I'm thinking out loud here, so I welcome your feedback on this one.  I doubt I'm the first to think of this, but a Google search along these lines has turned up nothing.

Let's start with the seventh inning of last night's game.  Jamie Moyer left the game with the bases loaded, no outs.  Geoff Geary came in and let Moyer's three runners score, along with another runner of his own.  He left with the bases loaded and one out.  Mike Zagurski relieved Geary, allowing two of Geary's runners to score.  He ended the inning leaving both of his own runners on base.

Now, according to traditional ERA calculation, Moyer gets credited with 3 runs in 0 innings because the three guys he put on base scored, even if after he left the game; Geary gets credited with 3 runs in 1/3 of an inning, because he got one out but one runner of his scored when he was in the game and two runners scored after he left; and Zagurski gets credited with 0 runs in 2/3 of an inning, even though he let up two runs, because both runners who scored on his watch were Geary's.

But why calculate ERA this way?  Why not split up the allocation of runs based on how many bases each pitcher is responsible for?

So, for last night's seventh inning, Moyer left with bases loaded and each of those three guys scored.  Instead of getting held responsible for 3 runs, why not 1.5 instead - 1/4 for the guy on first, 1/2 for the guy on second, and 3/4 for the guy on third?  That way, he's responsible for where he left the guys who ultimately scored.  Geary then gets credited with the other 1.5 runs (of the 3 overall we're talking about) - 3/4 for the three bases he let the runner on first move, 1/2 for the guy on second, and 1/4 for the guy on third.

Likewise, for the next three runs, Geary gets a full 1 run for Brandon Phillips, whom he let on base and allowed to score.  Then, the next two runs, he gets only 1.25 - because the guy on second (1/2) and the guy on third (3/4) when he left scored under Zagurski's watch.  Zagurski then gets 1/2 for the guy on second and 1/4 for the guy on third for a total of 3/4 of a run.

To me, this seems much more intuitive than the standard ERA calculation of giving full run responsibility for a guy you put on base but that another pitcher allows to score.  It accomplishes two things: it more accurately limits the responsibility of the pitcher who left with men on base and it more accurately shows how the pitcher coming in afterwards does with inherited runners.  Both of these are natural faults of the traditional ERA metric.

There are certainly more advanced stats out there for evaluating relievers.  Baseball Prospectus has WXRL and ARP - win expectation and adjusted runs prevented.  But both are complicated and impossible to calculate quickly.  WXRL relies on a general win expectancy matrix; ARP relies on a run expectancy matrix.  My ERA proposal is easy to calculate with simple play-by-play information.

One detraction of my possibly-new formulation is that it doesn't hurt a pitcher who leaves the game with runners on base who don't eventually score or help a pitcher who is good at stranding runners, as it only counts runs that score.  This is certainly a detraction, and Baseball Prospectus's more sophisticated stats do account for this.

But, the normal ERA has this same fault.  Without resorting to the more complex and impossible-to-calculate-easily BP stats, wouldn't dividing up the runs give us a more complete picture of ERA?