What is ERA+?

I often use the statistic Adjusted Earned Run Average (ERA+) in my posts about baseball history.  I believe many readers of this blog have a general idea of what ERA+ means and why it is useful in historical comparisons.  However, I have seen it misinterpreted in several places around the internet, so I'm going to try to clear up any confusion here.

I'll start with an example of how the ERA+ measure can be useful.  Back in 1906, St. Louis Cardinals hurler Buster Brown had a 2.64 ERA finishing 21st in the National League.  Nearly a century later in 1998, the legendary Roger Clemens led the American League with a 2.65 ERA pitching for the Toronto Blue Jays.  So, we have two pitchers with almost identical ERAs but Clemens actually had a much better season than Brown. 

How can two pitchers with essentially the same ERA have such dissimilar rankings in their leagues?  The reason is the vastly different contexts in which they played.  Brown pitched at the height of the Deadball Era while Clemens pitched in the high-powered run scoring environment of the late 1990s.  In 1906, the league ERA was 2.62 and, in 1998, it was more than two runs higher at 4.65.  

Since ERA doesn't always do a good job of comparing the quality of pitchers across eras, many analysts like to use ERA+ which adjusts for the league average ERA and the home park of the pitcher.  In general, an ERA+ of 100 means that a pitcher had an average ERA relative to his league, an ERA+ of more than 100 indicates that he was better than average and an ERA+ of less than 100 indicates worse than average.

Brown's 99 ERA+ in 1906 says than he was very close to average while While Clemens 176 ERA+ tells us that he was far above average.  One can find the ERA+ statistic for any pitcher in any season at Baseball-Reference.com.

The specific interpretation of ERA+ is where some people get confused.  There is a common misconception that an ERA+ of 176 means that Clemens was 76% better than league average.  What it really means is that the league average was 76% worse than Clemens.  It sounds like the same thing, but it's really not.

In order to see how Clemens performed relative to the league average, it is necessary to take the reciprocal of ERA+ and then subtract from 100.  The reciprocal of 176 is (100/176)=0.57 or 57%.  So Clemens was 100-57= 43% better than league average after adjusting for league and ballpark.  So, that's how we interpret ERA+.  If that's enough for you, then stop here.  If you want to see a detailed calculation then read on.

Detailed Calculation of ERA+
 
ERA+ involves a two-step formula with league-adjusted ERA (Lg Adj ERA) calculated first:

Lg Adj ERA = (Lg ERA/Pitcher ERA) x 100

ERA+ = (Lg Adj ERA + Lg Adj ERA x PF)/2

where PF = Park Factor = the amount by which a ballpark inflates or deflates the ERA of a typical pitcher.

Let's use Jake Peavy's 2007 season with the Padres as an example:

ERA = 2.54

Lg ERA = 4.43

PF for Runs = 0.80 for Petco Park

Lg Adj ERA = (4.43/2.54) x 100 = 174

ERA+ = (174 + 174 x 0.80)/2 = 157