How good is your covid math?

Let’s put it to a test, estimating vaccine effectiveness on some real life data …

In yesterday’s post, we channeled Dr, Marty Makary’s conclusion that “The CDC has failed in its primary function to deliver data to guide our pandemic response.”

Often, the CDC has relied on data from Israel.

Israel was one of the first countries to start vaccinating … and is doing the best job, by far, of systematically gathering, analyzing and reporting vital data that can be squeezed to draw clarifying conclusions.

For example, below is a chart that Israel’s Dept. of Health recently released.

The key summary statistic: Vaccinated people accounted for 64% of Israeli Covid deaths in August.


Is that good news or bad news?

Specifically, what do the numbers say about the efficacy of the vaccines? Good or bad?

Take a minute, think about those questions … and maybe, crunch a few numbers before reading further


At first glance, the numbers are disappointing for pro-vaccinators.

A reasonable inference: It looks like the vaccine is grossly underperforming the protection from death promised from the clinical trials.


But, not so fast, mes amies.

Let’s work through the numbers.


Death rate among unvaccinateds

Multiple sources indicate that the Israeli adult population is about 6 million … and about 80% have been vaccinated.

Math note: Don’t sweat the precision of either of those numbers. Ballpark-precision is good enough for this analysis.

If so, about 4.8 million Israeli adults have been vaccinated and 1.2 million haven’t … that’s aa 4 to 1 ratio.

Key Question: What was the August death rate among unvaccinated Israelis?

Answer: It’s 181.7 covid deaths per million unvaccinated adults  (218 / 1.2 million = 181.7 deaths per million)

Compared to what?


Death rate among vaccinateds

What about the August death rate among vaccinated Israelis?

Answer: It’s 81 covid deaths per million vaccinated adults  (389 / 4.8 million = 81 deaths per million)

Conclusion: The death rate among the unvaccinateds is more than double that of the vaccinateds.

That puts a new paint job on the numbers, right?

It’s safe to conclude that vaccinations save lives.

But, by how much?


So, how effective are the vaccines?

Massaging the numbers, they imply that the actual vaccine effectiveness (protection from death if vaccinated) is about 55%.

Here’s the math…

If the vaccines had zero effectiveness, one would have expected about 872 deaths among the vaccinated people (4.8 million times the unvaccinated rate of 181.7 deaths per million).

But, there were only 389 vaccinated deaths reported … that’s 55% lower than the 872 that would be expected if the vaccinated people were unvaccinated.

English translation: Based on Israel’s August data, the vaccines are about 55% effective in preventing covid deaths.

Is that good news or bad news?


But, clinical trials promised 95%

When the vaccines were emergency-approved,, there were vague warnings that the “durability” of their effectiveness would wear down over time.  But, there wasn’t data to indicate the severity of the drop or its time-phasing

The Israeli numbers help calibrate the curve.

Based on the above fatality data, has waned from a high of, say, 95% shortly after second shots … down to 55% … a drop of about 5% per month post-vaccination.

That’s in the range of several ad hoc targeted studies that have been reported.

Note: In its booster request, Pfizer claimed  that it’s vaccine’s effectiveness  vaccine declines from 96.2% percent at seven days after dose 2 to 90.1 percent two months later to 83.7 percent up to six months later. 



The point of this exercise was to illustrate how much “juice” can be squeezed from just a few meaningful numbers (e.g. the Israeli reporting of fatalities broken down by vaccination status)

Wouldn’t it be nice if the CDC collected and reported such data in enough detail for it to be useful.

But, as Dr. Makary observes, it doesn’t.

Fortunately, Israel does … or we’d be flying totally blind.

3 Responses to “How good is your covid math?”

  1. Dan F Says:

    For an interesting 3rd vaccine discussion (using some data from Israel), check out this link:

  2. How good is your covid math? — The Homa Files | Ups Downs Family History Says:

    […] How good is your covid math? […]

  3. The Homa Files – Featured Blogger of the Week April 1, 2022 | Ups Downs Family History Says:

    […] How good is your covid math? — The Homa Files Direct link: How good is your covid math? […]

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