Someone tested it, and with FAW activated, the misses were practically nonexistant.. Regular beamshots still have perhaps 5-10% miss, FAW have less than 1%
It's not less than 1%.
I've been using FAW more commonly since the update, as it was actually made useful. Even so, I still miss more times with it active than I do with it inactive.
Yesterday while doing a community authored mission, I noticed that I was missing quite a bit, even against small fighters. However, this was also the same deal when I did my B'trans a few days ago going up against Romulans.