Alex Bregman doesn’t possess a baseball off-switch. “He’s obsessive in the best way,” said teammate Trevor Story. When Bregman was a growing up in New Mexico, he yearned to be a big leaguer.

Still, spend some time around the Red Sox and it’s impossible to miss the impact Alex Bregman has had on his new team. He leads them in most offensive categories, but that’s only part of his ...