Run Expectancy and Reliever’s ERAs

The lowest ERAs in the league every year are turned in by relievers, and in 2009 relievers as a whole have allowed 0.4 less runs per nine innings that the starters (4.8 vs. 4.4). Most would agree that starters are generally better pitchers, so why is it that runs are scored at a higher rate on their watch? Bill James had the answer years ago.

We can talk about batters not being able to adjust to a relief pitcher – adjusting to the new release, arm angle, movement and velocity is hard – but there’s something much more fundamental that separates starters and relievers: when they enter a game. Starters always start every inning from the beginning with none out, whereas relievers often come in with one or two outs, and their runs allowed stats are treated as though the bases were empty when they entered.

Taking a hypothetical league-average pitcher, we can see the difference between starters and relievers. The league average starter will enter every inning with no runners and no outs. His run expectancy (2009 stats) is 0.51 runs for that inning, or about 4.65 runs per nine. If a reliever enters with 1 out, assuming he performs at the league average, his run expectancy is about 0.28 runs for that inning, equating to 3.8 runs per nine. If he enters with 2 outs, his run expectancy is 0.1 runs for the inning and 2.76 runs per nine. So basically, the very same pitcher has a huge advantage if he enters the game with 1 or 2 outs.

Given an average middle reliever who gets 1/3 of his appearances in each situation – 0 outs, 1 out and 2 outs – his expected runs allowed is about 4.00, even though his true figure would be 4.65 if he started. By virtue of occasionally entering games mid-inning, relief pitchers are given an advantage in ERA and runs allowed stats.

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One Response to Run Expectancy and Reliever’s ERAs

  1. [...] or not relief pitcher, Andrew Bailey, should make the list. I should really hold relievers to a separate standard, considering they naturally have lower ERAs. I’ll have to work on [...]

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