wERA: Rethinking Inherited Runners in the ERA Calculation

There are many things to harp on about traditional ERA, but one thing that has always bothered me is the inherited-runner portion of the base ERA calculation. Why do we treat it in such a binary fashion? Shouldn’t the pitcher who allowed the run shoulder some of the accountability?

As a Nationals fan, the seminal example of the fallacy of this calculation was Game 2 of the 2014 Division Series against the Giants. Jordan Zimmermann had completely dominated all day, and after a borderline ball-four call, Matt Williams replaced him with Drew Storen, who entered the game with a runner on first and two outs in the top of the 9th and the Nats clinging to a one-run lead. Storen proceeded to give up a single to Buster Posey and a double to Pablo Sandoval to tie the game, but he escaped the inning when Posey was thrown out at the plate. So taking a look at the box score, Zimmermann, who allowed an innocent two-out walk, takes the ERA hit and is accountable for the run, while Storen, who was responsible for a lion’s share of the damage, gets completely off the hook. That doesn’t seem fair to me!

I’ve seen other statistics target other flawed elements of ERA (park factors, defense), but RE24 is the closest thing I’ve found to a more context-based approach to relief pitcher evaluation. RE24 calculates the change in run expectancy over the course of a single at-bat, so it’s applicable beyond relief pitchers and pitchers in general, and is an excellent way to determine how impactful a player is on the overall outcome of the game. But at the same time, it does not tackle the notion of assignment, but simply the change in probability based on a given situation.

wERA is an attempt to retain the positive components of ERA (assignment, interpretability), but do so in a fashion that better represents a pitcher’s true role in allowing the run.

The calculation works in the exact same way as traditional ERA, but assigns inherited runs based on the probability that run will score based on the position of the runner and the number of outs at the start of the at-bat when a relief pitcher enters the game. These probabilities were calculated using every outcome from the 2016 season where inherited runners were involved.

Concretely, here is a chart showing the probability, and thus the run responsibility, in each possible situation. So in the top example – if there’s a runner on 3rd and no one out when the RP enters the game, the replaced pitcher is assigned 0.72 of the run, and the pitcher who inherits the situation is assigned 0.28 of the run. On the flip side, if the relief pitcher enters the game with two outs and a runner on first, they will be assigned 0.89 of the run, since it is primarily the relief pitcher’s fault the runner scored.

Screen Shot 2016-12-04 at 9.35.13 AM.pngLet’s take a look at the 2016 season, and see which starting and relief pitchers would be least and most affected by this version of the ERA calculation (note: only showing starters with at least 100 IP, and relievers with over 30 IP).

Screen Shot 2016-12-07 at 9.39.40 PM.png

The Diamondbacks starting pitchers had a rough year this year, but they were not helped out by their bullpen. Patrick Corbin would shave off almost 10 runs and over half a run in season-long ERA using the wERA calculation over the traditional ERA calculation.

On the relief-pitcher side the ERA figures shift much more severely.

Screen Shot 2016-12-07 at 9.40.37 PM.png

Cam Bedrosian had by normal standards an amazing year with an ERA of just 1.12. Factoring inherited runs scored, his ERA jumps up over two runs to a still solid 3.18, but clearly he was the “beneficiary” of the traditional ERA calculation. So to be concrete about the wERA calculation – it is saying that Bedrosian was responsible for an additional 9.22 runs this season stemming directly from his “contribution” of the runners who he inherited that ultimately scored.

The below graph shows relief pitcher wERA vs. traditional ERA in scatter-plot form. The blue line shows the slope of the relationship of the Regular ERA vs wERA, and the black line shows a perfectly linear relationship. It’s clear that the result of this new ERA is an overall increase to RP ERA, albeit to varying degrees based on individual pitcher performance.

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While I believe this represents an improvement over traditional ERA, there are two flaws in this approach:

  • In complete opposite fashion compared to traditional ERA, wERA disproportionately “harms” relief pitcher ERA, because they enter games in situations that starters do not which are more likely to cause a run to be allocated against them.
  • This does not factor in pitchers who allow runners to advance, but don’t allow that runner to reach base or score. Essentially a pitcher could leave a situation worse off than he started, but not be negatively impacted.

The possible solution to both of these would be to employ a similar calculation to RE24 and calculate both RP and SP expected vs. actual runs based on these calculations. This would lose the nature of run assignment to a degree, but would be a more unbiased way to evaluate how much better or worse a pitcher is compared to expectation. I will attempt to refactor this code to perform those calculations over the holidays this year.

All analysis was performed using the incredible pitchRx package within R, and the code can be found at the Github page below.


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The Kudzu Kid

This is great! Thanks for making the code public as well.

John Autin
John Autin

Very interesting and worthwhile effort. Thanks for sharing it.

I do think you would get even more meaningful results by focusing on expected vs. actual runs, as you alluded to at the end.

As you said, shifting ERA to wERA harms relievers disproportionately to starters. But more precisely, it harms RPs who inherit a significant number of runners disproportionately to all other pitchers, including most closers.

For example, last year’s 20-Save men ranged from 4 to 25 inherited runners, averaging 13 IR; whereas 75 RPs had more than 25 IR, and 29 had at least 40 IR.

At the same time, raw numbers on inherited runners and strand rates can’t account for the LOOGY effect, where they may “strand” runners by merely passing them on to the next RP in the same inning.

So I think using expected vs. actual runs is the way to go. I look forward to your next report!