There are no statistics you can find on this, but apparently, you didn't start watching the Twins in 1961 until now. Players very seldomly went up and down. The pitchers pitched until they got knocked out of the game, not because they were so fragile there was a pitch count. There were no in-depth training strategies to maximize strength and speed compared to today. Same with the football players of that era. Jim Marshal said he never lifted weights. They just exercised.
My best guess is when they walked away at the end of the season; they left it all behind until training camp or spring training. This probably allowed their bodies to heal and rejuvenate.
Players are bigger and stronger today but more fragile as well. Crazy dichotomy, don't you think? Do you have any statistics to prove me wrong.