You could use Batting Runs (how many runs above league average his production is worth - similar to RAA, which is a component of WAR). Batting Runs + Basestealing runs probably gives you a solid total offensive picture of his run value.
There is RC, which isn't too bad either.
SLOB corrleates to run value decently well, too. It's OBP * SLG, which is a cousin to the more well known OPS (OBP + SLG). Sadly, I can't find the comparison chart I once saw of all the correlations to runs scored, but SLOB and OPS were close to each other.
BABIP is easy enough to calculate, so if you were curious about some guys it wouldn't be hard to figure. It is interesting though that it shows for pitchers but not hitters but is less a "pure" skill for pitchers than hitters (pitchers can influence their BABIP allowed, but there's a lot that they can't do anything about either - at least irl...The Show is different due to H/9 and it's influence on the game engine).
The only problem with BABIP is it's hard to know what a guy "should" have based on his ratings. A guy might check in with a .260 BABIP, which is much below average (assuming the league in MLBTS is around .300 like the real MLB), but without knowing if, say, his 60 contact and 40 power should be doing that or not, it's harder to tell if that .260 is because of "bad luck" or if he is just doing what he should be as a below average hitter.
Also, without having a batted ball profile (different batted ball types have different expected BABIP), it's a piece of missing information. This brings up a problem with The Show...hitters don't have a batted ball tendency like real hitters and the engine is too random with batted ball types for both hitters and pitchers, even when using influencing on Directional. I still have a hard time getting Chris Davis to hit 50% flyballs or Yelich 60% ground balls, for example.
So I wouldn't worry a ton about BABIP other than either to find very high or very low values or as just a "I wonder what he has" sort of thing.