Who’s Responsible?

On June 8, 2007, the Pirates took a 4-2 lead into the bottom of the seventh inning against the Yankees. Here’s how the Yankee seventh played out (courtesy of Retrosheet):

YANKEES 7TH: Cairo doubled to left; Damon grounded out (first unassisted) [Cairo to third]; Jeter singled to left [Cairo scored]; GRABOW REPLACED GORZELANNY (PITCHING); Abreu singled to left [Jeter to third]; TORRES REPLACED GRABOW (PITCHING); Rodriguez was hit by a pitch [Abreu to second]; Posada singled to right [Jeter scored, Abreu to third, Rodriguez to second]; MARTE REPLACED TORRES (PITCHING); Matsui was called out on strikes; Cano flied to center; 2 R, 4 H, 0 E, 3 LOB.  Pirates 4, Yankees 4.

The Pirates’ pitching didn’t do itself proud, to be sure. The tying run was credited against Gorzelanny, and Torres got the blown save. Grabow’s contribution to the outcome doesn’t show up directly in any statistical category (except his hits allowed). Yet I would suggest that Abreu’s single off Grabow was the telling blow in the inning - the one event that moved the Pirates from a situation in which they were still fairly likely to hold the lead into a situation in which they were very likely to lose the lead.

What I’m putting out here is nothing new. It’s implicit in most of the prior studies on relief pitcher performance, going back to Doug Drinen’s 1998 BBBA article and most of what Tango has written on relief pitching - the idea that a relief pitcher who is not credited with a blown save can still bear a major share of the responsibility for the loss of a lead. The idea that I have here is this: the primary responsibility for a lost lead should go to the pitcher who was responsible for the event that moves the probability of losing the lead above 50%.

Suppose we apply this to the seventh inning PBP listed above. The Pirates were facing an offense that scored 6.4 runs per game at Yankee Stadium in 2007. Using Dave Studenmund’s WIn Probability spreadsheet, we can determine the probability that an offense will score at least “n” runs in any base-out situation - for example, a team that scores 6.4 runs per game will normally score two or more runs in an inning 17.8% of the time, so that was the probability that the Pirates would lose a two-run lead at the start of the seventh inning. Use those probabilities yields the following outcomes:

Pitcher		Lead	Outs	1B	2B	3B	Play			Prob Before	Prob After
Gorzelanny	2	0	0	0	0	2B			17.8%		30.2%
Gorzelanny	2	0	0	1	0	GO, 2-3			30.2%		18.8%
Gorzelanny	2	1	0	0	1	1B, 3-H			18.8%		32.8%
Grabow		1	1	1	0	0	1B, 1-3			32.8%		67.6%
Torres		1	1	1	0	1	HBP, 1-2		67.6%		69.9%
Torres		1	1	1	1	1	1B, 3-H, 2-3, 1-2	69.9%		100.0%

The single that Grabow allowed to Abreu moved the probability of losing the lead above 50%, and thus Grabow would, under the definition I am proposing, be the pitcher who would be “credited” with a lost lead.

Basically, there’s no issue 98% of the time here - the primary responsibility for losing a lead belongs either to the pitcher who put the tying run on base or the pitcher who allowed it to score. In the 1954-2008 Retrosheet data I’ve identified fewer than 600 games like the one above where the pitcher who would be credited with a lost lead did something other than put the tying run on or allow it to score. What I’m trying to do with this is two things - more closely pinpoint specific pitchers responsible when teams don’t hold leads, and put a value on held leads and lost leads so that it’s easier to compare relievers of the past to relievers of the present. A relief pitcher of the ‘60s who had 23 saves and eight blown saves might very well have been as effective, given the circumstances under which he pitched, as one who saves 47 of 50 today.