Before Friday's home opener against the Angels, manager Joe Girardi said that he made the change because it would create more difficulty for opponents to navigate the lineup with left-handed relievers in the late innings.
"If you think that's a story, wait until I take over [Derek] Jeter's spot in the leadoff spot," Rodriguez quipped. "That'll be a real story. No matter where you hit, you've got to just basically produce.
"It does one thing -- it presents a situation or a decision for the opposing manager each and every day. At some point, someone should get a pretty favorable matchup."
Girardi said that he had toyed with the idea of making the switch in Baltimore on Wednesday after seeing how the Rays utilized left-handed relievers in the season-opening series at Tropicana Field.
Girardi plans to use this order moving forward against righties. Rodriguez will continue to serve as the cleanup hitter against left-handed starters, with Cano batting third.
"Everything is good," Cano said. "I feel good at the plate, and everything is going to be fine. I would say that I'm just happy to be in this lineup. Batting fourth isn't going to make [any] difference."
Rodriguez said that he spoke to Girardi about the move, adding, "That stuff doesn't really matter. You show up to play wherever they put you, you go out and play and you try to win a ballgame."
Girardi said that the switch was not a reaction to boost production. Rodriguez entered Friday's game hitting .174 (4-for-23), while Cano was hitting .250 (7-for-28). Neither player had collected an RBI, while No. 5 hitter Mark Teixeira was batting .200 (5-for-25) with one RBI.
"Sometimes, when you think of lack of production, you move people down in the lineup," Girardi said. "They're still three and four and five. So, no, it really has nothing to do with that. It's more [about] just making it more difficult on the other clubs."