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The protection afforded from the second booster dose is not as large, by sheer magnitude, as the primary series or the first booster dose. However, this is partially because these second booster doses are being deployed when viral transmission cases are approaching the lowest levels recorded (albeit with some local surges in some locales). There is some evidence that protection against infection (including mild infections which do not require hospitalization) may be of shorter duration (1-2 months), but this could be an effect of the Omicron subvariants which we know are much more transmissible. However, the protection against hospitalization and death appears to be longer-lasting.
The specific question you ask for “How much additional protection did I receive?” might be answered by data from Israel; the figure below is a summary slide from a recent CDC ACIP meeting (slide #32, )
In Israel, 4th doses (second booster doses) of Pfizer mRNA vaccine were administered beginning in January 2022 and the incidence of infections were followed. When comparing the effect on prevention of infection (including mild disease) and severe disease, there was a significant reduction in both infections and severe disease with the second booster compared to persons receiving only the first booster. This study did not compare the effect of the second booster against the unvaccinated or those only receiving the primary series, but you can imagine that those effects would be much larger.
Therefore, I want you to feel confident that you have improved your protection against Covid and have made the correct decision.