I'm just not sure what BAbip tells you with respect to a hitter... all stats should be expected to regress to some mean.. we can just glance at Bradley's BA/SLG/OBP etc and know that he's going to regress. I don't think the fact that his BAbip tells us much.
Seems like it, as you mention, has more value for pitchers. First because they have less control (although obviously some pitchers do get hit hard so their line drive % is related to BAbip and is under their control), but also because they always have more or less the same fielders behind them, so BAbip can be a measure of how much they got screwed by a bad defense.
Anyway, I think for both hitters & pitchers BAbip is most useful for determining how lucky someone is in a relatively small sample. As you get later in the season, an out-of-whack BAbip for a hitter is not as likely to be a measure of how lucky they are. Yes Bradley will regress-- it is a near certainty he will not perform as well for the rest of this season or next-- but I don't think we need to rely on an idea that he's been lucky and his hits have fallen in to foresee this.
Seems like it, as you mention, has more value for pitchers. First because they have less control (although obviously some pitchers do get hit hard so their line drive % is related to BAbip and is under their control), but also because they always have more or less the same fielders behind them, so BAbip can be a measure of how much they got screwed by a bad defense.
Anyway, I think for both hitters & pitchers BAbip is most useful for determining how lucky someone is in a relatively small sample. As you get later in the season, an out-of-whack BAbip for a hitter is not as likely to be a measure of how lucky they are. Yes Bradley will regress-- it is a near certainty he will not perform as well for the rest of this season or next-- but I don't think we need to rely on an idea that he's been lucky and his hits have fallen in to foresee this.