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From a RP fatigue discussion in the General Strategy section:
coyote303
Posts: 1137
Joined: Thu Aug 23, 2012 2:01 pm
Location: Colorado
Re: RP Fatigue
A new series does not reset reliever fatigue. The only time you have rest days are just before and during the playoffs, and those days are clearly marked on the schedule. There are no rest days during the regular season, and game 3 (and sometimes game 2) of one series affects game 1 of the next series.
Remember, if a pitcher pitches two consecutive games, he will be fatigued if he pitches in a third. (Exception: if he pitches less than a full inning in one of those two previous games.) So Arroyo almost certainly pitched in game 44 as well as game 45. He was able to pitch in game 48 unfatigued because he didn't pitch in game 47.
If a pitcher enters a game at F9, he is considered completely fresh. So, previous pitch counts won't make him get fatigued faster.
I don't know what the pitch count cutoff is where a pitcher needs more than one day of rest to become rested (which Gullet exceeded and was thus fatigued in game 46). Perhaps someone can enlighten us.
(Based on my interpretation of the above, the answers to your two questions are No and No).