOT failure.