MASHANTUCKET, Conn. — David Ortiz has been with the Red Sox since 2003, only two years after John Henry and Tom Werner took ownership of the team.

Their fortunes have been intertwined since, Ortiz leading the Sox to three World Series championships.

Ortiz will retire after the coming season and if his final at-bat is not in the postseason, Henry will be bitterly disappointed.

“It would be a big disaster. It will be terrible if he doesn’t end his career in the postseason,’’ Henry said on Friday night at the team’s “Winter Weekend’’ event at Foxwoods Resort Casino.

Giving Ortiz a meaningful final game will take some doing. The Red Sox have finished in last place two years in a row since the 2013 championship, losing 175 games after a series of poor roster decisions.

Henry, who also owns the Globe, is optimistic after the signing of ace starter David Price and trade for closer Craig Kimbrel. The hiring of Dave Dombrowski as president of baseball operations appears to have added stability to the organization.

“In all honesty, I felt good about last season,’’ Henry said. “There’s one thing that we’ve learned the last few years — it’s getting more and more difficult to predict anything.’’

Said Werner: “[Dombrowski] is one of the great, outstanding executives in baseball. I think that he provides a real sense of leadership. . . . We’re very pleased with the transition.’’

There are issues to be addressed off the field, too.

Werner said the Red Sox have a meeting next week to look at options for extending the protective screen behind home plate. The Red Sox are following Major League Baseball’s recommendation for all teams to add protection for fans sitting close to the plate.

The new screens, Werner said, would be in place by the home opener on April 11.

Baseball’s collective bargaining agreement expires after the season and negotiations could lead to significant changes in the game.

Henry passed on a question about revenue sharing, joking that he didn’t want to be fined by commissioner Rob Manfred.

Henry and Werner said they favor the National League using a designated hitter. Werner believes “a few more’’ NL teams are now in favor of it.

“I don’t think that’s necessarily going to happen so quickly,’’ he said. “I look at it as a good thing personally because I like offense in baseball.’’

Said Henry: “I think it would be great for the game to have a level playing field in the World Series, and we have so many interleague games.

“For one team, maybe both teams, are disadvantaged depending on the park they’re in.’’

During a town hall-style discussion later in the evening, Werner told fans that he believes the National League adopting the DH is inevitable.

Approximately 6,000 fans are expected to attend the three-day event. With only a few exceptions, Ortiz being one, most of the notable players will be on hand.

Hall of Famer Wade Boggs is one of the Red Sox alumni at the event. The team announced in December that his No. 26 would be retired.

“It’s the final piece of my baseball puzzle, to have my number retired by the Red Sox,’’ Boggs said.

Boggs believes the honor was delayed as long as it was because he left the Red Sox to play for the Yankees in 1993.

He compared his situation to the movie “Castaway.’’

“I sort of feel like Tom Hanks. I’ve been on an island for 20 years. Now I get to come home and enjoy the lobster. I’m back in the Red Sox family,’’ he said.

Boggs said his agent, Alan Nero, is discussing the idea of a role with the Red Sox.

“We’re going to talk, absolutely,’’ Boggs said. “Like I said, I’m back. Whatever role they want me to play, I’m back in the fold. . . . I think there’s a certain role I can fill.’’

Peter Abraham can be reached at pabraham@globe.com. Follow him on Twitter @PeteAbe.