eERA (beta) - adjusting for Inherited Runs

On June 3, 2011 the Nationals were battling the Diamondbacks with Yunesky Maya on the mound. In the bottom of the 5th inning, the score was 1-0 in favor of Arizona. Four batters and one out later, the bases were loaded, and Stephen Drew was at bat. Jim Riggleman came out and brought in lefty specialist Doug Slaten, who had at the time a sparkly ERA of 2.19 for the season. Drew hammered the first strike he saw for a triple which scored all three of the runners Maya had put on base. Coffey then entered the game and stranded Drew at 3rd base, keeping Slaten’s shiny ERA intact once more.

The way in which each Earned Run is tied to a runner who is put on base is one weakness of the ERA statistic when measuring performance. To this point, Slaten had allowed 50% of inherited runners to score, yet his ERA didn’t show it. It was after this game that Slaten was sent to the disabled list with was said to be an elbow injury.

Unfortunately, the only decent statistic for tracking how a pitcher backs up his teammates is the Inherited Score Percentage, which just shows what percentage of inherited runners a pitcher allows to score. Though useful in its own way, it does not allow comparison between pitchers with the ease of a statistic like ERA, and it has no regard for starting pitchers, who of course never have inherited runners on their hands.

I looked at this problem, and wondered if it would not be possible to split each earned run that scored as an inherited run up between the two different pitchers involved. The formula would have to be simple. At first, I decided to simply score each base given up by a pitcher to a runner who eventually scored as .25 runs earned. Soon, though, it became clear that it would be far more equitable, and not much more difficult, to incorporate some situational statistics.

0 0.380 0.600 0.826
1 0.253 0.410 0.652
2 0.123 0.227 0.289

That chart contains Tom Tango's calculations, based on Retrosheet data, of the chance a runner has to score from a given base by out. Using these percentages, I was able to divide up earned runs between pitchers. If, for example, a starting pitcher is pulled with one out and a runner on 2nd who later scores, that pitcher is credited with .41 runs, and the relief pitcher who let that runner score is credited with .59 runs. Using a season of play by play data, I was able to track who really earned some of those earned runs everybody has been earning.

In the example above, Slaten took over from Maya with the bases loaded and allowed all three runners to score. Normally, that would mean three earned runs for Maya, but under this system, those three runs would be split up. Maya left with the bases loaded and one out, which means he gets (.253+.410+.652) runs - 1.315 ER . Slaten allowed them to score, so he picks up the balance of the three earned runs - 1.685 ER. It is certainly no perfect system, but it gives us new information than simple ERA does not. I call it eERA (earned Earned Run Average).

Here is a chart showing the 2011 Nationals pitching staff, ordered by innings pitched.

Name IP ER ERA Run Diff eERA % diff IS IS%
John Lannan 184 76 3.71 -3.95 3.52 -5.3%
Livan Hernandez 175 87 4.47 -3.96 4.21 -5.8%
Jordan Zimmermann 161 57 3.18 -2.03 2.91 -8.7%
Jason Marquis 120 53 3.97 -3.96 3.74 -5.7%
Tom Gorzelanny 105 47 4.03 -0.65 4.00 -0.7% 0
Tyler Clippard 88.1 18 1.83 3.10 2.16 17.9% 10 22%
Drew Storen 75.1 23 2.75 -1.84 2.49 -9.4% 2 20%
Ross Detwiler 66 22 3.00 0.17 3.02 0.8% 1 25%
Henry Rodriguez 65.2 26 3.56 0.82 3.66 2.8% 7 35%
Chien-Ming Wang 62.1 28 4.04 0.00 4.04 0.0%
Todd Coffey 59.2 24 3.62 1.06 3.28 -9.8% 7 19%
Sean Burnett 56.2 24 3.81 8.98 5.10 33.8% 19 44%
Collin Balester 35.2 18 4.54 0.81 4.78 5.2% 4 44%
Yunesky Maya 32.2 19 5.23 -1.54 4.56 -12.9% 0
Ryan Mattheus 32 10 2.81 3.46 3.66 30.1% 8 28%
Tom Milone 26 11 3.81 -0.78 3.38 -11.1%
Stephen Strasburg 24 4 1.50 0.00 1.50 0.0%
Doug Slaten 16.1 8 4.41 6.71 7.71 75.0% 15 47%
Cole Kimball 14 3 1.93 2.07 2.91 50.9% 4 80%
Brian Broderick 12.1 9 6.57 -0.33 6.55 -0.3% 5 100%
Brad Peacock 12 1 0.75 1.34 1.75 133.7% 2 100%
Craig Stammen 10.1 1 0.87 0.35 1.17 34.8% 1 11%
Chad Gaudin 8.1 6 6.48 -0.29 6.30 -2.8% 1 14%
Atahualpa Severino 4.2 2 3.86 0.35 4.53 17.4% 2 50%

Run Diff: Run differential between Earned Runs and earned Earned Runs.
IS: Number of inherited runners allowed to score.
IS%: Percentage of inherited runners allowed to score.

Starting pitchers enjoy, as would be expected, a lower eERA than ERA. Taking off even this prorated portion of inherited earned runs scored lowers their ERA by over five percent in some cases, which is far from insignificant.

There is a lot of variation among relief pitcher performance here. As expected, Doug Slaten’s eERA is much higher than his ERA – a stunning seventy-five percent higher. No other Nationals pitcher has an ERA, eERA, FIP or xFIP as high as Slaten’s 8.11 eERA. Also struggling this year was Sean Burnett, whose eERA was more than a full run higher than his ERA.

Much more surprising are the numbers belonging to All-Star Tyler Clippard, who put together a stellar season, yet has an eERA that is eighteen percent higher than his ERA. While he did not allow an abnormally high number of inherited runners to score, a lot of the runs he gave up came via the home run, which allows runners to score from 1st base quit easily regardless of the number of outs.

One relief pitcher who recorded a lower eERA than ERA was Drew Storen, as he locked down the closer role and had a terrific year. The only two inherited runners to score on his watch were scored as unearned runs.

eERA (beta) is a young and undisproven statistic. It is only vaguely scientific, yet I believe it helps cast light on the shameful racket that is ERA laundering. Every year, hundreds of major league starters and relievers are saddled with earned runs they never truly earned, and one of their teammates quietly reaps the benefits of the system. eERA is one more small step toward exposing this corruption and bringing justice to the way performance in pitching is calculated.

Don’t be satisfied with ERA when you can have earned Earned Run Average.

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