As to running, here's what Cressey has to say:
The current practice utilized for conditioning is for pitchers is to go for a long run the day after a game to “flush” the sore arm of lactic acid, or minimize muscle soreness to recover faster for the next game. These theories are not supported by the current literature and the physiology of the sport.
In the current research study examining the physiology of pitching, Potteiger et al. (1992) found no significant difference between pre-pitching and post-pitching blood lactate levels of six college baseball players after throwing a 7-inning simulated game. Even though during an inning there is a slight lactate production of 5.3-5.8 mM, (which is not high, considering resting lactate is 1.0mM), it does not cause a buildup of lactic acid in the arm of a pitcher after a game. As a comparative example, a high lactate response would occur from squatting for multiple reps at about 70% 1RM; this might produce a lactate level of about 8-10mM (Reynolds et al., 1997). Furthermore, jogging to flush the arm of lactic acid after a start is unnecessary and not supported by the literature, especially since we learned all the way back in 2004 that lactate was not the cause of muscular fatigue ; even the New York Times reported on this in 2007! A lot of coaches simply haven’t caught wind yet – in spite of the fact that exercise physiology textbooks have been rewritten to include this new information."