First off let me just get it out of the way that I don't know if this stat already exists or would be considered completely useless and redundant. However, I don't think it exists and I think it has some value...
I would call it something like Batting average independent on-base percentage. You would calculate a player's batting average using hits/PA instead of AB to get a "true" batting average, which you would then subtract from OBP. That number would show a players ability to reach base other than getting a base hit.
The potential value behind it would be quickly being able to compare two players with similar OBP and see which one is doing it more with their hitting. I realize you could simply subtract BA from OBP in your head and get a pretty good idea of it that way but this would be a little more accurate and of course you could rank larger numbers of players.
I got the idea from when I saw ISO and thought this would be somewhat similar? I'm assuming that if there were a useful stat someone would've thought of it before me, but maybe not.
Quick example:
2009 David Ortiz: 129 hits in 627 PA for a "true BA" of .206 subtracted from his OBP of .332 for a BAiOBP of .126
2009 Juan Rivera: 152 hits in 572 PA for a tBA of .266 subtracted from his OBP of .332 for a BAiOBP of .066
Now I don't know if it's useful to anyone to know that David Ortiz reached his .332 OBP more so from doing things other than hitting far more than Rivera did. Unless, one was expecting him to maintain his BAiOBP of .126 in 2010 while hitting something more respectable with a tBA of say .235-.240. This stat might allow or help to project someone OBP in the future if they increase/decrease their batting average.
If I just wasted 2-3 minutes of your life from reading this, I apologize.
