In 2005, Major League Baseball created its Comeback Player of the Year award, given to one player from each league who “reemerged on the baseball field during a given season.” For the past 10 years, it has served as a nice little tip of the cap to players who rebounded from injuries or underperformance.

But this year, a candidate unlike any other has emerged. Like the award itself, which was initially sponsored by Viagra, he has a past association with performance-enhancing drugs. And like many past winners, his mere presence...