“If the ball’s different, and intentionally different, I guess the one thing I would ask is just some transparency,” Morton said. “If the league is trying to do something different and get a different result with balls in play, I think for history’s sake and for the integrity of the game that there would be transparency.”

Statistics also affect players’ paychecks, through free agency and salary arbitration, noted Jake Odorizzi, a right-hander for the Minnesota Twins, one of four teams on a pace to break the season home run record set last year by the Yankees. Odorizzi would welcome an explanation from M.L.B.

“If there’s something that’s potentially altering that, just come out and say it,” Odorizzi said. “I think, as players, we’ve gotten to the point now where we’ve accepted it.”

Manfred insisted that the league has been open about the issue, pointing repeatedly to his study, which determined that while the ball was not harder, it was producing less drag through the air. The league has struggled to identify the cause of that phenomenon, but it has tried; M.L.B. officials said their researchers had even developed lasers to study the height and width of the ball’s seams.

Yet because every ball is made with natural materials and hand-sewn in Costa Rica, they said, an array of variables is always in play. The league wants stricter manufacturing parameters to produce more consistency, but says that is not easy to achieve.

“You need to appreciate how small the variations are in the manufacturing process that can produce a change in the way the ball performs,” Manfred said, adding later, “The challenge for us is to get better control over that variation, tighten those specifications and get more comfortable with how that ball’s going to perform from year to year.”