Yes it does. Just replace the vaccine with snake oil and follow it to its logical conclusions.
I'll use some BS numbers to make the point. Let's assume: study population of 100, 20% of the population had a prior infection, half are given the snake oil.
Starting conditions:
1. Never infected, Never Snaked: 40
2. Prior infected, Never Snaked:10
3. Never infected, Snaked: 40
4. Prior infected, Snaked: 10
Now let's assume wave 2 happens. 20% of the never infected gets infected, and 0% of the previously infected get reinfected.
Both groups 1+2 combined and 3+4 combined have an average infection rate of 16% for wave 2. The groups are equal because snake oil is bullshit.
What the Ars author was suggesting is to compare group 1 with group 3+4 combined. Now you have a 20% infection rate vs a 16% infection rate. The snake oil appears to have an (20-16)/20 = 25% effectiveness just by including previously acquired immunity.
I'll use some BS numbers to make the point. Let's assume: study population of 100, 20% of the population had a prior infection, half are given the snake oil.
Starting conditions:
1. Never infected, Never Snaked: 40
2. Prior infected, Never Snaked:10
3. Never infected, Snaked: 40
4. Prior infected, Snaked: 10
Now let's assume wave 2 happens. 20% of the never infected gets infected, and 0% of the previously infected get reinfected.
Both groups 1+2 combined and 3+4 combined have an average infection rate of 16% for wave 2. The groups are equal because snake oil is bullshit.
What the Ars author was suggesting is to compare group 1 with group 3+4 combined. Now you have a 20% infection rate vs a 16% infection rate. The snake oil appears to have an (20-16)/20 = 25% effectiveness just by including previously acquired immunity.