Thread by @alexandreafonso

Great opportunity to show slides from my methods class (1/n)

https://twitter.com/mehdirhasan/status/1408605085962211332

If you only look at the people infected and see that half of them were vaccinated, you might think the vaccine is not effective. You'd be wrong.

Let's take an example. You're interested in the best strategy to score goals: long balls or short passes?

If you only look at goals (aka infections) and see that a majority were the result of long passes, you may think long passes are the best way to score goals.

What you don't see if you only look at goals (or infections) is the very high number of long balls that did *not* result in goals.

If you look at all goal attempts (or all people exposed to the virus) instead of only those that resulted in goals, you'd see that a much smaller proportion of long balls (aka vaccinated people) resulted in goals (infections).

So in fact, short passes have a much higher probability to result in goals, aka non-vaccinated people have a higher probability to be infected. Something you cannot know if you *only* look at infection cases/goals. You're ignoring all those that were exposed but not infected.

So to know whether the vaccine is effective or not against the delta variant, you'd need to compare the infection rate between vaccinated and not-vaccinated people, not look only at positive cases of infection as the headline does.

Let's imagine 99 people out of 100 are vaccinated. There are 2 infections: 1 vaccinated and 1 not vaccinated. It is true that 50% of the infected are vaccinated, but what counts is that 100% of the non-vaccinated were infected while only 1.01% of the vaccinated were.

Of course, the football example is inspired by the story of Charles Reep, the man who "ruined decades of English soccer" fivethirtyeight.com/features/how-o…

See here his article from 1968 showing that a majority of goals were the result of short sequences of passes. jstor.org/stable/2343726