Base Rate Fallacy

This is a very good graphic:

When a headline says "half of hospitalizations are vaccinated" it is innumerate fearmongering that will make people who are bad at math misinterpret that as "vaccines are only 50% effective", or worse lies.

An increasing ratio of hospitalized vaccinated is an inevitable result of increasing vaccination rates. It is a marker of success, not failure.

E.g.: "About two-thirds of people who die on UK roads are wearing a seatbelt, but this is a consequence of usage rates of nearly 99%."

Explaining probability, statistics and combinatorics to the public is really, really hard. This stuff is extremely nonintuitive even without dealing with the grifters. Here's a really good, easy to understand video on Bayes theorem.

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13 Responses:

  1. jwilkes says:

    I get it. But now I'm stuck imagining the zombie apocalypse that would result from 10% of the vaccinated population ending up in the hospital with covid.

    It's like explaining John Cage's 4'33 as what happens when you listen to an audio recording of a couple being eaten alive by a grizzly bear with the mute button on.

  2. vc says:

    There's a similar perception problem when it comes to crime stats.

    People will use lower per-capita crime rates as arguments against those complaining of increased crime, perhaps unintuitively both can be true. The per-capita rate drops, but not enough to outrun population growth, so the absolute crime numbers on the ground are still higher than before.

  3. jwz says:

    I have no idea what you're trying to say with that analogy, so I question "useful".

    • djm says:

      bucket A == vaccinated. Larger numerically, but smaller percentage-wise
      bucket B == unvaccinated, smaller numerically, but larger percentage-wse

  4. Dude says:

    Yeah, you're gonna have to explain that, because it sounds A LOT like that Skittles analogy used by right-wingers.

  5. Michael Sternberg says:

    People judge risk incorrectly because they base their intuition on what they hear and see, and that is pretty much only the stuff inside the black circle of this post’s graphic, give or take a bit of blur, and loud histrionics from the minority.

    The news media at large does not care to report about events that are frequent, because those are not “interesting”, or novel, if you like, and therefore would not sell or bring in clicks. (Some effect of information entropy?)

    See also: chance of death from terrorism compared to those from traffic accidents and other “banal” causes, and the amount of money spent to mitigate those causes.

    • MattyJ says:

      I get all my news and science from this blog and Broke Ass Stuart, so I think I'm safe.

      • Eric TF Bat says:

        Do you remember the good old days when "I don't watch/read/listen to the news" was a sign of naivete and ignorance rather than an excellent method of self care and sanity maintenance? Gods I miss those days.

        (If it's not obvious, I support your methods 100%. Broke Ass Stuart, you say? Will google...)

  6. mike crowley says:

    Still waiting for the useful analogy...

    • Eric TF Bat says:

      I figured it was simple enough not to need an analogy, but you're right -- there are people who just won't get it.

      Try this. A certain town has a problem with its traffic: there have been ten accidents this week. An investigator discovers that four of the accidents were caused by people who drive Edsels, and six by people who drive every other kind of car. Is it fair to say that Edsels are safer than other cars? Remember, Edsels are pretty uncommon. In the whole town there are only seven Edsels but thousands of the other sort. What does it say about how safe Edsels are if more than half were involved in accidents? Nobody ever said that driving a BMW or a Toyota would mean you never have an accident, but it sure looks like your chances are better than if you pick an Edsel, right?

  7. MarcRummy says:

    I got a lot of flack from some people for not using "Real" numbers (obviously 50% of the unvaccinated population isn't in the hospital), despite my explaining that I used the simplest numbers I could think of to illustrate the concept the most clearly. Even though I made this as simple as I could, I can't tell you how many people simply responded with "So you CAN still get sick if you're vaccinated though, so what's the point?" Which inspired me to make this meme, lol. God help us.

    • Unvaccinated people account for a high percentage deaths now, so trying to correct this fallacy shouldn't even be necessary.

      Unfortunately, no amount of truth or logic will convince them otherwise. Not even their own deaths in many cases.

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