Its not incorrect, its just incomplete.
Here is where is it correct…
Lets go with a typical firearm is in the 150-160db range, and 140db is generally considered the threshold for “safe” hearing levels for short duration noise (those numbers are from memory so may be off a bit).
If you have something that is rated 30db NRR, your actual noise reduction is:
(NRR - 7) / 2 = reduction
(30 - 7) / 2 = 11.5
So if the firearm is 150db, then 30db NRR will reduce that noise by 11.5db, which means your ear gets 138.5 which falls under the “safe” threshold of 140db.
Note that if you double up on ear pro, lets say with foamies at 30db NRR and ear muffs at 22db NRR. You do add 5 to the higher of the two, and then do the same math. So that would be:
(35 - 7) / 2 = 14
** there are variables here like the firearm itself (some are louder that others), how close you are to the noise, is it indoors/outdoors, etc, etc.
Here is where is it incomplete…
The NRR rating on the box is an average of the NRR across different frequencies. So because the box says it reduces 22db NRR, doesn’t mean that it doesn’t block 30db NRR in the frequencies where a firearm makes its noise.
Using the Sordin’s as an example above (only because its one of the few I can find data on), it has great NRR in the frequencies above 1khz which is where firearms make the majority of their noise, but it doesn’t block lower frequencies well at all. So it has a low NRR listed on the box (the average), but it performs exceptionally well in frequencies that gun owners care about.
Where regular consumers like you and I are at a disadvantage is that NRR info is absurdly difficult to find. I don’t know why. It makes it difficult to make an informed decision. The best we can do is use other people’s reviews and perceptions as to how well they perform.
This type of data isn’t just important to gun owners. If you work in a factory, you want to make sure your hearing protection works in the frequencies of the machinery you are surrounded by.
Think of it like EPA gas mileage numbers. They list city, highway, and combined. But what if car dealers only showed you the combined MPG. If you drove exclusively in the city and bumper to bumper traffic that number would not be very useful to you at all, and quite misleading if that was the only number you were given.
Conclusion (sorta)
It’s not that we shouldn’t use the NRR on the box as a guideline. It is often the only metric we have for comparison across different models/brands of hearing protection. But we need to be aware that figure doesn’t tell the whole story. Getting people’s actual experience and perceptions of various brands of hearing protection is often the only way we know if they are good or not, but that isn’t great either as it’s very subjective.