BOSTON -- An incredible summer journey that took place at Tropicana Field and ballparks throughout the Majors is approaching its end with the most unlikely of scenarios staring the baseball world square in the face: The Rays are one win away from reaching the World Series. Since their inception in 1998, the Rays have been little more than a punchline for late-night comedy, staggering from one losing season to the next. That has all changed, and the Rays have turned the national pastime upside down by taking a 3-1 advantage heading into Game 5 of the American League Championship Series on Thursday at 8:07 p.m. ET.

"It's pretty unbelievable how far this club has come and what we've done and what we've accomplished," Evan Longoria said. "We've believed in ourselves from Day 1, but I think we have really proved a lot to the people looking from the outside-in on how this thing can come together for us as a team."

Needing just one win from becoming a participant in the Fall Classic is almost unfathomable for Tampa Bay, yet that's where the Rays find themselves.

"It's surreal," James Shields said. "It's crazy to me. I don't think it's sunk in yet. I think it will once we win this thing. Once we go ahead and go to the World Series. Right now, it hasn't really sunk in. Just getting here has been pretty impressive and a lifelong goal for me."

Carl Crawford, who experienced a lot of losing before this season, said the Rays' situation is in the "too-good-to-be-true" category.

"We can't believe what's going on right now," Crawford said.

Crawford smiled when asked if he could bring himself to say "World Series."

"A little nervous to say that -- almost don't want to say it, because you don't want anything to happen," Crawford said. "But we're just so close right now. You just hope we get there."

Game 5 starter Scott Kazmir is just over a year removed from expressing a desire to not be with the Rays. He has since enjoyed this season's ride and even signed a contract extension along the way. Now he can laugh about what he thought a year ago.

"A year ago at this time I was popping off and at home right now and watching the playoffs," said Kazmir with a chuckle. "Yeah, this is definitely a turnaround, a 180. What do you say? Honestly."

Count the Rays as amazed, but not surprised.

"I don't think surprise is the right word, because we have a lot of confidence in our ability to score runs and play the game," Carlos Pena said. "I think the best part about all of this is the way this team has approached these games. How poised we have stayed. And how focused we have been on playing the way we play and focusing only on what's going on in this clubhouse instead of looking outside of it. There's a lot to be said about that. This is a young team, and I think it is surprising to see a young team behaving in such a way."

The Rays aren't really even that surprised about their offense, which has surged in the ALCS. In the past three games, they have outscored the Red Sox 31-13.

"No, this is what we are," Longoria said. "We put pressure on pitchers, and the pitching and defense is always there. So, like I said, we've got to continue it. But we've been playing this way all year, it's just taken us a little longer to come onto the national stage and really show the rest of baseball we can play this way."

Despite the happiness inside the Rays' clubhouse, there is a feeling of understanding that there is work left to be done. Sometimes winning the final game is the hardest of all. Particularly against the likes of the Red Sox, who have made the chances of winning three games in a row seem almost probable. Fifteen times during the regular season the Sox won at least three straight games. The Sox had one winning streak of seven, two streaks of five, three streaks of four, and nine streaks of three.

"We're pleased we're in the position we are, and we're very happy with the way we've played," Pena said. "At the same time, I think all of us understand we have to come back and play again Thursday."

B.J. Upton said the idea of winning one more game and advancing to the World Series will be on everybody's mind, but it can't be an all-consuming thought.

"Obviously, you're going to think about it, but you can't look too much into it man, it's still a long series," Upton said. "There's still three games left. They've been in this position before. They know how to handle it. We just can't take it for granted. We've just got to keep doing the same things we've been doing. Playing team baseball, doing the little things, and we should be all right."

J.P. Howell said the team needs to keep its position in the proper perspective.

"We're playing [Game No.] 171 Thursday," said Howell. "I'm trying to avoid thinking that we need just one more win, man. But it's definitely in the back of our minds. When we're up by a lot, in the 'pen we're saying, 'Is this really happening?' But we're just going to go with this, keep riding it out, and hopefully it won't hit us until it's all said and done."

Rays manager Joe Maddon said he will not say anything special to his team about their situation.

"I honestly believe it's not necessary," Maddon said. "It's a unique situation. Every year, every team is unique. We're a different team, they're a different team than they were last year. Everything is different. The world has changed."

Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.