BOSTON — From worst to first to worst again.

For three seasons the Boston Red Sox have ridden a seesaw that has them in last place in the AL East. But unlikely as it seems, they can still be competitive in a mediocre division.

“No one has given up anything,” Manager John Farrell said Thursday. “No one has conceded anything.”

The Red Sox finished last in the division in 2012, losing 50 of their 76 games after the All-Star break in Bobby Valentine’s only year as manager. Just as unexpected was their World Series championship last year.

In spring training players vowed to focus on this season and “turn the page” from that success. Instead they’ve nearly ripped the book apart.

The Red Sox have the fewest runs in the AL. Only one team in the league has fewer homers.

Their longest losing streak last year was three games. This year they’ve had skids of 10, five and four.

Their record after 95 games last season was 58-37. This season it’s 43-52.

And they trail the first-place Baltimore Orioles by 91/2 games.

But hope remains.

“We’ve got a lot of baseball to play,” right-hander Clay Buchholz said. “Especially in this division, it doesn’t really matter what your record is at the end of the year, just as long as you’re at the top of the board.”

Boston opens a three-game series at home Friday night against the Kansas City Royals.

“There’s additional significance to the games when you play the teams ahead of you,” Farrell said. “After we get through Kansas City, I believe we have the next (13 games) or four consecutive series against teams that are ahead of us. So 67 games remaining, each one has increasing significance.”

The Red Sox’s success at signing veteran free agents last season was stunning – Koji Uehara, Mike Napoli, Shane Victorino, Jonny Gomes, Stephen Drew. Their failures this offseason – A.J. Pierzynski, Chris Capuano, Grady Sizemore – all are gone.

Injuries have limited Victorino to 21 games. Drew is batting .151 in 28 games since returning.

Losing center fielder Jacoby Ellsbury to the Yankees was made costlier by the inability of his slick-fielding replacement, Jackie Bradley Jr., to hit.

But the Red Sox won four of their last five games before the break even if it was against mediocre competition – the Chicago White Sox and Houston Astros.

Left-hander Jon Lester is having his best season as the staff ace with a 9-7 record and 2.65 ERA, John Lackey is a solid No. 2 starter and Buchholz retired the last 17 batters in a shutout over the Astros in which the Red Sox scored a season-high 11 runs Sunday.

Uehara has saved 18 of Boston’s 43 wins, has a 1.65 ERA and made the All-Star team.

“We’ve got some good pitching performances lately,” Lester said. “Our bullpen has been solid all year.”

Now the Red Sox must hope young players whose roles have increased can develop quickly enough for them to pass four teams in the division. If not, they may unload veterans such as Gomes and right-hander Jake Peavy to contenders.

Top prospect Xander Bogaerts began the season as the shortstop and was hitting .304 two days after moving to third base to make room for Drew. Since then he’s hit .116 (14 for 121).

“Hopefully we turn this around and turn the whole season around,” he said.

Mookie Betts began the season as a second baseman with the Portland Sea Dogs but moved up to Boston as an outfielder. Catcher Christian Vazquez was promoted from Triple-A Pawtucket after Pierzynski was designated for assignment July 9 and has five hits in 11 at-bats.

Rubby De La Rosa has been an effective starter since first being called up May 31.

But the best youngster is Brock Holt. In 61 games the leadoff hitter is batting .327 and has a better on-base percentage than David Ortiz and Dustin Pedroia while playing seven positions.

Ortiz has 20 homers but is batting just .255 after three consecutive seasons of .309 or better.

Peavy is 1-8 but has been hurt by the poor offense. He lasted into the eighth inning Saturday in a 3-2 loss at Houston.

“He did a great job,” catcher David Ross said. “We just didn’t score enough runs for him.”

Or for any pitcher this season.

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