NEW YORK — Jason Bay was introduced as a member of the Mets on Tuesday morning. Mets G.M. Omar Minaya presented him with a No. 44 jersey, and hockey Hall of Famer Rod Gilbert also gave the native of Trail, British Columbia, a Rangers jersey. Bay pronounced his excitement to join the Mets, a team that he said interested him from the beginning of the free-agency process, and his bemusement about the sort of rumors that made the rounds — both about his interest in going to New York and his health — over the course of the free-agency process.

Asked about leaving the Sox, Bay said that he was open to the idea of returning to Boston at season’s end.

“What it boiled down to, I just think the Mets wanted me more,” he said.

Here are some of the highlights from Bay’s press conference.

Introductory remarks

I just want to say thank you to Jeff [Wilpon] and Omar [Minaya] and everyone else that made this possible. It’s obviously a big deal, a big day for me. I’m very, very excited to be here. We were talking about it before and I told my agent when the season ended last year, when you looked around and looked at some of the voids teams had and what I could provide, there was a short list of teams I wanted to go to. The New York Mets were on that list. To be able to be here, to be with a team and in a place I want to be at, in this city and this market and everything, you only get a chance to do this once or twice in your career, and I’m very grateful and very honored to be here.

Why were the Mets on the short list?

First of all, the chance to win. Regardless of what happened last year, you look at the players on this team and it’s a very good team. I think coming in, I offer a little bit of a fresh perspective as an outsider. I don’t really know what went on last year. I know a lot of guys got hurt. But from a straight talent standpoint, it’s a very good team. That was big — a chance to win. I was in a situation in Pittsburgh where I enjoyed my time, but we didn’t win. Then I went to Boston, and really found that winning was a big part of that. And the market and meaningful games, being in Boston, kind of feeling that, having that . . . the window for me to play is very short. If you don’t take advantage of it now, you may never get that. New York is one of those places that, regardless of what sport you play or what you do, it’s the center of everything. Like I said, there were a lot of reasons [why I signed].

Any concerns about power or defense in Citi Field?

For those of you who don’t know, and I’m sure most of you do, Pittsburgh is very spacious as well, and you play half your games on the road. I’m not really concerned. It’s something that’s there, but you go out and I’m confident in the type of player I am. Ballpark or not, I’m still going to do what I do. So that had zero factor in anything in my decision. Defensively, in Pittsburgh it was big there as well. The first few years there, I felt like I was a good outfielder. I got banged up a little bit in ’07, then I went to Boston. There ain’t a lot of room to run around. It’s a challenge to go out there and prove to everyone that I can play pretty good defense. I’ve said before, I’m by no means Torii Hunter out there. I know that. But I still think I’m pretty good. It will be a chance to show everyone that I can be.

You replaced Manny Ramirez in Boston. Does that help you with what you’ll see in New York?

I think it is a huge factor, not only for myself but for the Mets. As long as you toil a little bit in anonymity in some smaller places, I think a lot of people have questions as to if so-and-so can do it here, can they do it here, can they do it here? Through no fault of anyone, unless you get a chance to do it, you can’t prove it. I went to Boston. I’m sure a lot of people said the same thing — even myself. I was like, ‘This is the chance to do it.’ I think that has really prepared me, a lot moreso than coming here from a smaller market. That doesn’t seem daunting. For me, it’s just another year. I kind of feel comfortable having that under my belt.

Any concerns about coming to New York?

There were no concerns. Obviously, right when the season ended and you get the free agency [exclusivity] period and all of a sudden that ends, the Mets were the first team, right from the get-go. My agent actually flew to New York and met with them. Very good, positive meeting. They were all along, after the Winter Meetings, there wasn’t probably a 48-hour window or something where we didn’t talk. So right from the get-go, they were very persistent. They wanted me. I really appreciated that. And then, basically, after the Winter Meetings, it probably seems like it took a long time, but after the Winter Meetings it took less than maybe a week or 10 days or something. We actually had agreed in principle before Christmas. There was a myriad of reasons — I don’t think any of us were even in the country; I was just in Canada, so it wasn’t that far — but to try to get this all done. It probably looks like it took a lot longer than it did. But in reality, it didn’t.

How important was it for you to pick a team you thought could win?

It was one of if not the biggest factor. Like I said, my previous situations, I earned a lot about what type of team I want to be on and the type of atmosphere I want to be under. This was the first chance for me to get a choice. I had been traded and just told where I had to go. To kind of sit down and talk about what are the factors, being on a team with a chance to win, as a competitor, that’s huge when you have a choice. Like I said, record-wise, I know what happened here on the surface, with guys getting hurt. I think that I offer a perspective where, if you look from a talent standpoint. The lineup, if you have everyone healthy you have an amazing lineup and arguably you have the best pitcher, fresh perspective, I don’t see how that can’t be good.

After the season ended, how much did you want to go back to the Red Sox?

It was pretty basic. The season ended in Boston. Once the season ended, they were on the short list. They had the criteria that I was looking for. Ultimately, what it boiled down to, I just think the Mets wanted me more. That’s what it felt, and it felt like it fit. Through no fault of anybody’s, I ended up here. This is where I wanted to be and I’m happy about it.

How much of this was about the money? Was anyone else close?

We can leave the second part of that question [out]. I don’t think we need to get into where I ultimately could have been. Ultimately, I’m here. That’s what I’m focusing on. At some levels, people say it’s not always about the money. The money’s nice — don’t get me wrong. But you bust your tail and put yourself in a position to go somewhere. Money aside, you still have to make that choice. You still have to make a decision. Like I said, New York, it was the perfect fit for everything. We hammered out the contract in almost a week. It was pretty easy. Both sides were happy. I wouldn’t have signed the contract if I didn’t want to be here and wasn’t happy. That couldn’t be further from the truth. That’s why I did it. This is one of the biggest days of my life, and I’m excited.

What did you think of Peter Gammons’ statement that you’d rather play in Beirut than Queens?

I kind of heard about that around the way. It’s funny, maybe to my own detriment a little bit, we kind of cut off all contact until this was done. Basically, if I addressed everything that was false, I’d just be addressing that and not addressing the things that were true. There was a lot written. Where you come up with Beirut, I don’t know. … That’s the funny thing. No one refuted it. I never talked to anybody. No one knew my position on anything except for my family and my agent. People have opinions — that’s fine. To say those were my opinions and that’s the way I felt, that hurts a little bit. But, once again, you can’t control it and it couldn’t be further from the truth.

What is the state of your shoulder and how did you hurt it?

I actually never hurt my shoulder. That was once again me not refuting much. It just kind of took on a life of its own. I had surgery on it in 2003. It’s been great ever since. I saw [Mets doctor Richard] Altchek. Everything was great. It was, again, just one of those things that took on a life of its own. No concerns. I don’t have any concerns whatsoever.