WEST SACRAMENTO >> The production alone does not fully encapsulate third baseman Matt Chapman’s value to the Giants. To manager Bob Melvin, Chapman is also the team’s unquestioned leader.

“The intensity he brings on the field every day — he’s kind of the heartbeat of the team,” Melvin said.

Following a one-game rehab assignment with the Triple-A River Cats on Friday and a nearly monthlong absence, that heartbeat returned Saturday as Chapman was activated off the injured list and back in the Giants lineup.

Chapman was the Giants’ cleanup hitter, right behind designated hitter Rafael Devers, for the second game of their three-game series against the Athletics at Sutter Health Park.“I wanted to come back as fast I could,” said Chapman, who missed 23 games after he sustained a right-hand injury on June 8 against the Atlanta Braves. “I don’t like watching. I want to be out there, helping the guys. I (rehabbed) as fast as the Giants would let me.”

Chapman was injured when he dived back to first base on a pickoff attempt, and he said he was able to beat his expected return date by about a week.

It couldn’t have come soon enough for Melvin, who saw his team go 9-14 in Chapman’s absence. The swoon included losing two of three to the rebuilding Chicago White Sox and being swept by the below-.500 Miami Marlins.

The Giants’ 11-2 loss to the A’s on Friday marked their eighth defeat in 11 games, and entering Saturday, San Francisco was one game out of a playoff spot.

This season, the Giants were 37-28 with Chapman in the lineup before Saturday. He was 10th among all big league third basemen in fielding percentage (.960). He also had a team-leading 2.7 WAR rating.

“From the minute he’s gotten here, he’s embraced the leadership role, and he plays a certain style of baseball that we play,” Melvin said of Chapman. “It’s huge to have him back, not just the production part with what he does on the field, it’s his presence in the dugout, on the field, and in the clubhouse. He’s a big part of the group.”

In Chapman’s absence, the Giants had to patch together the third base position.

Casey Schmitt took over for Chapman and put together one of the best stretches of baseball in his career. However, he got injured after taking a sinker to the hand,

Christian Koss, in turn, took over for Schmitt. He, too, played well. He, too, got injured, sustaining a left hamstring injury that will sideline him until after the All-Star break.

Melvin had to get creative after losing Koss — their third-string third baseman.

Wilmer Flores made a rare appearance at third base on Tuesday. Brett Wisely got the starting nod on Wednesday and Thursday. On Friday, Sergio Alcántara started at the hot corner in his first action with San Francisco this season. He went 0-for-4 with two strikeouts.

With Chapman’s return, the Giants designated Alcántara for assignment, and Schmitt is getting better after he started a rehab assignment Saturday night in Triple-A.

“We’re getting closer to having more of a stable lineup,” Melvin said. “Since (Chapman’s) has been out, we’ve had to mix and match a little bit to get our hotter guys up (in the lineup). When we were playing our best baseball, we had more of a stable lineup. So hopefully, we can get to that.”