Everything you always wanted to know about: ERA+ and ERA-

The world of advanced baseball statistics can be an intimidating place for those of us who slept our way through advanced algebra or haven't been a follower of the Bill James revolution from the beginning.

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Still, that doesn't mean that we should feel left out when it comes to another way of understanding and appreciating the game we all love. With that in mind, BLS stat doctor Alex Remington will explore a new advanced statistic each week during the offseason, just as he did two offseasons ago, providing a simple primer for the uninitiated.

Today's statistic: ERA+ and ERA-

What ERA+ and ERA- mean: ERA+ and ERA- are ways of measuring a pitcher's earned runs allowed in ways that are much more neutral than ERA, a statistic which can be distorted by park effect and league effect (like offensive context of the era, from the Deadball Era to the Steroid Era). They are very similar to OPS+, which I wrote about in January 2010.

The real difference between ERA+ and ERA- is scale. In ERA+, a bigger number is better, and in ERA-, a smaller number is better. ERA+ looks the way it does because it has the same scale as OPS+, and you can find it on Baseball-Reference.com. ERA- is the one used on Fangraphs, and it was created for basically aesthetic purposes. Conceptually, when it comes to ERA, a smaller number is better.

More technically, as Patriot (Brandon Heipp) writes:�

ERA+ does not tell you that a pitcher's ERA was X% less or more than the league's ERA. It tells you that the league's ERA was X% less or more than the pitcher's ERA...
[On the other hand, an ERA-] of .75 means that the pitcher allowed runs at 75% of the league average, or that he allowed 25% less runs per inning than the league average.

So Kyle Lohse had an ERA+ of 108 last year. That means that the NL league ERA, controlling for the parks he played in, was 8 percent higher than Lohse's ERA. He also had an ERA- of 92, which means that he allowed runs at 92 percent of league average.

How to calculate ERA+ and ERA-: Basically, ERA+ is equal to Park Factor times League ERA divided by the pitcher's ERA, times 100, and ERA- is the exact inverse of that.

ERA+ = (PF * LgERA / ERA) * 100
ERA- = (ERA / (PF * LgERA)) * 100

(A slightly different formula is currently being used on Baseball-Reference, as explained here. But the above formula is the classic one.)

As I explained in the OPS+ article, a simple way of calculating Park Factor is the following:

((Runs scored at home + Runs allowed at home)/(Home games))/((Runs scored on the road + Runs allowed on the road)/(Road games))

League ERA is simply the aggregate of all earned runs allowed in the league, times nine, divided by all innings pitched.

What ERA+ and ERA- are good for: Basically, ERA is pretty lousy for comparison. The difference between Fenway Park and PETCO is massive, and when you're thinking historically, the difference between 1968 Dodger Stadium and 2000 Coors Field is obviously even bigger.When you're trying to compare one pitcher's performance to another, it's best to compare their ERA+ or ERA- rather than their ERA.

When ERA+ and ERA- don't work: As Patriot points out, one of the biggest pitfalls can simply be linguistic. For each stat, what does "better than league average" mean? For ERA+, a higher ERA+ means that league ERA was higher than the pitcher's ERA by that proportion; for ERA-, a lower ERA- means that the pitcher's ERA was lower than league ERA by that proportion.

The other main drawback may seem obvious: ERA+ and ERA- are fundamentally based on earned runs, a very traditional but somewhat strange stat, based largely on scorekeepers' judgment and tradition on what constitutes an error ? and as we all know, many of the worst fielding mistakes are never called errors, because the fielder never even touched the ball. Much as ERA is not as good a predictor of true talent as FIP (which I wrote about last year), ERA+ and ERA- are not necessarily good predictors of whether a pitcher will have a good year next year. It's just a better descriptor of how good they were this year.

Why we care about ERA+ and ERA-: One of the best things about baseball stats is that they facilitate comparisons between players. ERA can be so distorted by the park a player plays in, or the context of the league or era, that it can be hard to make good comparisons. Kyle Lohse had a 3.39 ERA this year, which sounds pretty good, but it's hard to know just how good it was. But his 108 ERA+ is much easier to compare. For example, it's the same as Ol' Stubblebeard himself, Hall of Famer Burleigh Grimes, who put up a 108 ERA+ from 1916 to 1934. I bet you could win a bar bet on that.

Previous lessons: BABIP,�OPS+,�FIP,�wOBA,�WPA,�WAR,�UZR,�J-HOFFA, Win Shares

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