Thanks again to Dr. Doom for contributing this series on Pitcher WAR measurement. If you missed Part 1, you can check it out here. In Part 2, Dr. Doom takes a closer look at ERA+. More after the jump.

Greetings again, my fellow stat-heads! In my last post, we discussed the Pythagorean Record (which states that winning percentage is roughly equal to the square of runs scored divided by the sum of the squares of runs scored and runs allowed) and the simple concept I called “decision proportion” (which states that total decisions are roughly equal to total innings pitched divided by nine).

In this post, we’re going to be talking about ERA+, found on baseball-reference.com. This metric is, of course, one of the greatest things Baseball-Reference has ever done. As I recall (those of you still around from the olden days can correct me if I’m wrong), this was, along with OPS+, the first *new* metric to debut on the site, and it generated* a lot* of discussion on the old B-R blog. And, with good reason – it completely changed how we talked about players. This was before the days of WAR, and these new stats were a revelation – summarizing OPS or ERA in a number that was neither park-dependent nor era-dependent. It was love at first sight.

I’m going to ignore OPS+ here, because while it is helpful to talk about the offensive equivalent, it has a wrinkle that a lot of people don’t like, so I’d rather not discuss that here (but, If you want to get into it in the comments, please do). For now, let’s stick to pitching, since we’re talking about building a pitcher WAR framework.

**The Basics**

ERA+ is simply formulated by taking the *league* ERA and dividing it by *pitcher* ERA. Why league over pitcher? Because then a *higher* number is better, and that makes ERA+ numbers look more like OPS+ numbers (we will talk about this more later; for now, let’s just go with it). It’s League ERA over Pitcher ERA (I’m just going to go ahead and assume you don’t need an ERA explained to you if you’ve found your way to this site), then multiply by 100 to make it look pretty.

For example, Chad Kuhl of the Pirates last year had a 4.35 ERA, while the NL as a whole had a 4.34 ERA. Taking league over pitcher, we get 4.34/4.35, or .9977; multiply by 100 (99.77), round to the nearest whole number, and you get 100. Chad Kuhl was average at preventing runs last year. That’s not a surprise to anyone who watches a lot of baseball, I don’t think.

But here’s the thing: not all players are as easy to figure as Chad Kuhl. This is because Kuhl played in a relatively neutral park. What do we do about, for example, Clayton Kershaw? His ERA was 2.31 last year… but he got to play his home games in Dodger Stadium. Using the same basic calculation that we did for Kuhl, we would have Kershaw with a 188 ERA+; however, Baseball-Reference shows him with a 179. What gives?

Well, Baseball-Reference numbers take into account the fact that *ballpark matters*. We could do the whole calculation here, but I’m just going to ask you to trust the Baseball-Reference numbers, rather than having us figure this out for every pitcher. So, from now on, instead of calculating ERA+ ourselves, we’ll just use the B-R numbers that are so easily accessible.

**The Criticisms**

There have been some critiques of ERA+ over the years, and I want to discuss them here, so we all know what we’re getting into. What we’re talking about can be dissected at a pretty granular level (as WAR often has been), so I want all the cards out on the table. In other words, I think the quirks are important to acknowledge, because we’re going to be building a WAR metric off of this, so I think we can take some time to learn where our weaknesses or vulnerabilities may lie.

First, there’s the idea that this uses league/pitcher, rather than pitcher/league. I mean, it was done for simplicity’s sake, but the problem is that, at the extremes, it *really* doesn’t scale well. To use a famous example, take Rollie Fingers‘ Cy Young and MVP season of 1981. If we took pitcher ERA over League ERA, we would see an “ERA-” of 30. That is, Rollie Fingers allowed 30% as many runs as an average pitcher. That’s phenomenal. But with League/Pitcher, we see an ERA+ of 333! (not a typo). That just looks like *too* big of a number. It leads to comparisons like, “Rollie Fingers was about twice as good as Steve Carlton in 1972, since Lefty “only” had a 182 ERA+.” Well, that’s just silly. A lot of people think it looks better to see it where Fingers has a 30 and Carlton has a 55. The scaling just looks better. Plus, you can end up with a denominator of zero for a pitcher if he allows zero runs (something that *really* messes up ERA+). For what it’s worth, Fangraphs uses ERA-, and those numbers are readily available if you don’t want to make the conversion yourself (which you can do by dividing 10,000 by either ERA+ or ERA- to get the inverse).

Second, Baseball-Reference has, pretty much forever, used 3-year park adjustments. That is, the park factor used for a season is NOT how that park performed *that year*, but also includes how that park performed in the year *prior* and the year *following*. This is supposed to help eliminate the problem of, for example, really wonky weather in one season, something which might, for that season, exaggerate or minimize a park’s normal effects. Instead, using a three-year factor, there’s a lot more stability in the park effect numbers. True, but also, it means you’re comparing things to a baseline that isn’t authentic; the weather that one year might have been really different – extra windy, or hot and dry, and that might actually have made it a more difficult pitcher year. Honestly, though, most of the time, this doesn’t make *that* big of a difference. Off-hand, I can’t think of any examples in which this criticism really fundamentally changes anyone’s final numbers (but, if you know one, please tell us in your comments). Back when these things were new, we discussed stuff like this a LOT more often… but that was over a decade ago, so I can’t remember it all anymore. Brand-new stadiums, without three years of data, always messed stuff up… but that gets corrected once a stadium is three years old, so it’s not an issue with “historical” analysis like this.

Third, a valid criticism of ERA+ is that it uses ERA rather than RA. That means you’re *always* reverting to the question of which runs are “*earned*“, which, in baseball, means that human judgment starts to enter the equation. In contrast, Baseball-Reference and Fangraphs (under “RA9”), in their WAR calculations, use Runs Allowed, not Earned Runs. Subtle distinction, but something worth talking about, especially when a pitcher allows an unusually high number of unearned runs and thus does comparatively better by ERA+ than he would by a metric based on RA. Again, *most* of the time, this doesn’t matter too much, but there are small differences depending on the pitcher. Nolan Ryan, for example, gave up about 10 unearned runs per year, whereas Tom Seaver allowed about 7½, and Curt Schilling only 4. Steve Carlton gave up 11 and Gaylord Perry nearly 13; the point is, it has an effect.

Fourth, and finally, we have defense. Obviously, ERAs are dependent upon the defense playing behind you. I know I’d rather have Andrelton Simmons manning shortstop than Yuniesky Betancourt. Wouldn’t you? Obviously, defense has an impact. There’s no way for ERA+ to take that into account, because there’s no way for *ERA* to take that into account. This is why Fangraphs uses FIP (Fielding Independent Pitching) numbers. They take *only* home runs, walks, and strikeouts into account. The FIP discussion is for another day (or today, if you want to hash it out in the comments below), but for now, just know that what we do in our final part of the series *can* be done with FIP-, if an enterprising person who favors Fangraphs’ model is interested in making those calculations.

**Conclusions**

ERA+ does the job, really, in spite of its flaws. It certainly gives us a number we can use for the purposes of these calculations. In Part 3, we’ll be taking the information we’ve discussed in these first two parts and applying it to build a WAR metric, by which I mean a number we can use to indicate the value of a pitcher’s contribution. Hopefully, even if you’ve been a little bit bored through these first two parts of the series, you’ll be able to enjoy the third part!