FORT MYERS, Fla. — David Ortiz added so much to the Red Sox offense during his tenure with the team. But his presence did tend to curtail the running game.

Any runner on first base with Ortiz at the plate almost always had to stay put. Stealing second base would invite the opposition to walk Ortiz intentionally or at the very least give him nothing to hit.

In the post-Ortiz era, players such as Mookie Betts and Xander Bogaerts could find more opportunities to run.

“We would like to run as much as possible,’’ manager John Farrell said on Saturday before an 8-7 victory against the Twins. “Our guide is always going to be our success rate. We’ve done a good job the last three years.

“Last year, late in the season, we were not as efficient with trying to steal bases. But it’s part of spring training and part of the mind-set we’re trying to create.’’

Stealing at a rate of at least 75 percent is the goal for the Sox and most teams. The Sox have a success rate of 78.1 percent under Farrell and last season were 83 of 107 (77.5 percent).

But the Sox were only 24 of 38 (63.1 percent) after the All-Star break. Farrell suggested it was the result of opposing pitchers paying closer attention to runners and being quicker to the plate.

“That’s where we have to be mindful about our opportunities,’’ he said.

Bogaerts, who has set a goal of stealing at least 20 bases, isn’t sure Ortiz’s retirement will turn the Sox loose. But he does acknowledge the offense will be different.

“If you were on base in front of Papi, you didn’t take any chances,’’ Bogaerts said. “Maybe now we’ll be more creative. But we still have a lot of great hitters.’’

Leading man

In his first spring training appearance, Dustin Pedroia lined a double off the Faux Monster in his first at-bat and went on to score a run. He hit leadoff and the plan is to keep him there.

Pedroia batted leadoff in his final 47 starts last season. The Sox were 30-17 and he had a .394 on-base percentage.

Pedroia has never been a full-time leadoff hitter in the majors. Until last season he had not started more than 29 games in that spot, and that was in 2007.

“When he moved to the leadoff spot — which is a spot prior to last year might not have been his most desirable spot — you can’t deny the tone he set for our offense, the quality of the at-bats he put together,’’ Farrell said.

“He just allows some of those guys in behind him to possibly take advantage of their power.’’

Pedroia denied ever disliking it.

“I’ve hit leadoff all my life,’’ he said. “Show me where I said that. It’s fine.’’

Told that former Terry Francona frequently mentioned it, Pedroia scoffed.

“I just want to hit. It doesn’t matter where,’’ he said.

Taking a shot

When the Twins shifted to the right side against him in the second inning, Pablo Sandoval bunted to the left side. The pitcher, Phil Hughes, threw him out by a step. The crowd applauded Sandoval’s hustle.

Farrell also liked the effort. Combating defensive shifts has been a point of emphasis in camp.

“It was a chance to work on it,’’ Farrell said. “It was an opportunity presented and good to see him take some initiative, a little game awareness to it.’’

Batting righthanded, Sandoval had a two-out RBI single in the fifth inning. Sandoval was 2 for 41 batting righthanded in 2015 and abandoned switch-hitting as a result. He has returned to it this season.

Rodriguez returning

Eduardo Rodriguez and Craig Kimbrel faced hitters for the first time, throwing a round of batting practice. 

Pitching coach Carl Willis said Rodriguez is lined up to start on Thursday against the Rays. He was pushed back a bit because of an injured right knee.

“Today we saw after the first four or five pitches, his ability to repeat that good location,’’ Willis said. “Saw a really good curveball, top to bottom. It’s a progression. I think what we’ve seen since the first day of spring training, each time he’s stepped to the mound it’s been a little bit better.’’

Chris Sale worked what amounted to two innings of live BP. He is scheduled to make his first start on March 6 against the Astros at West Palm Beach.

Good bench

With Dave O’Brien on a college basketball assignment for ESPN and Jerry Remy recovering from a relapse of lung cancer, Tom Caron and Steve Lyons called the game for NESN. They will handle the bulk of the spring duties . . . ESPN analyst Jessica Mendoza shagged balls in the outfield during practice and made a leaping catch on a ball hit by Andrew Benintendi, who credited her with stealing a home run. Mendoza was a four-time All-American outfielder while a softball player at Stanford and played in two Olympics . . . The Sox do not have a player in camp older than 33.

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