A bogus stat in my book: Why do middle relievers get an unfair advantage with respect to era?
They do...can you tell me why?
In general, though, ERA is a rather poor stat to use when evaluating relief pitchers, particularly those who only come in for a batter or two. The stat works best for pitchers who throw complete innings - starters primarily, though most closers also throw full innings. If you're in for a batter or two, your ERA doesn't get dinged if you allow an inherited runner to score but it does go up if you're taken out and a runner you allowed scores on a later pitcher. Better stats for relievers are OBA (On-Base Against) for general skills and IRA (inherited runs allowed) to show how they do in critical situations.
So, here's my best asnwser, by way of a pure guess.
Your "bogus stat" doesn't apply to just middle relievers. It applies to closers as well, since closers don't always come into the game to start an inning.
Runners who are already on base when a pitching change is made are the responsibility of the pitcher who allowed them to reach base. Period. If one of them scores, that run is charged against the pitcher responsible for putting him on base. Always. In fact, there is a rule about which pitcher is responsible for the runner, depending upon how the runner reaches base, if the pitcher for whatever reason is replaced DURING the batter's plate appearance.
The role of the relief pitcher, when he comes into the game with at least one runner already on base, is to save that run for his teammate. That's why there are specific statistical categories that apply only to relief pitchers - first batter efficiency and inherited runners allowed or stranded.
To say that the relief pitcher should be charged an earned run for allowing another pitcher's runner to score is like saying that you are responsible for setting a curfew for your neighbour's child.
No matter which way you want to look at this, you're looking for 10.16 of the rulebook.
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