Baseball Prospectus, among other sources, publishes Run Expectancy charts (subscription required). These nifty little tables outline with a three-by-eight grid the average number of runs that score after a given baserunners/outs situation. For 2004, the chart looked like this:

Runners, outs, Run Expectancy:

---, 0, 0.54
---, 1, 0.29
---, 2, 0.11
1--, 0, 0.93
1--, 0, 0.55
1--, 0, 0.25
-2-, 0, 1.16
-2-, 1, 0.71
-2-, 2, 0.34
--3, 0, 1.47
--3, 1, 0.96
--3, 2, 0.46
12-, 0, 1.45
12-, 1, 0.97
12-, 2, 0.36
1-3, 0, 1.85
1-3, 1, 1.22
1-3, 2, 0.52
-23, 0, 2.13
-23, 1, 1.47
-23, 2, 0.62
123, 0, 2.25
123, 1, 1.59
123, 2, 0.81

Under the "Runners" column, a dash represents an empty base and a number represents an occupied base. So "1-3" indicates baserunners occupying first base and third base, with second base open.

One neat trick that this chart allows you to do is figure out how many runs a particular play is worth. For example, a leadoff triple changes the run expectancy of an inning from 0.54 to 1.47, so a leadoff triple can be considered to be worth 0.93 runs, on average. A home run with runners on second and third with one out changes the run expectancy from 1.47 to (3 runs already scored) + (expectancy of bases empty and one out, 0.29) = 3.29, making the home run worth 1.82 runs. (You'd expect a three-run home run to be worth exactly three runs, but that ignores the probability of the two runners on base being driven in by subsequent batters). This concept is certainly not new, as I have seen it from time to time in various analyses of teams' performance in different situations.

I've used the chart in a similar fashion, but from the pitchers' standpoint. For each pitcher that the Mariners have used, I've figured out the Run Expectancy when he entered an inning, and the Run Expectancy (factoring runs actually scored as well) when he left the inning. So if a pitcher started an inning with the bases empty and none out and allowed one run before being replaced with two outs and a runner on first, the pitcher's Runs Over Expected Runs (ROER) would be:

Expected Runs entering the inning: 0.54
Actual runs scored: 1
Expected additional runs when the pitcher left the game: 0.11

ROER = 0.54 - 1 - 0.11 = -0.57

So this hypothetical pitcher (We'll call him Obby Bayala) cost the Mariners 0.57 runs over what could be expected.

I think that ROER is a good indication of a pitcher's overall value to a team, factoring in the difficulty of the situations that pitchers are thrown into and the difficulty of situations left to others. So a short reliever whose job is to put out the fires started by others gets credit for not allowing inherited runners to score (something ERA ignores completely, simply giving the runs to the pitcher that put the runners on base), and a starting pitcher that consistently leaves runners on base to the relievers is penalized regardless of whether the bullpen bails him out. Starting pitchers, who begin every inning with the bases empty and none out, are rewarded for pitching much more innings than the relievers.

For the 2005 Seattle Mariners, the pitching staff has shaped up like this:

Pitcher, ROER:

Ryan Franklin, +5.94
Aaron Sele, +5.25
Shigetoshi Hasegawa, +2.93
Jamie Moyer, +2.93
Julio Mateo, +2.26
Jeff Nelson, +1.44

Ron Villone, -0.94
Bobby Madritsch, -1.27
J.J. Putz, -1.46
Eddie Guardado, -1.85
Gil Meche, -3.36
Matt Thornton, -4.28

Not surprisingly, Ryan Franklin rates as the Mariners' most valuable pitcher so far and Matt Thornton ranks as the most costly.

The case which best illustrates why I like ROER over ERA is that of Eddie Guardado. Guardado sports a nice little 2.50 ERA, despite a not-so-good -1.85 ROER. Guardado allowed four runs in the ninth inning of last week's 7-6 loss against the Rangers. Three of those runs were recorded as unearned after Bret Boone missed an easy grounder. If Everyday Eddie had pitched out of the jam created by Boone's error, his resulting good ROER would match up nicely with his excellent ERA. ROER does a good job at identifying the cases that ERA misses: pitching out of trouble caused by bad fielding, preventing inherited runners from scoring, and not leaving baserunners to subsequent pitchers.

Throughout the season I'll be updating the Mariners pitchers' ROER, and posting them permanently on the sidebar.