There's very strong evidence, particularly against the Delta variant[1]. That paper cites a 33.5% effectiveness after one dose, compared to 87.9% after two doses of the Pfizer/BioNTech vaccine.

[1]: https://www.medrxiv.org/content/10.1101/2021.05.22.21257658v...

That includes the lag time. A single dose is supposed to be about 80% effective once immunity develops. They don't know how long that will last and thus have the second shot to increase effectiveness and hopefully longevity.

It's likely that the 80% figure you mention was based on protection against "ancestral type" virus, as would have been measured in the main trials. The gap between first dose and second dose protection is larger for Delta variant than for other variants, as documented in the paper I cited.

But the issue, is that if you had your first dose 2 days before being infected, you count as being infected after 1 dose.

We need to compare "1 dose, x days after first dose" and "two doses, x days after first dose" to compare the same thing

That is not consistent with the "Vaccination status" definition in the paper I cited. The tl;dr on that is that "first dose" starts 21 days after vaccination, and "second dose" 14 days after.

Also, to get a better sense of the timeline for vaccination effectiveness, take a look at a chart like this one: https://www.technologyreview.com/2020/12/10/1013914/pfizer-b...

If you wait 21 days after the first dose, or 14 days after the second dose. Unless everyone had their second dose 7 days after the first one you still don't compare the same thing.

We need something like, 21 days after the first dose, and split the result between people who got one dose and those who got two. We also need to make sure that the repartition of ` age since first dose` is the same for the two doses group and the single dose group.

Is it worth getting a third dose?

Yes, this was covered in the trials for both vaccines.

pfizer trial showed first dose by itself was extremely effective. check out the chart here: https://www.businessinsider.com/how-well-pfizer-shot-works-a...

Much of the data comparing efficacy of 1 vs 2 doses doesn't wait until 10-days after the first dose, which defeats the point. That being said 2 doses is more effective, just not by as much as you'd might think.

edit: replaced the above link because it was pay-walled