From what I understand, they "fixed" the speed training. Previously it wasn't working properly so it doesn't actually "do" anything, making it rather moot.

As for how it actually works, I have no idea. I'm guessing that as long as your init does not "qualify", they have a huge damage boost or something like that. That said, the bar is really high, I'm almost 110k power and only have 5800 init on my move 1. Thou that's partly due to me being ftp, since init is one of the stat that you can relatively ptw easier.