Creating an ERA that truly takes defense into account

By COREY EIFERMAN

Baseball Prospectus’ 2006 collection of staff essays, Baseball Between the Numbers, includes a piece by Dayn Perry titled, “When Does a Pitcher Earn an Earned Run?” In it, Perry writes that, because of the subjective scoring of errors by a stadium’s official scorer, ERA doesn’t fully do what it’s meant to do, isolate a pitchers’ performance from his defense.

Perry’s essay sparked inspiration when I read it. I wanted to create a new stat to try to more fairly assign the debit for runs given up. What follows is something I put together as my own creation, with Sports Info Solutions assisting by providing data.

Earned Run Average is simply that, an average. The actual number of ‘runs’ multiplied doesn’t *need* to be a whole number, because the result itself won’t be.

Obviously, when a player hits a (non-inside-the-park) home run, yes, the fault is 100% on the pitcher. However, within a game, many runs that are scored are both the fault of the pitcher and the defense behind him.

In addition, when runners that are inherited by one reliever score, those runs are charged to the pitcher who bequeathed them. Since those runs are the faults of two separate pitchers, both pitchers should be debited.

At Sports Info Solutions, our system of Defensive Misplays is subjective, but still stretches far beyond the binary limitations of hits and errors. When a team puts up a crooked number capitalizing on an ‘error’ by the other team, the pitcher is freed of “earned runs,” but not when there’s a borderline hit or error that was ruled a hit. That pitcher gets charged a full earned run, even though it was partially his defense’s fault.

On the flipside, if a team commits an error with two outs, and then, say, six more batters come up, the official scorer may not call any of those runs earned. Even though after that crucial error, those subsequent baserunner advances weren’t the defense’s fault.

This is where my concept, which I’m calling Split Runs, comes in.

Split Runs asks this question: What if, since a runner who scores advances four total bases, the allowance of a run was looked at in one-quarter intervals? With the assistance of the SIS R&D staff, we were able to nail down a stat that takes every base, not run, taken by every runner who eventually scored, and assign it to the pitcher who was on the mound for that runner’s at bat. Then we count the number of bases that any Defensive Misplay accounted for and subtract that from the four bases he actually traveled. Finally, we add up the number of base advancements attributable to the pitcher, except in cases where there was enough offensive action afterward that he would have scored anyway.

You can still refer to a reliever’s Inherited Runners Scored, but Split Runs applies the context of each base-state situation they entered in. Normally, if pitcher A is taken out with bases loaded, and pitcher B enters and gives up a grand slam, pitcher A would have three earned runs, and pitcher B would be charged with one. With Split Runs, now pitcher A is instead charged with 1.5 runs and pitcher B is debited 2.5 runs, as the runner who was on third advanced 1 base (0.25 runs), the runner on second advanced 2 bases (0.5 runs), and the runner on first advanced 3 bases (0.75 runs).

Below are the Top 30 Starting Pitchers in spRA, and the Top 30 in ERA from 2020, minimum 40 Innings:

PitcherspRAPitcherERA
1Shane Bieber1.691Shane Bieber1.63
2Yu Darvish1.922Trevor Bauer1.73
3Zach Plesac1.953Dallas Keuchel1.99
4Trevor Bauer1.974Yu Darvish2.01
5Dallas Keuchel1.995Dinelson Lamet2.09
6Dinelson Lamet2.096Corbin Burnes2.11
7Corbin Burnes2.117Clayton Kershaw2.16
8Max Fried2.138Max Fried2.25
9Brad Keller2.189Zach Plesac2.28
10Tony Gonsolin2.2210Chris Bassitt2.29
11Jacob deGrom2.4211Tony Gonsolin2.31
12Kenta Maeda2.4612Jacob deGrom2.38
13Chris Bassitt2.4613Brad Keller2.47
14Clayton Kershaw2.5114Dustin May2.57
15Hyun-Jin Ryu2.5915Hyun-Jin Ryu2.69
16Kyle Hendricks2.6616Kenta Maeda2.70
17Carlos Carrasco2.6817Taijuan Walker2.70
18Dustin May2.6918Zach Davies2.73
19Zac Gallen2.7819Zac Gallen2.75
20Mike Clevinger2.9720Gerrit Cole2.84
21Gerrit Cole3.0221Kyle Hendricks2.88
22Justus Sheffield3.0522Carlos Carrasco2.91
23Blake Snell3.0623Zack Wheeler2.92
24Zack Wheeler3.0724Sandy Alcantara3.00
25Brandon Woodruff3.0825Mike Clevinger3.02
26Zach Davies3.0826Brandon Woodruff3.05
27Julio Urias3.1527Marco Gonzales3.10
28Steven Brault3.1628Adam Wainwright3.15
29Antonio Senzatela3.1929Luis Castillo3.21
30Marco Gonzales3.2030Blake Snell3.24

To better apply the defensive aspect, I’ll draw from one inning from this season that may have helped swing the NL Cy Young Award towards eventual winner Trevor Bauer.

On September 4, against the Pirates, the fourth inning began with an error by Joey Votto. Later, two runs scored on a triple by Anthony Alford. On that triple, Brian Goodwin had a Defensive Misplay (DM) for Slipping. Another run scored on a wild pitch, and the inning ended with the Pirates plating three runs, all unearned runs for Bauer.

By Split Runs, the defense was only responsible for .75 out of the three runs—0.25 for the one-base error by Votto, and 0.5 from the DM by Goodwin, whose misplay turned a double into a triple, thus allowing a runner on first to score when he might’ve held on third. That means Bauer would be charged 2.25 Split Runs.

Bauer finished with a 1.73 ERA, but his spRA was 1.97 over his 73-inning season. Yu Darvish wound up finishing with a lower spRA, 1.92, than his ERA, 2.01, over 76 innings, making this year’s Cy Young race closer than many thought.`

And here’s each Starter in the Top 30 of either ERA or spRA:

You can see a strong positive correlation, with Pearson’s coefficient for the correlation between spRA and ERA being .95.

However, there are plenty of pitchers with enough of a difference that make this measure of run prevention well worth tabulating and exploring.

The biggest outlier here is Justus Sheffield, who ranked 44th among qualifiers in ERA at 3.58, but 22nd in spRA at 3.05. Sheffield left seven runners on base in the 2020 season, and his relievers let six of those runners score. Those six earned runs equated to 2.75 Split Runs.

Here’s the leaderboard for Relievers in 2020:

PitcherspRAPitcherERA
1Erasmo Ramirez0.631Jacob Webb0.00
2Alex Colome0.712Devin Williams0.33
3Jake Diekman0.743Jake Diekman0.42
4Jesse Hahn0.784Jarlin Garcia0.49
5Devin Williams0.835Jesse Hahn0.52
6Nick Anderson0.966Nick Anderson0.55
7Yimi Garcia1.057Yimi Garcia0.60
8Kyle Zimmer1.088Erasmo Ramirez0.63
9Codi Heuer1.249Alex Colome0.81
10Matt Wisler1.2410A.J. Minter0.83
11Jacob Webb1.3511Adam Kolarek0.95
12A.J. Minter1.3512Chris Martin1.00
13Chris Martin1.3813Matt Wisler1.07
14Trevor Rosenthal1.5214Darren O’Day1.10
15Jordan Romano1.5315Nick Tropeano1.15
16Cesar Valdez1.5716Jordan Romano1.23
17T.J. Zeuch1.5917James Hoyt1.23
18Liam Hendriks1.6018Cesar Valdez1.26
19Victor Gonzalez1.6619Tanner Scott1.31
20Cam Bedrosian1.6920Victor Gonzalez1.33
21Riley Smith1.7221Drew Pomeranz1.45
22Brad Hand1.7422Riley Smith1.47
23Joely Rodriguez1.7823Rafael Dolis1.50
24Drew Pomeranz1.8124Codi Heuer1.52
25Jeremy Jeffress1.8325Jeremy Jeffress1.54
26Jarlin Garcia1.8426Eric Yardley1.54
27Kyle Cody1.8927Kyle Zimmer1.57
28Andre Scrubb1.9028Kyle Cody1.59
29Bryan Garcia1.9729T.J. Zeuch1.59
30Caleb Thielbar2.0330Bryan Garcia1.66

Hansel Robles had a disastrous 10.26 ERA in 2020, but he did have a… less disastrous 7.29 spRA. Robles was hurt by how earned runs were charged. He was removed with the bases loaded twice in situations in which all three runners scored. Meanwhile, Blake Parker was the biggest beneficiary of classic Earned Runs among relievers, as his very good 2.81 ERA in 2020 doesn’t fall in line with his poor 5.06 spRA. Parker let five inherited runners score out of 14, including two from first base.

Every time there’s a Defensive Misplay leading to a run, the defense is charged a portion of a Split Run. Here are the 30 teams in terms of BIS’ flagship stat, Defensive Runs Saved, against Team Split Runs in 2020:

TeamSplit RunsTeamDRS
1Dodgers9.751Cardinals33
2Athletics10.752Dodgers29
3Twins12.53Indians27
4Brewers12.54Pirates26
5Indians135Rays24
6Reds146Cubs23
7Tigers14.257White Sox23
8Cubs14.58Twins22
9Royals14.59Mariners17
10Astros15.510Rockies15
11Nationals15.511Astros12
12Cardinals15.7512Rangers11
13Rays16.2513Reds6
14Rangers1714Giants6
15Pirates17.2515Padres3
16Diamondbacks1816Marlins0
17Angels1817Orioles-1
18Red Sox18.2518Yankees-1
19White Sox19.2519Diamondbacks-2
20Marlins19.7520Red Sox-2
21Orioles20.2521Braves-8
22Blue Jays20.2522Royals-10
23Padres21.2523Brewers-14
24Braves22.7524Tigers-14
25Mets23.2525Athletics-19
26Yankees23.526Mets-22
27Phillies23.527Angels-26
28Mariners24.7528Phillies-33
29Rockies2729Blue Jays-39
30Giants29.2530Nationals-43

The World Series Champion Dodgers had the fewest Split Runs against them in the league, falling in line with their No. 2 overall ranking in Defensive Runs Saved. You can see that the Giants were middle of the pack in Team DRS but their misplays cost their pitchers the most total Split Runs, at 29.25.

It’s one thing to have a collective defense consistently make good plays at the right time; it’s another to prevent mistakes from happening at the most crucial times, and mistakes that could swing a game towards the other team.

If a pitcher has a higher spRA than ERA, then at least a portion of unearned runs were partially his fault. If a Pitcher has a higher ERA than spRA, then their defense made a few misplays behind him that weren’t called errors, and/or relievers came in and were unable to put out that pitcher’s fire, causing the pitcher’s ERA to go up, possibly unfairly.

I believe Split Runs works because it gets closer to a proper measurement of damage the pitcher allowed. There is some room for improvement (i.e. potentially adding in Good Fielding Plays to mirror how the system handles Defensive Misplays) but even just the splitting of responsibility between pitcher, defense, and subsequent relievers is a strong start.

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