Soon after Boston’s third World Series championship in 10 years, that bearded bunch decided to put it behind them and focus on what they must do to keep winning.

“It was a dream come true last year,” pitcher Jake Peavy said. “It’s a new year. I think that’s been a slogan of ours on the text messages that we’ve been exchanging with the guys, ‘Hey turn the page, it’s a new year, it’s 2014.’ We haven’t done anything and, obviously, some teams in our division got awfully better.”

The Red Sox won’t be sneaking up on them, not after rebounding from a 69-93, last-place finish in the AL East to a 97-65 record, a 28-win improvement.

“You’ve got the bull’s-eye on your back,” second baseman Dustin Pedroia said. “You want to get everybody’s best, so I think it’s going to be a fun challenge for everybody.”

John Farrell’s disciplined, businesslike approach worked in his first year as Boston’s manager. That, and the influx of players to improve the toxic clubhouse chemistry, made the one season under the animated Bobby Valentine seem like a distant memory.

Those players, including Jonny Gomes, Mike Napoli and Shane Victorino, return. The Red Sox lost center fielder Jacoby Ellsbury to the New York Yankees then signed Grady Sizemore as a possible replacement. Sizemore missed the last two seasons with knee and back injuries that required surgery but has had a healthy, productive spring training.

“In this group, no one’s going to let anybody sit back and relax,” Pedroia said. “We’re always going to push each other and make sure that we’re respecting the game and playing the game the right way. If we do that, we should be all right.”

Replacing Jacoby

Ellsbury’s last year with Boston was outstanding. He hit .298 with nine homers, 53 RBIs and 52 stolen bases as the leadoff hitter. Then he signed a seven-year contract as a free agent. Rookie Jackie Bradley Jr. entered spring training as his probable replacement. But Sizemore, a three-time All-Star with the Cleveland Indians, has been aggressive in the field, productive at the plate and, most importantly, healthy. That low-risk signing could yield high rewards.

Solid starters

The rotation was so deep that when Ryan Dempster announced on the second day of spring training that he would take the year off for physical and personal reasons, little changed. Jon Lester, John Lackey, Felix Doubront, Peavy and Clay Buchholz already had the top five spots. Then the Red Sox added veteran depth with Chris Capuano, who begins the season in the bullpen. They also have several young prospects led by Brandon Workman.

What a relief

The Red Sox already had a dominant closer in Koji Uehara. Then they signed Edward Mujica, who had 37 saves for St. Louis last season and provides protection for Uehara. Mujica lost his closer’s job after struggling in September and pitched only two innings in the postseason, which ended when the Cardinals lost the World Series to the Red Sox in six games. Junichi Tazawa and Craig Breslow return as an outstanding setup duo.

Papi power

David Ortiz won’t be distracted by negotiating squabbles. He agreed Sunday to a 2015 contract with a club or vesting option for 2016 and a club option for 2017. Now Big Papi can concentrate on his hitting. He had 30 homers last season then added five in 16 postseason games and was World Series MVP after hitting .688. The Red Sox, who led the majors in runs last season, also should get power from Napoli (23 homers last year), Middlebrooks (17 homers in 94 games) and Pedroia, who’s healthy after surgery for a torn ligament in his left thumb he played with all season that limited him to nine homers.

Middle men

The three big changes are up the middle with the departure of Ellsbury in center, Stephen Drew at shortstop and Jarrod Saltalamacchia at catcher. The Red Sox let all three leave rather than sign them to multiyear deals. Sizemore must show his durability, rookie Xander Bogaerts must live up to his billing as a productive, everyday player and A.J. Pierzynski must adjust to a new pitching staff.

“You always are learning something,” Pierzynski said. “It’s going to be a yearlong process, hopefully, that goes deep into October.”

Sizemore signed a one-year, $750,000 contract loaded with incentives during the offseason. Despite injuries that have kept him from playing in the majors since Sept. 22, 2011, Sizemore has had an excellent spring, batting .303 in 33 at-bats and scoring five runs.

“Honestly, I’m just looking at the next day and not looking too far ahead — you can’t get too far ahead,” the 31-year-old Sizemore said.

“I’m happy with how everything has gone … and didn’t expect to feel this good or comfortable so soon. I’m happy with that aspect,” the three-time All-Star with Cleveland said.

“We’re all perfectionists, so I want to play better each day like everyone else,” he said.

Sizemore is competing for the starter role with top prospect Jackie Bradley, Jr., who has struggled this spring, batting just .173 with five RBIs and 16 strikeouts. Bradley was 0 for 4 Tuesday batting ninth and playing right field.

Red Sox manager John Farrell said he expects to take the rest of the week to have internal discussions and make the call between Bradley and Sizemore. Farrell adds that the team is unlikely to carry both Sizemore and Bradley.

“There’s still a lot of discussion on who our starting center fielder will be,” Farrell said. “We’re looking at these next three days as a physical test. Grady has responded to the plan we put forth, but we still have much to discuss.”

Bradley, a 23-year-old rookie, was considered the front-runner entering camp.

But Sizemore, who hasn’t played in more than 100 games since 2009, has had an excellent camp and put him ahead despite durability questions.

Sizemore’s workload has increased in the past week, with the Red Sox having him play in five of their last six games.

“Everything’s been positive that I’ve done so far — body’s felt good, just keep building off that and put consecutive days together,” Sizemore said. “Still need to swing at good balls because I’m going out of the zone still, but I do feel like I can start the regular season.”

Will Middlebrooks also hit a solo homer as the defending World Series champions won for just the ninth time in 24 games this spring.

Wil Myers and Jose Molina both drove in runs for the Rays, who are still a Grapefruit League best 15-6-3.

STARTING TIME

Rays: In his first outing since being chosen the team’s fifth starting pitcher, Jake Odorizzi gave up three earned runs on four hits, including a home run, walked two and struck out five over five-plus innings. He threw 92 pitches, 58 for strikes.

Red Sox: Clay Buchholz gave up two runs in six innings, allowing three hits, two walks and striking out five over 84 pitches.

“It was good up until the sixth inning,” he said. “I’m comfortable with the pitches because there’s more movement on them, especially the two-seamer. You’ve got to let the ball work for you.”

BEDARD RELEASED

Tampa Bay released veteran pitcher Erik Bedard, just days after he lost out in a three-way competition for the Rays’ fifth starter spot with Odorizzi and Cesar Ramos. Tampa Bay will use Ramos for long relief.

Bedard had a 6.88 ERA over 17 innings with 13 strikeouts and two walks this spring. He had an opt-out clause in his minor league deal, and can now sign with any team.

“That does not preclude the potential for him to come back to us at some point,” Rays manager Joe Maddon said. “I would like to believe that if it doesn’t work out, based on our relationship that we built, that he would want to come back to us, because we would really like to have him back.”

“I’m hoping he gets another job on the major league level, but if not, that he would come back to us would be great,” he said.

ROSTER MOVES

Rays: Maddon announced outfielder Brandon Guyer made the opening day roster. The bullpen has not been finalized, with Josh Lueke and Brandon Gomes still in the mix. Prior to the game, Maddon told pitcher Mark Lowe and infielders Jayson Nix and Wilson Betemit they did not make the team.

COBB SPEAKS, COMPANY LISTENS

After Cincinnati closer Aroldis Chapman was hit in the face by a line drive and Tampa Bay righty Alex Cobb spoke about the lack of progress in protective headgear hats for pitchers, the company developing the product had a rep at Rays camp.

Cobb missed two months last season after being struck in the side of the head with a liner in a game at Tropicana Field. He talked Tuesday to a representative for 4Licensing Corporation, the parent company of isoBLOX, which has developed the padding that is sewn into rim of the caps.

Cobb and Maddon called the prototype “awkward” while Cobb said the hat is still too big, heavy and hot.

“I like where the company is going out and getting the feedback from our opinions,” Cobb said. “That’s their big interest, but it’s still not practical by any means. And I haven’t even thrown with it on because it’s just not where it needs to be. It’s going in the right direction, though.”

TRAINER’S ROOM

Rays: The swelling around the cut pitcher Matt Moore sustained to his lower lip after being hit with a line drive Sunday has gone down significantly and the lefty isn’t expected to miss his upcoming start. The injury required four or five stitches.

“I feel fortunate to come away with only that,” Moore said. “It wakes you a bit when one gets you up top.”

Red Sox: Outfielder Shane Victorino was held out as a precaution due to soreness in his side, but is expected to play Wednesday. Farrell said Victorino may play in more minor league games in end the spring, just in case a DL stint is needed.

Craig Breslow will pitch in a minor league game Thursday and after that, Farrell believes the team will have a better assessment on where he will start the season. Breslow threw 18 pitches Monday vs. Class A Baltimore players. His start to the season was delayed after last year’s heavy workload.

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