Athletes like to say they are trying to improve all the time. It is mostly lip service, as all they’re really doing is tweaking their foot placement or slightly modifying their arm delivery. They are not rearranging their daily lives to make these adjustments.

But the New York Giants star wide receiver Odell Beckham Jr. is carrying out an unusual tactic when he’s not on the field, one that few athletes have even considered. He’s living his life as a secret lefty.

Beckham’s...