I think the answer to the mystery is found the final paragraph of Nicholas Bakalar’s story:

Over all, there may be another factor contributing to the long lives of players: Major League Baseball has a robust retirement program, regarded as among the most generous in professional sports. Players get substantial pensions even after spending just a few months in the big leagues, and all players qualify for full medical benefits beginning on the first day they join a team.

I am a sucker for any article about baseball that isn’t about trades or the pennant race.