ERA+
ERA+ is the ratio of the league's ERA (adjusted to the pitcher's ballpark) to that of the pitcher, meaning 100 * lgERA / playerERA. Greater than 100 is above average and below 100 is below average.
Criticisms of ERA+[edit]
Unlike other indexed measures, ERA+ breaks with the mold and puts the league value that it is indexing against in the numerator rather than the denominator, all in an attempt to get the "bigger is better". A value should always be indexed against something, and that something needs to be in the denominator. The result of this index is that it is not apparent that you need to take its reciprocal if you want to add it to something else.
As an illustration, if you see Pedro with an ERA+ of 300 and a league average pitcher with an ERA+ of 100, then the arithmetic mean (simple average) of the two will end up looking like an ERA+ of 200. But, because the players own ERA is in the denominator of ERA+, a harmonic mean needs to be used: 2/(1/300+1/100) = 150. That is, you’ve got to reset ERA+ to the right scale, then you can add it up (denominators now the same), and then re-inverse it back to the original scale.
That is:
- Pedro: 1.50 ERA, lg of 4.50, ERA+ of 300
- Other: 4.50 ERA, lg of 4.50, ERA+ of 100
The correct average is : 3.00 ERA, lg of 4.50, ERA+ of 150. Using the simple arithmetic mean of the seasonal ERA+'s gives the incorrect answer of 200.
