There are lots of different ways to quantify the success of pitchers. Earned run average, walks + hits per inning pitched, strikeout rate, whiff rate, chase rate, ground ball rate, and even field-independent pitching are just some of the stats that we, as fans, use in our arguments about who the best pitcher in baseball is and why. But one group of stats that gets forgotten in the shuffle of hurler mathematics is the group of “against” stats. I’m talking about all the hitting stats we know and love, but flipped for pitchers. The one that gets dropped the most on TV or in conversation is batting average against (or BAA), but there’s also on-base percentage against, slugging against, and even on-base-plus-slugging against. The reason why these stats are easy to grasp is because we’re all too familiar with the good and bad benchmarks of these stats on the hitting side, so flipping the script with the same formula just makes sense. Let’s use the following as an example: out of all starting pitchers of the 2022 season, Patrick Corbin has one of the worst BAAs at .331. Paul Goldschmidt's batting average currently sits at .331. Paul Goldschmidt is going to win the NL MVP and Patrick Corbin stinks. Makes sense? Good.
So, with this “stat reversal” method in mind, I wanted to use a pitching stat to benchmark hitters, and thought that a fun way to do so would be to use earned run average. Although I don’t like catch-all stats, ERA is probably the closest stat of that variety that I think encapsulates a pitcher’s ability the best. It’s simply the amount of runs a pitcher gives up rationalized to a nine-inning average. In other words, giving up two runs in six innings results in an ERA of 3.00. Seems easy enough to translate ERA into “earned run average against” (or ERAA), right? Well, sort of. The calculation for ERA is as follows: nine times the amount of runs given up divided by the number of innings pitched. The “nine” represents the nine innings in a standard baseball game, so that part of the equation is fine to stay as is. It’s the actual numerator and denominator of the stat that makes determining how to calculate ERAA complicated. Hitters aren’t measured by the amount of innings they hit because that’s just ridiculous; they’re measured by their plate appearances and at-bats (free passes to first of any kind and sacrifice hits are not considered at-bats). And as for “runs,” measuring hitters by how many runs they produce (not RBIs or runs scored, by the way) is extremely analytical and challenging to quantify. But even with these barriers in front of me, I was determined to put my thinking cap on and work this problem out. Thus began the saga of earned run average against.
First, I had to determine what I was actually trying to numerically visualize. Saying “earned run average against” and reversing the ERA formula for hitters is no "eureka moment" to say the least. But after contemplating this thought for a while, here’s the question I came up with that ERAA is trying to answer: how good would a lineup be if the same hitter batted 1-9? Yes, I understand that this question makes ERAA purely theoretical, but I was genuinely curious! Plus, with a basic conceptualization of good versus bad ERA, earned run average against could be a great way to see how potent a hitter really is. Ok, so now let’s talk about the components of the ERAA equation, starting with the easier one: innings “batted,” I guess. As I said before, there’s no sensical way to say how many innings a batter has played. That’s a very weird way of describing a hitter’s opportunities. It might be easy to just divide a player’s total plate appearances by three because there are three outs in an inning, but no pitcher pitches “at par.” In other words, the average pitcher definitely does not face the minimum amount of batters in a single inning. So, the question had to be answered: what’s the average number of batters a pitcher faces per inning pitched? If you look at every single inning pitched since World War II, that number sits right around 4.25. And if you look at just the 2022 season, the 2022 average batters faced per inning is also around 4.25. So, that’s my constant. For ERAA, innings batted equals plate appearances divided by 4.25. Great, now let’s talk about that numerator.
Of all the advanced metrics that get tossed around these days, one of the better ones that you don’t hear about is runs created (or RC). No, not weighted runs created plus (or wRC+), which is mentioned without context so much that you’d think it’s the second iteration of Einstein’s energy equation. I’m talking about one of legendary statistician Bill James’s first statistics he ever created. To quote Major League Baseball’s website, runs created “estimates a player's offensive contribution in terms of total runs, [combining] a player's ability to get on base with his ability to hit for extra bases… [it] measures how well a hitter completes one of the central focuses of his job - creating runs.” Although the original formula is quite basic, its technical younger cousin is actually more accurate. It looks a little something like this.
When you use that formula for individual games, you can come within a pretty small percentage of how many runs a team really scored. I tested this with a few box scores and it came out exactly as advertised, so it became my numerator for ERAA, representing “runs responsible.” I could’ve gone with more analytical and common stats like batting runs, which is used in wRC+ and wins above replacement, but opted for runs created because I liked its simplicity and provability. The one drawback to using runs created for individual batters is that it works better as an aggregating stat, but there’s a lot about ERAA that you can take with a grain of salt, and I’m fine with that! If you want to let me know if a stat like this already exists or if there’s a more optimal way to display the message I’m trying to convey, please reach out! But for the time being, the formula for ERAA is as follows: nine times runs created divided by the quotient of plate appearances divided by 4.25. After putting all the numbers together using a couple of different filters, I came up with the Excel file linked below (updated as of 8/13/2022).
There’s certainly a lot to take in with these numbers, but that’s why I’m splitting this post in two! Tomorrow, I’ll talk about some takeaways from the all-time and 2022 ERAA leaders and why I think some players deserve more or less love than they receive. Today, I’ll let you read over this godforsaken spreadsheet with all your brainpower so you’re ready for more statistical nonsense tomorrow! So long for now, from your favorite non-statistician statistician.
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