Right-hander Chien-Ming Wang was originally slated to start for the Yankees on Monday, but was pushed back to Tuesday to accommodate Andy Pettitte, who would have started Sunday.
"With Pettitte pitching, I kept Cliff out, even though he has decent numbers against him," Rays manager Joe Maddon said. "Primarily with Cliff, I'm just concerned, just coming back, playing that game [Sunday]. And he did a lot of base running [Sunday]. And after all, it's knee surgery, regardless of the techniques involved in today's surgery situations. I just wanted to make sure he was well today, and then we've got some righties coming up, so maybe we could pop him a couple of days in a row.
"So it actually may have worked out well, holding him back. They have no lefties in the bullpen today. So as the game is in progress, there's a chance he'll pinch-hit and stay in the game."
The 35-year-old Floyd was activated from the 15-day disabled list (right knee surgery) Saturday after missing 30 games. He played his first game Sunday and went 2-for-4 with two RBIs, raising his average at Tropicana Field to .388 (31-for-80). He is hitting .368 with two home runs and seven RBIs for the season.
Despite sitting against the lefty Monday night, Maddon said the left-handed-hitting Floyd will be used as the DH against some left-handers this season.
"Tonight could have been one of those nights, based on his numbers from the past," Maddon said. "Coming into today, I was talking to [head athletic trainer] Ronnie [Porterfield] at the end of [Sunday's game], and I was a little bit concerned about boom-boom, right from the beginning. I've seen in the past where guys come off injury and you get excited about it, and then you start using him a little too quickly and you have a little hiccup. So I'd rather be a little bit cautious with him right now, because I believe he's going to have a stellar season."
Maddon explained what he will look at when considering whether to use Floyd against a left-hander.
"Sometimes I just look at his swing plain and how a pitcher pitches," Maddon said. "And you look at how well a lefty does against a lefty. And you look at all those things and how his data is in the past.
"Last year and the year before, he didn't play enough against lefties to really get a good description of how well he can do [against left-handers]. But we've got Jon [Gomes] there to DH also, so for right now, it's something we may do. But I want to look at it. And again, just like we talked about Jon with certain righties, we'll probably use Cliff [against] certain lefties."
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.