COVID vaccine lives saved post hoc fallacy

The argument in the news today is that the COVID vaccines saved 20 million lives in their first year of availability.  Of course that is completely unprovable, but it makes a great sound-bite for all the COVID-Karens out there. First the story, completely lacking in any scientific detail:

Nearly 20 million lives were saved by COVID-19 vaccines during their first year of availability, but even more deaths could have been prevented if international targets for the shots had been reached, researchers reported Thursday.

...The researchers used data from 185 countries to estimate that vaccines prevented 4.2 million COVID-19 deaths in India, 1.9 million in the United States, 1 million in Brazil, 631,000 in France and 507,000 in the United Kingdom.

An additional 600,000 deaths would have been prevented if the World Health Organization target of 40% vaccination coverage by the end of 2021 had been met, according to the study published Thursday in the journal Lancet Infectious Diseases.

Of course there's a problem with how deaths were reported and co-morbidity but let's not get bogged down with factual considerations...

The main finding — 19.8 million COVID-19 deaths were prevented — is based on estimates of how many more deaths than usual occurred during the time period. Using only reported COVID-19 deaths, the same model yielded 14.4 million deaths averted by vaccines. [emphasis mine]

Sorry, not scientific. (1) Correlation is not causality (2) Comorbidity was handled in a sub-par way - among other things, there was a funding related incentive to attribute as much as possible to COVID and (3) it entirely discounts potential demographic markers or any other potential impacts that happened during the same time.

And lastly, there's this:

Post hoc (a shortened form of post hoc, ergo propter hoc) is a logical fallacy in which one event is said to be the cause of a later event simply because it occurred earlier. "Although two events might be consecutive," says Madsen Pirie in "How to Win Every Argument," "we cannot simply assume that the one would not have occurred without the other."

They are counting the number of increased deaths, but how could they know how many there would have been without the vaccine?  They make no mention of how they arrived at the number of deaths there would have been without a vaccine being available. They only know how many more deaths there were, attributable to COVID (and not even factoring any of the caveats I mentioned above). So where did the total lives saved come from?  It's pure bunk.

Here's a mathematical representation.

Total Deaths in period - Normal deaths for a period = # COVID deaths (incremental to normal years). 

Then what?

Lives saved = # inoculated - #inoculated but still died.  Nothing in the formula above addresses these numbers and it further assumes that everyone vaccinated who did not die was saved by the vaccination. Not that they may have never been exposed.  Not that they may have natural immunity.  Not that they did not contract COVID and subsequently recovered.

Garbage science, at least in all the media reports I have seen so far.