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In short — “set roles” simplifies the managers’ job.
That too.
If knowing what your job is going to be when you go to work makes you more comfortable, (and therefore more productive), why should the same not be true of the bullpen arms?
And that too. No doubt. Though as you're aware, the relievers who do complain about "no set roles" are, 90% of the time, actually complaining that they're getting garbage time. :- )
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This is kinda neither here nor there, but did you ever read "Ball Four," Sandy? :- )