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Chad Billingsley & Bequeathed Runs

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Chad Billingsley has struggled of late, putting up a 1-2 record and 7.52 ERA in July. Over on Dodger Thoughts, Jon Weisman noted just how well Billingsley has pitched in his first five innings, allowing just 2.78 runs per nine innings.  Jon also noted:

I'm not saying Billingsley can't pitch past the fifth inning. But if he gets in trouble past the fifth inning, the Dodgers have enough bullpen depth that they don't need to try to wring every last pitch from him. They don't need to punish him with their expectations of him.

It is an intriguing thought, to be sure.  In the comment section, Tripon made the following observation:

Part of the pain is finding a reliever who can limit the runs when Chad is eventually pulled with men on bases.

He's been unlucky there.

With Tuesday's sixth inning implosion by Billingsley fresh in my mind, I decided to check to see if that was indeed the case.  What can I say?  I'm an inquisitive person by nature.  If there was a website called Sunrise-Reference.com, I would double check it often just to make sure the sun actually rose in the east.

Instead, I used Baseball-Reference.com to find Chad Billingsley's game logs, then used the invaluable run expectancy matrix from Baseball Prospectus.  In case you need a refresher from my analysis of Guillermo Mota's inherited runs, the run expectancy matrix looks at each base-out situation.  For instance, if a team has runners on second and third with one out, it is expected (based on actual play-by-play data this season) to score about 1.42 runs the remainder of the inning, on average. 

In Billingsley's case, we are not looking at inherited runs, but rather bequeathed runs.  We're going to use this to look at the ten starts in which Billingsley left with men on base:

Date Bases Outs Exp Runs Scored Runs Saved
April 23
1-- 1 0.53546 0 0.53546
April 28 12- 1 0.92188 1 (0.07812)
May 19 1-- 1 0.53546 0 0.53546
June 9 1-- 2 0.21968 0 0.21968
June 14 1-- 0 0.88079 0 0.88079
June 30 1-- 2 0.21968 0 0.21968
July 5 -2- 0 1.13399 1 0.13399
July 10 123 0 2.28376 1 1.28376
July 17 -2- 2 0.32289 0 0.32289
July 28 12- 2 0.46053 1 (0.53947)
Totals 7.51412 4 3.51412

Billingsley's relievers have only allowed four of his runs to score.  Perhaps it is fresh in our mind since three of those runs have occurred in the last month, but the fact is that based on the situation Billingsley left them in, the relievers "should" have given up even more, about three and a half runs more.  In only two of these ten starts did Billingsley's relievers give up more runs than average.  If anything, Billingsley has been lucky, perhaps if only slightly.