LAS VEGAS — Even as the night wore on Tuesday, the New York Mets tried to couch their words in theoretical terms, but they could not hide their enthusiasm for the truth — that they agreed to a deal in principal with the prize of the bullpen free agent market, Francisco Rodriguez.

The Mets and KRod agreed on a three-year deal worth $37 million with a fourth-year option that would push the deal to more than $50 million. The only

holdup is a physical, which will take place today in New York, and the Mets will have filled the biggest hole on their roster.

“Theoretically — that’s the word on the street, right?” Mets manager Jerry Manuel said with a smile. “No question, if you can acquire a player such as that, any time you acquire someone at that level, it raises the level of everybody else. It’s almost like saying Johan [Santana] is pitching. You see a different spirit with your team. To have a guy at the end of the ballgame is very important, very critical.

“In the way that we lost so many close games late, I think that was critical for us to — theoretically — address this thing here. We have addressed it very well.”

The need for the Mets became the most critical priority when Billy Wagner not only was lost for the final two months of the 2008 season, but could miss the entire 2009 season after undergoing Tommy John surgery. As the Mets stumbled down the stretch last season, putting the likes of Luis Ayala, Aaron Heilman and Ricardo Rincon on the mound in save situations, they could only dream about a closer like Rodriguez.

K-Rod, after three straight seasons of at least 40 saves, set a major league record with 62 saves in 2008 for the Los Angeles Angels. But he seemed bound to be priced out of the Mets’ range, with his agent initially suggesting a five-year, $75 million deal would be the asking price and the Mets still due to pay out $10.5 million to Wagner this season.

But the troublesome economy, a glut of closers available and the absence of any other big-market teams in the bidding pushed the price into a realistic range, allowing the Mets to pounce. And they did, meeting with Rodriguez face to face Sunday night almost as soon as he landed, and then continuing the talks through Monday until his agent, Paul Kinzer, said late that night that he was optimistic a deal would be done.

Now the Mets can turn their attention to other needs, having secured the late innings with the closest thing to a sure thing on the market.

“The reason we’ve been looking at him is obvious,” Mets General Manager Omar Minaya said. “He’s young. He’s shown besides the save record, which is something that’s appealing, he’s a competitor.”

Rodriguez sometimes rubbed his Angels teammates the wrong way with a perceived selfishness as he pursued the record. But his former manager, Mike Scioscia, had only kind words for his departing closer.

“I don’t think I’ve met anybody as tough mentally,” Scioscia said. “He’s got a talent that plays anywhere. If you’re a closer and you’ve got that talent, you should be able to pitch anywhere.”

Rodriguez expressed that to the Mets in the meeting Sunday, enthusiastically telling them of his desire to be on the New York stage.