The ol' fake-to-third-throw-to-first move is dead. Long live the fake-to-third-throw-to-first move. It's a balk now, and while a couple of pitchers have forgotten, for the most part, the move is extinct.
But has it made a difference? Baseball-Reference.com looked at the data and thinks it just might have:
Stolen-base success rate
No outs, runners on first and third
One out, runners on first and third
Two outs, runners on first and third
Slight correlation, except for one out. Which makes me wonder about statistical noise and samples, which makes me wonder about the whole thing. But for the most part, players are getting to second base easier without the fake-to-third move. It doesn't seem like a big deal, but maybe it is.