Expected Bases: a new baseball metric

The Runs-Batted-In (RBI) metric is seriously flawed, but on base percentage is not quite perfect either.  If one manages to get on base at the cost of a force-out elsewhere, the value of getting on base is diminished.  For example, let's consider an all-to-common baseball scenario: an otherwise perfect grounder to third results in a force out because of the runners on 1st and 2nd base.  The net effect of such a base hit was no improvement in runner position.  We are in the same situation we started, so this base hit should count for naught.  Even worse, if this grounder led to a double play, we are worse off than we started, even though the batter himself may safely make it to first base.

As a statistician in clinical research, such a situation immediately started me thinking about comparing the change in position of base runners before and after each hit (pre/post measures are my bread and butter).  The trouble with this method of accounting is that if we credit a gained base to the hitter, we must necessarily take it away from someone else if the runner fails to score.  This would naturally fall to the last out of the inning if we stick with our pure pre/post comparisons.  However, this doesn't seem quite fair, so perhaps we ought to split bases lost at the end of the inning equally between all hitters that were responsible for outs.

Breaking down some examples may be instructive.  Let's consider a bases-loaded scenario: a grand-slam advancing first, second and third base-runners home (3+2+1 = 6 bases) and yourself as well (4 bases) would net 10 bases for your team.  Alternatively, ending the inning would lose first, second, and third base (-1-2-3 = -6 bases) by contributing the last out(s).  A triple play to end the inning should bear all the blame for these 6 bases (6 bases lost or -6 bases), but grounding into a double should bear 2/3 of the blame (-4 bases), and a fly, ground, or strike out to end the inning should bear a third of the blame (-2 bases).  Still, not all bases are not created equal, so it's possible this metric can be additionally weighted to reflect the different expected runs from 1st, 2nd, and 3rd respectively.

Such a metric would consider a strike-out, ground-out, or pop-fly that fail to advance base runners as equivalent.  This may seem a bit naive as hitting outcomes seem "better" than striking out.  However, in the long-run, strike-outs will seldom advance base runners (except perhaps with errant pitch or dropped third strike requiring a force out at first), pop-outs will occasionally result in a tag-up advance, and ground-outs may advance base-runners, and so this metric may be able to distinguish between the hitters that advance runners more often than not.  The fact that this single statistic can distinguish between a sacrifice fly that advances a second base runner to 3rd and also a capture a ground-out that advances two runners should be encouraging enough to give it an extra look.