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7/2/2014 7:10 P.M. ET

Slowly but surely, Rays turning things around

Tampa Bay picking up steam following three-game sweep of Yankees

NEW YORK -- Back when the Rays resembled Don Draper falling, falling, falling with no bottom in sight in the opening sequence of "Mad Men," manager Joe Maddon kept insisting his touted team would turn it around.

Things had to get better, he reasoned, because they certainly couldn't get much worse.

Maddon turned out to be prophetic. In concluding a sweep at Yankee Stadium with a 6-3 win Wednesday afternoon, Tampa Bay solidified its claim as the hottest team in baseball. That made it five straight wins, seven of its last eight and 14 of its last 21.

"That's what we kept telling ourselves when it was going bad," said starter and winning pitcher Jake Odorizzi. "It can't continue this way. We'll work through it -- and we have. We stayed true to what we've been preaching and things have straightened out for us. We're starting to get back to the baseball we're used to."

The nagging question, of course, is whether a team that remains 9 1/2 games out of first place in the American League East and 10 behind in the AL Wild Card race has a realistic chance to get back in contention.

Maddon clearly does. He predicted before the series opened that his team was about to get "toasty." And he wasn't talking about the oppressive heat and humidity that settled over Yankee Stadium for these games.

Maddon likes that he confidently used three different relievers -- Joel Peralta, Grant Balfour and Brad Boxberger -- in ninth-inning save situations during the series. Maddon liked that he got contributions from up and down the lineup. The tie-breaking, two-run homer in the sixth came off the bat of shortstop Sean Rodriguez, who came into the game batting .205.

"We're getting a different bus driver on a daily basis. That's kind of neat," Maddon said. "That's what we need. That's what we have to be. We are built as a group and everybody has to do their job. That's the concept I'm trying to promote."

And he really likes that, as a team, the Rays are starting to hit. Through June 10, they were 15 games out of first and 18 games under .500. They were also batting .242, ranking 23rd in baseball, and averaging just 3.58 runs per game. In 21 games since, they're averaging 4.48 runs per game.

"Primarily what makes me confident is that we're starting to hit the ball now," said Maddon. "Overall, you're seeing good pitching. The big difference recently is that we're not giving up the big innings as a staff. Among the bullpen, you're seeing some really good arms, so I'm confident about that. Defensively, for the most part, we've been playing a better level of defense.

"But the biggest difference is we have to score runs, and we're starting to do that. I've seen better at-bats, especially against left-handers, because the righties who are supposed to hit lefties all of a sudden are.

"All that, plus I believe in our guys. I believe in our players. You would have had to be with us every day to see how awkward that first part of the season was regarding everything going against us. And to our players' credit, none of our players gave in to it. And right now, we're not quite there, but we're gradually building into our best baseball. But it hasn't arrived yet."

The Rays still have a steep hill to climb and at least two different clocks to watch. One is the looming July 31 non-waiver Trade Deadline. That's how long the front office has to decide whether or not to deal ace David Price before the end of the season. The other is the 75 games and counting until the regular season ends.

The math remains daunting. Let's assume for this exercise that in this parity-driven season, it will take 88 wins to make the postseason.

To reach that, Tampa Bay would have to go 50-25 the rest of the way. That's a .667 winning percentage, which is far higher than Oakland's best-in-baseball .607 mark. The Rays would also have to leapfrog eight teams to claim the second AL Wild Card slot.

That can be a little misleading, though. Price, thinking out loud on Monday, noted how quickly everything can change. As an example, he pointed out that if the Rays went on a 7-3 run while the first-place Blue Jays went 2-8 at the same time, Tampa Bay would pick up five games in less than two weeks.

The Rays remain in a precarious position. They have already used up much of their margin for error, and they'll need some help.

On the other hand, every team in the AL with the possible exception of Oakland has had some vulnerabilities exposed.

Leaving New York, the mood in the Tampa Bay clubhouse was buoyant.

"I wouldn't necessarily call it confidence, because with wins comes confidence. With success comes confidence," Rodriguez said. "I think it's just that as a team we're starting to flow better. Guys are starting to understand better, whether it's their role or the things they can do and not trying to do any more than that. When you're winning, you always feel good. When you're losing, it's hard to swallow."

It doesn't get any easier, though. Next stop: Detroit, then home to play the Royals and Blue Jays before the All-Star break.

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