Indeed they do. DonnyFL has a video somewhere with downrange noise data for a springer with and without a moderator. Downrange it is a substantial dB difference, similar to a PCP. At the shooters ear, it's effectively zero benefit to put a moderator on a springer.
I havent been able to measure an improvement at my ear but that is where the measuring device comes in. It would probably take a spectrum analyzer to give a perfect picture of what is happening at the ear. As others have noted a phone isn't really the best tool for doing detailed sound work. I guess it is kind of like using a butcher knife to skin a racoon. You can do it but it isn't the best tool for the job. One MIGHT be able to measure a difference at the ear if one was only looking at higher frequencies.
Donny's guy (Izzy, I think is his name) in the video was using a hand held dedicated sound meter. Shooting my R9 in the basement with and without a moderator seems to me to be about the same general volume but a different timbre.
